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Information, Syllabi, Homework, and Resources for Dr. Mohsen Maesumi's Courses

The History and the Philosophy of this Site
I became interested in Internet-based instruction in 2001. I developed a set of videos for Calculus I which were used as the backbone of a course, MATH 2413, in 2006. I called it a "Now U-Try" course. Students viewed the videos at home; and class time was used exclusively for problem solving and discussion by students. Such an arrangement is nowadays called a "flipped" course. This is a very effective method, however it requires substantial effort and participation.
Since that experiment I have modified my policies so that my own courses reflect an "open" environment. This means students have access to their handwritten lecture and problem notes on exams, however, the classes are either traditional, or lab-based and collaborative. Elaborate pre-requisite skills are delegated to a software whenever feasible.
Open courses rely on a steady stream of substantial homework assignments, and these count heavily toward the final grade if supported by meaningful presentation, participation, and checks of homework notebook. Students benefit by making sure their notebooks are well-arranged and searchable; with index, table of contents, page numbers, definitions, theorems, graphs, methods, tables, examples, computer programs and worked-out examples.

Caution Wait

Caution

To the Students:
We will make substantial use of Internet-based instruction; and you need to be aware that, as it is with most technological breakthroughs, there are major benefits as well as risks associated with being online. Some of the risks are related to privacy, digital security, psychological dependency, distracted driving, repetitive motion injury, ergonomic injury, and the drawbacks of being motionless. Students are expected to pro-actively guard against such risks. You may also want to find your screen time and read an article regarding effects of exposure to radio-frequency radiation.


Cardinal

  Potpourri:
 A. Nature by Numbers, Cristóbal Vila's fanciful tribute to the world of Fibonacci numbers.
 B. A homework from 3800 years ago, calculate  2  to six decimal places!
 C. She is a, ... computer, the story of Charlotte.
 D. Richard Feynmann, The Messenger Series, seven ancient physics lectures for general audiences.
 E. Mathematics of Democracy: Making Sense Out of Consensus. Is there a perfect voting system? Here is a surprising answer.
  Find about the mathematical mysteries of "the best" voting systems and the search for that holy grail.
  Article by Dana Mackenzie for Society for Industrial and Applied Mathematics (SIAM).
 F. Fractals of 3n+1, Inigo Quilez.
 G. Archimedes, Chris Rorres.
 H. A Walk in the Park, Malcolm Roger Smyth.
 I. The Odd and the Perfect: Mathologer, Burkard Polster; 3Blue1Brown, Grant Sanderson; Numberphile, MSRI.
 J. Numbers and our world: CV00, CV01, CV02, CV03, CV04, CV05, One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, ...
 K. Mathematics in Movies.

Kids going to school
kids going to school 1 kids going to school 2 kids going to school 3


Dog ate his homework

Courses Taught

General Information

Class Policies

Partial Differential Equations, 4302/5325 Office Hours, Tutor/LU Schedule Online Readiness/Proctorio
Ordinary Differential Equations, 3301 Hints for Desmos Student Profile
Numerical Analysis, 4315/5315 WebAssign Hints/Errors Student/Faculty Email
Linear Algebra, 2318 Specialized Online Calculators Absence and Attendance
PreCalculus II, 2312 Downloadable Software Recommendations
Calculus I, 2413 Online Course Repositories Appeals and Students' Data
Statistics, 1342 Games Class Regulations Sheet
Calculus II, 2414 Access Code Honor Code
Calculus III, 3435 Handbooks Late Homework
Precalculus I, 2311 Cost of Math Errors Calculators
Real Analysis, 3380 On Learning Privacy Issues
Complex Analysis, 4310 Homework Help Votes, Time Extensions
Discrete Mathematics, 2305 Handwritten Math ForOfficeUse
TeX Evaluations
Competitions Late Registration/DRC

Time Out Chair

 

COURSES

Calculus

 
Calculus I, Math 2413
Last update: Fall 2015.
  1. Resources:
    1. Video lectures by Maesumi, from prior years.
      Most of the apps in this link are Java based, so read the Java Warning below. The page is best viewed on Internet Explorer or FireFox or Adobe Reader.
    2. Calculus on Maxima (A Computer Algebra System is used to help with concept of calculus.)
    3. To review, or to check that you have the prerequisite for this course:
      PreCalculus Text 3rd ed, or 4th Beta version, by Carl Stitz and Jeff Zeager.
      A short summary appears in First chapter of the text we use, by Larson.
    4. Help with homework and lectures:
      • Look up similar problems in the text.
      • WebAssign gives a chance to see a solution and then asks you to do a similar problem.
      • WebAssign may have a video for you to watch.
      • CalcChat.com has solutions to most odd numbered problems of the text.
      • My lectures from prior years are available.
      • Mathematics department runs free tutoring in L209.
      • Study in a group. L211 can be a good place to start a study group.
      • DO ask your questions in class.
      • Submit questions via WebAssign.
      • Come to Office.
    5. Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2
    6. Apps and demos
      1. Apps for Calculus I Marc Renault, Shippensburg University. GeoGebra-based.
      2. Kepler's Laws of Planetary Systems (needs Flash, use IE or allow Chrome to run Flash)
      3. epsilon-delta definition of limits 1. (GeoGebra) Use a function with small slope to improve visiblity.
      4. epsilon-delta definition of limits 2, (GeoGebra)
      5. Visual differentiation 1. Slide the dot on x-axis to see tangent line move.
      6. Visual differentiation 2. Design a polynomial by moving the seven red dots. Then take its derivative.
  2. Information:
    1. Calculus I Fall 2015 syllabus
    2. Homework list for this section will be gradually placed on WebAssign, (our list will be a bit different from the the departmental list )
    3. Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2
    4. Book options: (There are several choices. If you have questions ask before purchasing anything.)
      1. The campus book stores sell the custom edition loose leaf version bundled with WebAssign for about $170. Follow the instruction that comes with your package. Loose leaf editions cannot be sold back to store once you open them.
      2. Another option is to buy the WebAssign directly from the publisher. If you are taking calculus I and II (and perhaps III) then you need the multi-term WebAssign. This sells for $118. WebAssign has the e-book version of the text. You need to be online to read the book. No offline/downloadable version is on WebAssign. Printing is allowed but is not efficient.
      3. If you buy WebAssign from third-party sellers or students make sure it is unused and check its "prefix" with the one for Larson 6th edition from this list WebAssign Prefix Check. (For example you can buy it from students who bought the package last year but their instructor did not use WebAssign.)
      4. Older editions of the text (with slightly different page and problem numbers etc) are also available online.
      5. To register your WebAssign you need a so called class key .
      6. To purchase from the publisher of WebAssign and/or register go to WebAssign website. During registration
           Click on "STUDENT"
           Click on "I Have a Class Key"
           Use the class key written in red above.
           Register with your full name as it appears on your transcript (no funny fake names, user names, fake account names, etc.)
        Check that my name (Maesumi) and your section 2413-4a or 2413-4b show up.
        When you buy from the publisher you generally have a grace/trial period of two weeks to pay, and another grace period to get a refund if you drop the course.
        Keep a record of your password. Do not register multiple times. Access code includes the e-book.
        For the multi-term version this is an LOE (lifetime of Edition) book giving you access so long as the current edition is in use. For a single term version it is just for this semester.


 
Linear Algebra, MATH 2318 (formerly 3328)

LinearAlgebra

Last update: Fall, 2019
Section 04, MWF, 11:30-12:25, GB 113.
Tentative test days: Fridays Sept 13, Oct 11, Nov 1, Nov 22,
Cumulative Final in class Wednesday December 4, 8:00-10:30 am

A focus point for Linear Algebra and Differential Equations
Another name for these courses is The Theory of Vibrations. All structures vibrate, from tiny molecules to gargantuan skyscrapers. An engineer wants to either enhance these vibrations, as in the case of the electromagnetic waves enetring a receiver of an electronic equipment like the antenna of a radio or TV, or he/she wants to dampen the vibrations, as in the case of cars, buildings and bridges.
Look at the following videos. It is clear that we need to understand how things vibrate in order to design them. Here is the famous Tacoma Narrows Bridge and the London Millenial Bridge. And here is a simple experiment of three structures that respond to a vibrating foundation. As a future engineer you are likely to be involved in the design of structural elements to counter the vibrations as in a The tuned mass damper. When it is come to electronics we typically want to accentuate vibrations in order to have the best possible reception. That is what we do on a vintage radio, for example, when we turn the tuner knob to get the best signal. Here is an optional Differential Equations Project in relation to this topic.
If we try to understand vibrations of the components of a system with respect to each other, as you see in the following videos: triple spring or double pendulum, then we need a substantial amount of linear algebra.
Of course, differential equations and linear algebra are topics that have a very wide reach and many applications. The focal point presented above is just one of many, vibration is however a topic that everyone can easily relate to. It is easy to see why differential equations play such a central role in phyics and engineering. The physical world is in a state of change. We want to understand, control, and predict these changes. "Change" is quantified by derivative, and "change" is related to "the current value" of the quantity that is changing. That is exactly what a differential equation is, an equation that relates the derivative to the function, as in dy/dt = 3y. This is an equation that says y is a function of t with the property that its derivative is three times the function itself.
When we consider the interaction of many changing components the we are dealing with a "system". The study of the change in a system then requires linear algebra as well as differential equations.

Partial Lecture Notes for Summer 2019 (These are easiest to see on Edge Browser. But you can also download them on other browsers. By the way, there is no gunrantee that these lectures will be available, so take notes as usual!)
07/10/2019 Vectors, Lecture 1.
07/11/2019 Dot product, length, unit vector, angle, projection, Lecture 2.
07/12/2019 Proof of dot product and projection formulas, equations of lines and planes, Lecture 3.
07/15/2019 Distance between points, lines, planes, nearest point, Lecture 4.
07/16/2019 Applications of vecrors, force, review of two problems from distance, Lecture 5.
07/17/2019 Origins of linear systems, triangular systems, echelon form, back substitution, Lecture 6.
07/18/2019 Echelon, Reduced Echeleon, Gaussian elimination, Gauss-Jordan elimination, elementary row operations, software for row operations, Lecture 7
See lecture from 02/28/2019 below (second recorded lecture from Spring 2019 semester).
07/19/2019 Exam 1
07/22/2019 Spanning sets, linear dependence and independence, applications of linear systems, balancing chemical formulas, Lecture 8.
07/23/2019 Applications of linear systems, Resource management, Network analysis, Basic electrical circuits, Lecture 9.
07/24/2019 Matrix Operations, Transpose, Symmetry, Multiplication:: as linear combination, as row product, as column product, as outer product, Lecture 10.
07/25/2019 Matrix multiplication, commutativity, power, diagonal matrices, transpose, axioms of matrix operations, Lecture 11.
07/26/2019 The inverse of a matrix, Gauss-Jordan steps for finding inverse, existense, 2*2 case, powers and transpose, Lecture 12.
07/29/2019 Elementary matrices and their inverses, permutation matrices, factorization of a matrix into elementary matrices, Graphing MA=B with Dr Nykamp, App No 15, Intro to Eigen Analysis, Dr. Strang App No 20, Lecture 13.
07/30/2019 EigenAnalysis: E-values, E-vectors, E-spaces, 2*2 examples, real distinct eigenvalues, Lecture 14.
07/31/2019 Exam 2
08/01/2019 EigenAnalysis: Justification from Vibration of Systems, complex eigenvalues, Lecture 15.
08/02/2019 Complex eigenvalues, complex eigenvectors, repeated roots, geometric multiplicity, algebraic multiplicity Lecture 16.
08/05/2019 Properties of determinants, rational root theorm, solving cubic equations, Lecture 17.
08/06/2019 Solving cubic equations, 3*3 examples, algebraic and geometric multiplicity, Lecture 18.
08/07/2019 Finding powers of a matrix times a vector, M^n X, power or exponential of a matrix, Diagonalization, Lecture 19.
08/08/2019 Applications to systems of first order differential equations, X'=M X, Population Forecasting, Lecture 20
08/09/2019 Applications to systems of second order differential equations, X''=M X, Couple Oscillators, Lecture 21
08/12/2019 Final

  1. Resources:
    1. 3D Cartesian Coordinates
    2. 3D Vector Operation Plotter
    3. Linear combination of two vectors in 2d
    4. Span of two vectors in 3d use IE/Edge, or download and use flash.
    5. Force diagram for block on inclined plane
    6. Visualization of the intersection of three planes Wolfram Mathematica, requires Wolfram CDF player , download file to run
    7. Linear Algebra Toolkit, Calculator by Przemyslaw Bogacki, Old Dominion University
    8. Linear Algebra Calculator, Gang XIAO.
    9. Interactive Linear Algebra Exercises, Gang XIAO. Enter "linear algebra" as a search term.
    10. Linear Algebra Demos, Bates College.
    11. Row Reducer, step-by-step elementary row operations, (Gauss-Jordan steps), by Dan Gries.
    12. Matrix Multiplcation Demo, Wolfram Mathematica, requires Wolfram CDF player , download file to run.
    13. 2D Mapping, of a quadrilateral region, D.Q. Nykamp, University of Minnesota. (Interactive)
    14. 2D Mapping, of letter F, Wolfram Mathematica, requires Wolfram CDF player , download file to run.
    15. 2D Mapping, of letter z, P. Falstad. (Interactive).
    16. 3D Mapping, D.Q. Nykamp, University of Minnesota. (Partially interactive)
    17. Determining Eigenvectors by Exploration, D.Q. Nykamp, University of Minnesota.
    18. Exploration of Eigenvectors, Strang, MIT.
    19. T^N, a linear Algebra Game, Twist, Tumble and Travel to your Target; A Transformation Teaser by Andries van Dam and Jean R. Laleuf, Brown University
      (Picture of a house is given, you are to translate, rotate, reflect, and stretch it until it fits into a target image.)
    20. Coupled Oscillators triple spring (Matthew Collett) or double pendulum, Understanding this phenomena requires concepts from this course and 3301 (modeling of the physics as a system of second order differential equations and the eigen analysis of the resulting matrix).
    21. Spanning sets: Example of "Feasible Space" from other fields of science and engineering:
      Kinght Tour in Chess
      Robotic Arm
      Ray tracing
    22. A system has many interacting elements, as in a bridge: Bridge 1, Bridge 2, Bridge 3, when we write the blance equations between the elements we get what is called a "system of equations".
    23. A linear system can be the result of a discretization process, breaking a continuous event into a finite set of interacting elements, as in a (N*M)^2 linear system resulting from a N*M imaginary grid for discretization of the steady state heat equation on a metal plate.
    24. Maesumi's Video Lectures WIN HTML + WMV or MAC/WIN PDF + MOV/MPEG, from a prior version of Linear Algebra course, based on Richard Hill text.
  2. Next Steps:
    If you are interested in a more advanced treatment there are many online resources for linear algebra. Here is a sample:
    1. 18.06 Linear Algebra, Dr. Strang, MIT, archived course.
    2. 18.06 Linear Algebra, Most recent class, MIT.
    3. Linear Algebra: Foundations to Frontiers, Course, Robert van de Geijn, Dr. Maggie Myers, The University of Texas at Austin.
    4. Linear Algebra: Foundations to Frontiers, (offerred from time to time on edX platform), Course, Robert van de Geijn, Dr. Maggie Myers, The University of Texas at Austin.
    5. Essense of Linear Algebra, Grant Sanderson
    6. A First Course in Linear Algebra, textbook by Robert A. Beezer.
    7. Linear Algebra, textbook by Jim Heffereon.
    8. Introduction to Matrix Algebra, textbook by Autar Kaw.
    9. Elementary Linear Algebra, Lecture Notes, Keith Matthews.
    10. Vector Algebra, Interactive text by Duane Q. Nykamp, University of Minnesota.
  3. Information:
    1. Syllabus Linear Algebra Fall 2019 Section 04
    2. Homework is to be done on WebAssign. For syntax hints and dealing with errors check
      WebAssign Hints 1 and
      WebAssign Hints 2 and
      The first homework on webassign.
    3. If you are buying your access code from Cengage then pay attention to the Unlimited subscription offered by them. If you are buying items from Cengage for more than one course it is likely that the subscription plan will cost you less than individual purchases.
    4. Registration on WebAssign is required. Owning a physical copy of text is optional. Text book: Linear Algebra: A Modern Introduction, 4e, by David Poole.
    5. Book and Access Options: You have several choices:
      1. Purchase WebAssign access code. It has ebook of text in it. $100 from WebAssign. The ebook is not downloadable, you have to be online to read it.
      2. Purchase custom package from KampusKorner or Campus Bookstore. It has loose leaf edition of textbook bundled with WebAssign. This costs about $50 more but is a better deal because you can read the text offline. Use a hole punch strengthener to reinforce the text and a binder to keep your book in good shape!
        Loose leaf textbooks usually cannot be sold once opened, but if you take good care of it KampusKorner or next semester students or some online sites "might" buy it back. Hopefully you become interested and read the whole book later!
      3. Purchase either one from third-party sellers. Unused/unregistered WebAssign access code (say from another course) might apply to this course as well. For the correct prefix Check Here. (This is a gray area so proceed with caution.) An older/used edition of text, typically available at nominal cost, can be useful for off-line reading.
      4. To purchase and/or register access code go to WebAssign website. During registration
           Click on "STUDENT"
           Click on "I Have a Class Key"
           Use the class key written in red below for Fall 2019. Enter each part in its box.
           lamar    8289    8231      
           Register with your full last name as it appears on your transcript, followed by first name and initials (this should be identifiable). Turn on all notifications.
           Check that it is for Lamar, Linear Algebra, Maesumi, MATH 2318, current semester.
        When you buy directly from WebAssign you generally have a grace/trial period of two weeks to pay, and another period to get a refund if you drop the course.
        Keep your receipt.
        Keep a record of your password.
        Do not register multiple times.
        Enter your name as it is on class roll.
        Protect your password.
        This is an LOE (Lifetime of Edition) book giving you access so long as the current edition is in use. Multiple registrations and unregistered students will be deleted.


 
Ordinary Differential Equations, MATH 3301
Last Update: Summer II, 2020
Goign forward there will be significant changes in the way this course is taught.

Schedule: Summer II, 2020, Section 07, online, 7 days a week, Tuesday July 7 - Monday August 10.
Requirements and policies in brief:
(0) Recent successful completion of Calculus I,II.
(1) WebAssign access code is required on the first day. Go to Registration Info.
(2) Warm-up Homework on WebAssign due July 8.
(3) Upload of Profile/Resume/Class Contract to WebAssign due July 10. There is a deduction of 40 points from each exam if Identity Information in Profile is late, incomplete, or inaccurate.
(4) Well-equipped computer, webcam, mic, digital camera (a quality webcam may do this too), min 25 MB/s broadband, updated Chrome Browser, ability to make PDF file from digital pictures. Proctorio installed on first day. More Info. A complete and independent second system for back up.
(5) Allocation of 135 hours to study per semester, for summer this means 27 hours per week.
(6) Proctorio-based Quiz July 9, 10
(7) Tentative Sectional Exams dates: Mondays,July 13, 20, 27, August 3, 10-12 PM
Cumulative Final Monday August 10, 10-12 PM.
(8) Go to the list of lecture videos and reading assignments.
(9) Homework will be posted on WebAssign. Upload of work is required.
(10) Work must be a single PDF file. Readable, in sequence, with no rotation, blur, small print, shadows.
(11) Homework 50%, Exams 50%. All exams count equally, i.e. each is 10% of final total grade.
(12) Some of the information below is from Spring 2020 when we had a combination of an on-campus and online course (due to coronavirus).

Attractor

A focus-point for Linear Algebra and Differential Equations
Another name for these courses is The Theory of Vibrations. All structures, from tiny molecules to gargantuan skyscrapers, vibrate. An engineer wants to either enhance these vibrations, as in the case of the electromagnetic waves enetring a receiver of an electronic equipment like the antenna of a radio or TV, or he/she wants to dampen the vibrations, as in the case of cars, buildings and bridges.
Look at the following videos. It is clear that we need to understand how things vibrate in order to design them. Here is the famous Tacoma Narrows Bridge and here is a simple experiment of Three structures that respond to a vibrating foundation. As a future engineer you are likely to be involved in the design of structural elements to counter the vibrations as in a The tuned mass damper.
When it comes to electronics we typically want to accentuate vibrations in order to have the best possible reception. That is what we do on a vintage radio, for example, when we turn the tuner knob to get the best signal. Here is an optional Differential Equations Project in relation to this topic.
If we try to understand vibrations of the components of a system with respect to each other, as you see in the following videos: triple spring or double pendulum, then we need a substantial amount of linear algebra.
Of course, differential equations and linear algebra are topics that have a very wide reach and many applications. The focal point presented above is just one of many; as vibration is a topic that everyone can easily relate to. It is easy to see why differential equations play such a central role in phyics and engineering. The physical world is in a state of change. We want to understand, control, and predict these changes. "Change" is quantified by derivative, and when "change" is related to "the current value of the quantity that is changing" then a differential equation is born. A famous differntial equation is Newton's law F=ma. The acceleration is a, which is the derivative of velocity v, which it turn is the derivative of position x with respect to time t. A mechanical problem is the description of the force F in terms of t,x, and v. Hence a problem in mechanics is immediately a differential equation. A differential equation, in general, is an equation that relates the derivatives of a function to the function itself, as in the simple example dy/dt = 3y. This is an equation that says y is a function of t with the property that its derivative is three times the function itself.
When we consider the change and interaction of several components of a structure then we are dealing with a "system". The study of the change in a system then requires linear algebra as well as differential equations.

Lectures from prior semesters. These are easier to view on Edge.
Spring 2020
01- 02/26/2020 Sky diver/parachute problem 23 from Section 2.3, Problem 1 from Homework 9
02- 03/13/2020 NonHomogeneous: trig forcing function ay"+by'+cy=F cos(wt),
03- 03/13/2020 Row REDUCER a program for solving systems of equations.
04- 03/17/2020 How to Choose Yp: Problems 6 and 3 HW 14
05- 03/23/2020 HW 14, Problem 10, Intro to Mechanical Vibrations
06- 03/25/2020 Problem 5 from Section 3.7, Mechanical Vibration
07- 03/27/2020 Exam #3
08- 03/30/2020 Damped Mechanical Vibrations Quasi-frequency, Quasi-period, threshold time.
09- 04/01/2020 Phase Shift, sum of two waves, intro to forced vibrations.
10- 04/03/2020 Phase Shift, beat, Laplace Transform
11- 04/06/2020 Laplace Transform of basic exponential and polynomials exp(at), cosh(bt), sinh(bt), t^n
12- 04/08/2020 Laplace Transform of products of polynomials, exponentials and trigonometric functions t cos(bt), exp(at) cos(bt), shifting, t^n f(t), exp(at) f(t)
13- 04/10/2020 - Good Friday Holiday. Read/View Multiple-Integration-by-Parts from Calculus
13a- multiple integration by parts YouTube
13b- Multiple Integration by Parts, Maesumi, a short cut similar to the ladder/tableau method.
14- 04/13/2020 Solving initial value problems using Laplace Transform
15- 04/15/2020 Review for Exam 4
15a- 04/15/2020 Review of Laplace Transform
15b- 04/15/2020 Review of Forced Oscillation
16- 04/17/2020 Laplace Transform Table This is an evolving document
16- 04/17/2020 Exam #4, Friday, 9:10-11:00.
17- 04/20/2020 Step Function 1 Switch and Delay formula
18- 04/22/2020 Step Function 2 Advanced Switch and Delay examples
19- 04/24/2020 Discontinuous Forcing Functions applications of step function
20- 04/27/2020 Review of Step Functions and Discontinuous Force Problems 6,8 HW 23; Problem 2, HW 24, Desmos
21- 04/29/2020 Laplace transform of periodic functions two examples
22- 05/01/2020 Proof of some general Laplace Transform formulas shifting, exp(at) f(t), f'(t), f(t-c)u(t-c), example discon. force
23- 05/04/2020 Last class

Fall 2019:
Section-2.2-Separable-Differential-Equations
Section-2.1-Integrating-Factor-Method
Section-1.1-Direction-Fields
Section-1.1-Stability-and-Direction-Fields
Section-1.1-2.3-Modeling-1st-Order-ODES
02/26/2019 Applications of ODEs in Finance and Rocket Position Calculation.
02/28/2019 Linear vs Nonlinear, Domain of existence, fall under drag force .
03/05/2019 Justification of 2nd order ode's from dynamics and F=ma, Linear constant coefficient cases (distinct real, complex conjugate, identical roots), initial conditions .
03/07/2019 examples of the three cases (distinct real, complex conjugate, identical roots) with initial conditions, Euler theorem, complex exponential .
03/12/2019 Spring break
03/14/2019 Spring break
03/19/2019 2nd order linear homogenous ode's, reduction of order, Euler 2nd order ode's, .
03/21/2019 Exam
03/26/2019 nonhomogenous 2nd order ode's, external force, PET functions, method of undetermined coefficients, exponential and trig forcing terms.
03/28/2019 trig identities for phase shift, polynomial forcing term, introducing resonance.
04/02/2019 Resonance in undamped systems.
04/04/2019 Mechanical Vibrations.
04/09/2019 Examples of Mechanical Vibrations.
04/11/2019 Laplace Transforms, Part 1, definition, constant and exponential functions.
04/16/2019 Laplace Transforms, Part 2, Hyperbolic sine and cosine, polynomials, circular sine and cosine and inverses.
04/18/2019 Exam
04/23/2019 Laplace Transforms, Part 3, L[exp(a t) f(t)], L[t^n f(t)], L[y'], L[y''], solving an ODE with Laplace transform .
04/25/2019 Laplace Transforms, Part 4, L[y^(n)], Partial Fraction Decomposition, solving an ODE with discontinuous forcing function, introduction to Step Functions .
04/30/2019 Laplace Transforms, Part 5, Step Functions, graphing, piecewise-defined functions, L[f(t-c) U_c(t)], inverse examples .
05/02/2019 Laplace Transforms, Part 6, Periodic functions .
  1. Resources:
      Frequently Used Software
    1. Direction Field Plotter, John Polking, Rice University.
      You need to install JAVA/JRE first. Then tap on "dfield.jar" on above page and download to your computer.
      (There is concern with security of JAVA. So this is a run-at-your-own-risk operation. I believe it is safe so long as you do not enable JAVA in your browsers, they automatically block JAVA. Further down, you find links to web-based direction-field plotters that do not require installation and do not use JAVA. However they are not as full-featured as this one.)
      A manual of DField by Nancy Chan, Harvard, 2004.
      Software also works on Unix-type operating systems.
      For MAC, software works only on Mozilla. MAC has its own internal software called Grapher.
      Using Grapher on MAC for ODEs, Scott Taylor, Colby College.
    2. Desmos a graphing calculator, Usage Hints, User Guide, Help, YouTube Channel, Blog
    3. Review of some calculus concepts
    4. Multiple Integration by Parts, YouTube, example of Tableau method
    5. Multiple Integration by Parts, a short cut similar to the ladder tableau method.
    6. Partial Fraction Decomposition, Dr Dawkins.
    7. Differentiation and Integration Formulas, Review from Calculus I and II. You need to be comfortable with these formulas before you start this course.
    8. Graphical and Numerical Solution of ODEs
    9. Direction Field Plotter Ariel Barton, U Ark
    10. Direction Field Plotter for single and system of 2 equations, Darryl Nester, Bluffton University.
    11. Direction Field Plotter for 2nd order and a system of 2 1st order equations, Stefan Waner.
    12. GeoGebra Direction Field Plotter, DNghiem.
    13. Demos
    14. Examples of fields: Velocity Field in Hurricane Sandy, Magnetic Field 1, Magnetic Field 2, Electric Field +-, Gravitational Field Earth-Moon, Image of Saturn's Polar Hexagonal Vortex, and the article,
    15. Resonance Simulator, by Carl Wieman, University of Colorado. Requires Flash, or use IE.
    16. Coupled Oscillators triple spring or double pendulum. Understanding this phenomena requires concepts from this course (modeling of physical systems as ODEs) and linear algebra. N-Spring.
    17. Acoustics and waves Dan Russell, Penn State
    18. Beat Wolfram Mathematica, requires Wolfram CDF player .
    19. Beats YouTube SMU, SFC Ron Kurus, Requires Flash. Interference of two waves which have nearby frequencies causes beats. We will see this in section 3.7.
    20. A simple pendulum.
    21. Graphical solution of second order ODE Mathematica Widget.
    22. Physics Science Resource Center, Pearson Publications. Requires Adobe Flash. Use IE.
    23. Johann Bernoulli and The Cycloid MyPhysicsLab, Vsauce, MathCurve, MacTutor, 3Blue1brown,
    24. Oscillations of a Single Spring, EriK Neumann.
    25. Forced Mechanical Oscillation, Wolfram Demonstration, requires Wolfram CDF player .
    26. Texts and other sources:
    27. Publisher's companion web site for the text, 8th ed, 9th ed, 9th+BVP, 10th+BVP, 11th ed, 11th+BVP,
    28. ODE Videos by Maesumi Win, HTML + WMV or Mac/Win HTML + MOV from 2006.
    29. A basic Euler solver for y'=f(x,y), To run it you need access to MatLab software.
      Either use a university computer that comes with the software (most labs in cs, math, engineering have it) or get an account as follows:
      Go to Lamar Matlab site
      Follow instructions (it will ask you to first make an account at MathWorks, using your Lamar email address.)
      You can use the cloud-based version or download a copy to your own computer.
      Once you have opened Matlab copy-paste the program above in the Editor Window of Matlab and save it.
      Read the program to understand the steps.
      Run it in the Command Window by a command as indicated in the file you downloaded, e.g.
      myeuler(1000,1,3,10,'y');
      Make sure you understand it well enough to be able to edit it for your assignments.
  2. Next Steps:
    If you are interested in a more advanced treatment there are many online resources for ODEs. Here are a few:
    1. ODE at MIT, Video of lectures given by Arthur Mattuck and Haynes Miller, mathlets by Huber Hohn. Includes videos, transcript, tools, exams, etc.
    2. Differential Equations in Action, Instructor: Jorn Loviscach, Course Developer: Miriam Swords Kalk.
    3. Differential Equations, course by KhanAcademy.
    4. Elementary Differential Equations with Boundary Value Problems, textbook by William E. Trench.
    5. Introduction to Differential Equations, textbook by Jeffrey R. Chasnov.
    6. Introduction to Differential Equations, MIT 18.031, archived on EdX.
  3. Information:
    1. ODE Syllabus Spring 2020
    2. If you are buying your access code from Cengage then pay attention to the Unlimited subscription offered by them. If you are buying items from Cengage for more than one course it is likely that the subscription plan will cost you less than individual purchases.
    3. ODE Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2.
    4. If you buy WebAssign from third-party sellers or students make sure it is unused and check its prefix with WebAssign. (this is a gray area so proceed cautiously)
    5. To purchase an access code or to register go to WebAssign. During registration on this site
         Click on "STUDENT"
         Click on "I Have a Class Key"
         Use the class key written in red below. Enter each of the three pieces in its own box.
         Class Key for ODE class is (check verification reply before paying to make sure you do not register in the wrong or old classes!) :
               lamar     3921     1454
      Make sure you see my current course in response, confirming that you registered for the right course.
      Register with your full name, only once, exactly as it appears on your transcript, otherwise it will be removed.
      Give an email that you check regualrly, turn on all notifications from WebAssign so you see latest announcements on time.
      Homework and ebook code from the publishing company is $91.70 for single term subscription (Multi-Term/Life Of Edition/LOE $122.00). The ebook is not downloadable, you have to be online to read it.
      If you get Cengage Unlimited Subscription plan please note that the physical copy of this book is NOT in their rental plan as the book is not published by Cengage.
      Any edition of the book is equally useful for offline reading.
      Some of the various editions look like these 8th ed, 9th ed, 9th+BVP, 10th+BVP, 11th ed, 11th+BVP
      The older editions are perfectly fine for offline reading. However some sections may be rearranged.
      The ebook that comes with your WebAssign code correponds to the 10th+BVP edition.

      When the access code is purchased from the WebAssign company you generally have a short grace/trial period to pay, and another period to get a refund if you drop the course.

    6. Course Content and Schedule:
      Average work load: 45 hours of lectures, 90 hours of homework per semester, for a toal of 135 hours, i.e. about 27 hours per week in summer.

      The Lecture Videos for this course are posted to a YouTube channel playlist .
      The sections and page numbers are according to the edition of text (10th) which is included with WebAssign as ebook.
      This list will be frequently ammended or modified, especially in so far as the deadlines are concerned.
      The current lectures and homework and their dates are as follows:

      Lecture 1a- Introduction to Ordinary Differential Equations
      Lecture 1b- Introduction to Ordinary Differential Equations
      Warm Up homework on Webassign due July 8

      Section 2.2 of textbook
      Lecture 2a- Separable Differential Equations
      Lecture 2b- Separable Differential Equations, Interval of Validity of Solution
      Homework 1, OHW1, due July 9
      Proctorio practice quiz 1, July 9

      Section 2.1 of textbook
      Lecture 3a- Integrating Factor Method
      Lecture 3b- Multiple Integration by Parts
      OHW2, due July 10
      Profile due July 10
      Proctorio practice quiz 1, July 10

      Pages of textbook.
      Type of equation , Section, Pages, Problems
      Homogeneous Equations, 2.2, 49-51, 29-38
      Bernoulli Equation, 2.4, 77-78, 27-31
      Brachistochrone, 2.3, 67-68, 32 (not assigned)
      Gompertz, 2.5, 90, 16-17 (not assigned)
      Lecture 4a- ODEs by Method of Substitution
      Lecture 5a- Direction Field
      Lecture 5b- Direction field, stability, Long-term behavior
      OHW4, due July 12

      Exam 1, Open Notebook, July 13, Homework 1-4, Sections 1.1-2.5, Lectures 1-5. Proctorio and Uploading required.
      Allowed: entirely handwritten notebook, basic calculator, Desmos, Dfield, exam page of webassign
      Not allowed: Someone else, homework keys, phones, phone calculators, any other site, homework pages of webassign, books, ebooks, printed items, second monitor, tablet
      When Proctorio says "Scan Your Room" count from 1000 to 1020 and slowly scan your working table
      Make sure your room is well-lit, work on an uncluttered table, appearance: as if you are in a classroom.
      If requirements of Proctorio are not met you may be asked to take another exam.
      If Identity Information part of resume/profile is not complete or inaccurate there will be a deduction of 40 points.

      Section 2.3 of textbook
      Lecture 6a- Modeling with first-order ODEs, Mixing Problem
      Lecture 6b- Modeling with first-order ODEs, Finance Problem
      Lecture 6c- Modeling with first-order ODEs, Population forecasting
      Lecture 6X1- Modeling with first-order ODEs, Drag force (extra)
      OHW5, due July 16

      Section 2.4 of textbook
      Lecture 7a- Interval of existence, Linear equations
      Lecture 7b- Interval of existence, nonlinear ODEs
      Lecture 7c- Interval of existence, nonlinear ODEs
      Lecture 7d- Interval of existence, nonlinear ODEs
      OHW6, due July 17
      Upload MUST be in PDF format. Significant deductions for late submission as well as for: non-pdf upload, rotated, fuzzy, out-of-sequence, unlabeled problems.
      Sections 3.1, 3.3, 3.4 of textbook in brief
      Lecture 8a- Introduction to 2nd order ODEs
      Lecture 8b- 2nd Order Constant Coefficient ODEs
      Lecture 8c- Exmaples, Threshold time
      OHW7, due July 18
      Upload MUST be in PDF format. Significant deductions for late submission as well as for: non-pdf upload, rotated, fuzzy, out-of-sequence, unlabeled problems.
      Sections 3.3 in detail
      Lecture 9- Euler Formula
      OHW8, due July 19
      Upload MUST be in PDF format. Significant deductions for late submission as well as for: non-pdf upload, rotated, fuzzy, out-of-sequence, unlabeled problems.
      Exam 2, July 20, Focus on Homework 5-8, Lectures since Exam 1, but need to be familiar with all topics. Same instructions as in Exam 1 apply. Upload MUST be in PDF format. Significant deductions for late submission (10+delay minutes)%, as well as for: non-pdf upload, rotated, fuzzy, out-of-sequence, unlabeled problems.
      Section 3.4 in detail
      Lecture 10- Method of Reduction
      OHW9, due July 22

      Section 3.5 of textbook
      Lecture 11a- Nonhomogeneous Equations, Method of Undetermined Coefficients
      Lecture 11b- Cases of Undetermined Coefficients
      OHW10, due July 23
      Lecture 11c- Resonance and Undetermined Coefficients
      Lecture 11d- Cases of Mathematical Resonance
      OHW11, due July 24

      Section 3.7 of textbook
      Lecture 12a- Free Mechanical Vibrations
      Lecture 12b- Free Damped Mechanical Vibrations
      Lecture 12c- Resultant or Amplitude, and Phase
      OHW12, due July 26

      Monday July 27,
      Online meeting on Blackboard Collaborate Ultra 1-2+ pm Texas time
      Test 3, focuses on HW 9-12, but need to know all topics, details to be announced , 10-12 pm Texas time.
      No HW July 28
      Section 3.8 of textbook
      Lecture 13- Forced Mechanical Vibrations
      OHW13, due July 31

      Laplace Transform, Chapter 6
      Section 6.1 of textbook
      Lecture 14a- Introduction to Laplace Transform
      OHW14, due Aug 1


 

Framer

Statistics, MATH 1342
Last Update: Summer I, 2017
  1. Information:
    1. Approximate Test Dates: Monday June 19, Friday June 30, Monday July 10.
    2. Syllabus Summer I 2017.
    3. Textbook: Collaborative Statistics, 2/e, Barbara Illowsky and Susan Dean (online version is free through Open Educational Resources).
      If you want the print edition ($44.50+$6 S/H) you need to order it from Print on Demand. Before ordering check arrival time to make sure it suits your needs.
    4. Purchase of WebAssign access is required for this course ($27.95). During registration:
         Click on "STUDENT"
         Click on "I Have a Class Key"
         Use class key lamar abcd xyzt
         Enter each part in a box; "lamar" in the first box, " abcd" in the second box, "xyzt" in the third box (do not type the quotes).
    5. Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2
    6. When you buy WebAssign access from the publisher's link above you generally have a grace/trial period of two weeks to pay, or get a refund if you drop from WebAssign, and hence from the course.
      Once done with registration check WebAssign Student Help Section to familiarize yourself, in particular pay attention to Browser Flash requirements.
      You have to check your WebAssign account on nightly basis for home work.
      Course material will be uploaded as the course progresses.
  2. Resources:
    1. Statistical Apps:
      1. Interactive calculators:
        1. Standard deviation calculator separate your data by commas .
        2. Grouped data calculator.
        3. Central tendency calculator, mean,mode,median, quartile,etc.
        4. Sample standard deviation from a grouped data with frequency Warning:
          the page uses letter sigma instead of letter s (it calculates sample standard deviation only but calls it sigma).
          Also your data has to be in group. If your data is 1,2,3 etc you ca make groups 0.5-1.5, 1.5-2.5, 2.5-3.5 etc so that midpoints are the actual data.
        5. Binomial Distribution Calculator. Matt Bognar, University of Iowa.
        6. Binomial and Cumulative Binomial Distribution App, David Irland, DI Management.
        7. Normal Distribution Calculator. Matt Bognar, University of Iowa.
        8. Normal Distribution Calculator, at the bottom of page. Give a,b, μ and σ get P(a < X < b) for a normal distribution.
        9. T Distribution Calculator, Matt Bognar, University of Iowa.
      2. Demos:
        1. PDF of Rolling a dice Kyle Siegrist, University of Alabama.
        2. Galton Board /Binomial Experiment, YouTube, marbles falling through pegs.
        3. Central Limit Theorem for Means, Distribution of averages from an arbitrary distribution approaches a normal distribution.
        4. Z vs t-distributions, (JAVA, use IE), As df increases they become same.
      3. Collections:
        1. Statistics Calculators, MathPortal.
        2. Statistical Apps, Matt Bognar, University of Iowa.
        3. Statistics Online Computational Resource (SOCR), University of California, Los Angeles.
        4. WISE,(Java, use IE), Web Interface for Statistics Education, Claremont Graduate University.
        5. Rice Virtual Lab in Statistics (Java, use IE), David Lane, Rice University.
        6. Random, Kyle Siegrist, University of Alabama.
        7. Collection of apps, Random Services
        8. GapMinder, statistical information about the world.
    2. Statistical Tables:
      1. Cumulative Binomial Distribution Table, Xander Faber, University of Hawaii.
      2. Z Distribution Table, area from left, listed from middle.
      3. Z Distribution Table, area from left, listed from left to middle.
      4. Z Distribution Table, area from center, 5 digits, National Institute of Standards and Technology, NIST.
      5. T Distribution Table, NIST.
      6. Table of random numbers.
    3. Video Courses:
      1. Collaborative Statistics, YouTube videos by Illowsky (also available on iTunes for free, search for ``collaborative statistics'').
      2. Collaborative Statistics, course.
      3. Against All Odds, Annenberg Learner.
      4. Descriptive Statistics, Khan Academy.
      5. Basic Probability, Khan Academy.
      6. SticiGui, Professor Philip B. Stark, University of California, Berkeley.
    4. Articles:
      1. Bayes' Theorem Dan Morris
      2. Monty Hall problem
      3. Probability puzzles


 
PreCalculus II, MATH 2312

precalculus

Last Update Summer II 2020.
Welcome to Online Precalculus II MATH 2312. Summer II, July 7- August 10.
This page is under construction, and will be changed frequently.
Blackboard does not give access to this course or its functionality until a few days before the course officially starts.

This is a compressed and accelerated course. It requires an allocation of 30 hours per week during the summer course.
It is designed for students who want to take Precalculus I and II in one semester or in summer. However, any one who has the prerequisites may take it.

The current draft for the course information is avilable, but is subject to change and additions, in particular with respect to assessment schedule.
Simple things you can do before course starts:
1- Read course syllabus
2- Prepare your resume/profile/course contract
3- Install Proctorio

In case you are using Aleks for the first time: here is the Aleks 360 description of itself. The research behind this software is explained here.
For the course text we use Precalculus 1st edition, by Julie Miller and Donna Gerken, published by McGraw Hill Education. The ebook of this text is part of ALEKS subscription. So you need not buy the physical text.

  1. Resources:
      Courses:
    1. Arizona State University Precalculus, on edX platform. This uses Aleks, just as we do! You may choose the free or certificate version.
    2. Videos:
    3. John Turner Videos covers the same text we use.
    4. Maesumi's previous precalculus course, 36 one-hour lectures based on a different text, downloadable in WMV format, easiest to view on Windows/Edge.
    5. Dr. Sarah Eichhorn and Dr. Rachel Lehman, University of California, Irvine, UCI Open PreCal.
    6. Stitz-Zeager, based on quizzes related to their text, listed below.
    7. University of Idaho Course, Parts A, B, C, review Precalculus
    8. Texts:
    9. PreCalculus 3rd edition, by Carl Stitz and Jeff Zeager. Has solved examples for each homework problem.
    10. PreCalculus 4th edition by Carl Stitz and Jeff Zeager. Beta version of the 4th edition.
    11. Trigonometric Delights, by Eli Maor. This text is not free!
  2. Apps and Demos:
      Exponential Functions:
    1. Exponential growth, a process that multiplies in time, (YouTube)
    2. A Exponential Function Story (Wikipedia,Wheat and Chessboard Problem)
    3. Exponential function b^x vs its rate of growth, introducing e the base of natural log
    4. Transformation of an Exponential function, graphing f(x)= a*2^b(x-h) +k
    5. Trigonometry:
    6. Angles on a Protractor 1, Angles on a Protractor 2
    7. Latitude and Longitude as a coordinate system on Earth (YouTube).
    8. GPS coordiantes an application of "degree, minute, second" or "DMS" convention.
    9. Wrapping the real number line on the unit circle (GeoGebra)
    10. Length and Area of a Sector (in radians) (GeoGebra)
    11. Area of a sector (in degrees) (GeoGebra)
    12. Graphs of Sine and Cosine (GeoGebra), radians
    13. Graph of Sine moving circle
    14. Graphs of Six Trig Functions Notation: y=af(bx+c)+d, where f is a trig function, x in radians (GeoGebra)
    15. Side-Side-Angle or SSA demo, Solving a triangle (the two-solutions or ambigious case)
    16. Graph of transformed sine function Notation: y=cf(ax+b)+d, x in radians (Desmos)
    17. Applications of Trigonometry:
    18. Oscillation vs Rotation UNSW, Australia
    19. Simple Harmonic Motion (SHM) demo by D. M. Harrison. Requires SWF Player.
    20. Symmetry:
    21. Reflection with respect to a line (GeoGebra)
      Choose/type the equation of a line
      x=0, i.e. y-axis, changing (x,y) to (-x,y) in an equation will reflect its graph in the y-axis, mirror or reflection line is x=0
      y=0, i.e. x-axis, changing (x,y) to (x,-y) in an equation will reflect its graph in the x-axis, mirror or reflection line is y=0
      y=x, i.e. 45-degree line, changing (x,y) to (y,x) in an equation will reflect its graph in the 45 degree line y=x
      y=-x, i.e. -45-degree line, changing (x,y) to (-y,-x) in an equation will reflect its graph in the -45 degree line y=-x
    22. Reflection with respect to a point (GeoGebra)
      changing (x,y) to (-x,-y) in an equation will reflect its graph in the origin,
           this is same as a double reflection, once in x-axis and a second time in y-axis, or a roation of 180 degrees
    23. Reflection in two lines (GeoGebra)
      A double reflection is equivalent to a rotation.
    24. Axis of symmetry of a vertical parabola (Desmos)
    25. Symmetry of a polyhedra requires Wolfram CDF player
    26. Symmetry of a chemical compound (choose a molecule from left menu, tap Operation on right menu)
      (Molecular Symmetry Wikipedia article)
    27. Conic Sections:
    28. Conic sections (GeoGebra animation)
    29. Conic sections (Shodor animation)
    30. Conic sections (YouTube video)
    31. Transformations:
    32. Transformations of a function y=cf(ax+b)+d (Desmos)
      * The base case is set by a=c=1, b=d=0,
        then adjust the paramters/sliders of the app so that it shows the following cases
      * Multiple actions have to be done in order specified, except
          actions in { } can be done in any order
          actions in horizontal and vertical directions can be done in any order.
      *If a variable z is replaced by az+b then movements in direction of z axis are according to (z-b)/a or z/a-b/a.
         That is move by -b and the scale by 1/a , or scale by 1/a and then move by -b/a.
         Alternatively you may have individual rules as listed below:
        Single Action
      1. y=f(x)+3, up by 3
      2. y=f(x)-3, down by 3
      3. y=3f(x), 3 times taller
      4. y=(1/3)f(x), 3 times shorter
      5. y=f(x+3), left by 3
      6. y=f(x-3), right by 3
      7. y=f(3x), 3 times faster or 3 times narrower
      8. y=f(x/3), 3 times slower or 3 times wider
      9. y=f(-x), reflect left/right, in y-axis
      10. y=-f(x), reflect up/down, in x-axis
      11. Multiple Actions
      12. y=-f(-x), reflect in origin, or {reflect in x-axis, reflect in y-axis}
      13. y=-3f(x), {3 times taller, reflect in x-axis}
      14. y=f(-3x), {3 times narrower, reflect in y-axis}
      15. y=f(2x+3), left by 3, then 2 times narrower
      16. y=f(2x+3), 2 times narrower then left by 3/2
      17. y=f(-2x+3), {reflect in y-axis, shrink horizontally by half}, move right by 3/2
      18. y=f(-2x+3), move left by 3, {reflect in y-axis, shrink horizontally by half}
      19. y=2f(x)+3, up by 3/2, then 2 times taller
      20. y=2f(x)+3, 2 times taller then up by 3
      21. y=-2f(x)+3, down by 3/2, then {2 times taller, reflect in x-axis}
      22. y=-2f(x)+3, {2 times taller, reflect in x-axis}, then up by 3
    33. Transformation of an Exponential function, graphing f(x)= a*2^b(x-h) +k
    34. Graph of transformed sine function Notation: y=cf(ax+b)+d, x in radians (Desmos)
    35. Rotaion of a figure (GeoGebra)
      changing (x,y) in an equation to (-y,x) will rotate its graph by +90 degrees (ccw)
      changing (x,y) in an equation to (y,-x) will rotate its graph by -90 degrees (cw)
    36. Polar Graphing:
    37. Polar coordinate graphing, r=f(theta) (Desmos)


     

    waves Partial Differential Equations, MATH 4302/5325
    Last Update: Spring 2020
    Location and Time: Lucas L209, TR 3:50-5:10
    Exams: Thursdays February 13, March 12, April 23, Cumulative Final May 12, 5-7:30

    If possible, I will put class lecture notes here while the classes are shifted online due to chronovirus.
    These are easier to view on Edge.

    Solution for exam 1 Spring 2020
    Wave 1
    Wave 2
    Heat Eq, Dirichlet/Neumann
    Derivation of Wave Equation for a spring
    Derivation of Wave Equation
    Laplace/Potential Equation
    Polar form of Laplace/Potential Equation 1
    Polar Laplace 2
    PDE Review

    Essential skills needed for PDE
    1- Most introductory problems in Fourier Series depend on the following integrals, it is best to make a table for these
    integral of x^n cos (a x), and x^n sin (a x), for n=0,1,2,3,4.
    View the following video and read the write up to refresh your calculus integration skills:
    Multiple Integration by Parts, YouTube, example of Tableau method
    Multiple Integration by Parts, Maesumi, an inline version of the ladder/tableau method.

    2- Graphing hints
    For graphing we have several choices, make an account in each to be able to send URL of your solutions
    a- for 2d graphs:
    Desmos, practice adjusting graph and slider range to improve presentation
    b- for 3d cases:
    b1- WolframAlpha, good for sums in rectangular domain x,y, but no sliders, no joystick, example type
    plot ( sum ( sin(k*x) * sin(k*y))/k^2 ,k,1,5 ), y=0..2 , x=0..2
    b2- GeoGebra 3D, has sliders and joystick, but to avoid equation editor issues type somewhere else and use CTRL V to paste, use ALT p to get pi, ALT t for theta, && for ^ , this sympbol stands for "and", example type
    If(0 < x < 1 & & 0 < y < 1 , Sum(Sequence( sin(n*x) * sin(n*y)/n^2 , n,1,N) ))
    N is the main slider
    b3- CalcPlot 3D, in the box in front of z= type the k-th term of series, use k or m for index, example
    series( sin (k*x) *sin(k*y)/k^2, k,1,5)
    no sliders or account memberships (so take a screenshot) but a nice joystick
    b4- for cylindrical coordinates (polar version of Laplace) we can use GeoGebra 3D as in
    a(r,t)=Sum(r^n cos (n t), n,1,5)
    Surface(r cos(t), r sin(t), a(r,t), r,0,3, t,0,2 pi)
    instead of theta I used t , you can use ALT t to get theta, ALT P to get pi, etc.
    It appears sliders/Sum/Sequence are not allowed in the Surface command
    Some instabilities were encountered when entering commands, so you type long command somewhere else and paste it using CTRL V

    1. Resources:
      1. Campus-wide licenses:
          MatLab
          Using your Lamar email make an account at MathWorks then go to Lamar Matlab site
          At above page, bottom left, you see several options,
          (1) "MATLAB Online" which allows you to program in web without downloading, and
          (2) "Download MATLAB" which allows you to download.
          IT says use a WIRED connection at home to perform this task, however I have done it on WiFi and downloaded overnight. This takes several hours as it is a very large download, so do it at home, and on a good connection!
          More details are available at Installation Guide.
          MatLab also provides you with its own cloud storage site.
          So you either need to install Matlab to your own laptop or connect to cloud version of MatLab or use a Lamar lab which has MatLab,
          most engineering and CS labs do, so does GB 113.
      2. Learning Matlab:
        1. MatTV, Charles F. Van Loan and K.-Y. Daisy Fan, Cornell University
        2. MathWorks Tutorials
        3. MathWorks MatLab Academy Tutorials
        4. Introduction to MatLab, Yossi Farjoun, MIT/OCW.
        5. MatLab Publish Tab, How to use MatLab to prepare a report or homework
        6. First MatLab homework:
          A basic Euler solver for y'=f(x,y), To run it:
          Open Matlab, open the Editor Window.
          Copy-paste the program in the Editor Window and save it.
          Run it in the Command Window, by using a command as indicated in the file you downloaded, e.g.
          myeuler(1000,1,3,10,'y');
          Make sure you understand it well enough to be able to edit it for your assignments.
        7. Solving a basic PDE/heat equation using MatLab:
          A basic solver for u_t=u_xx,
      3. Learning Mathematica:
        1. Mathematica for Applied DEs , V. Dobrushkin
      4. Review of Prerequisite Topics:
        1. Partial Derivatives, Khan Academy
        2. Multiple Integration by Parts, a short cut similar to the ladder tableau method.
        3. Partial Derivatives Demo, GeoGebra, S. Phelps.
        4. Partial Derivative as Slope, GeoGebra, A.S. Alberca.
        5. Derectional Derivative, GeoGebra, A.S. Alberca.
        6. Specific Heat Capaity, Wikipedia.
        7. Thermal Conductivity, Wikipedia.
        8. Thermal Diffusivity, Wikipedia.
      5. Graphing/calculators:
        1. Desmos, User Guide, Help, YouTube Channel, Blog
        2. GeoGebra Graphing Calculator
        3. Function Calculator by Xiao Gang
        4. Wolfram Alpha
        5. InstaCalc
        6. MathStudio
        7. CalcPlot3D, Paul Seeburger
        8. GeoGebra 3D
        9. GraphyCalc 3D
        10. 3D plotting on WolframAlpha accepts expressions such as "sum (sin(n pi x/4) sinh(n pi y/10)) n=1:3"
      6. Interactive Apps:
        1. Direction Field Plotter, John Polking, Rice University, Texas.
          (You need to install JAVA/JRE first. There is a security concern with respect to installing JAVA. So this is a "use at you own risk" operation.)
          Then tap on "dfield.jar" on above page and download to your computer. A manual by Nancy Chan, Harvard, 2004.
          Software also works on Unix-type operating systems.
          For MAC, software works only on Mozilla (direct installation won't work). MAC has its own internal software called Grapher.
          Using Grapher on MAC for ODEs, Scott Taylor, Colby College.
        2. Direction Field Plotter for single and system of 2 equations, Darryl Nester, Bluffton University. This is web-based and does not require installation.
        3. Direction Field Plotter for 2nd order and a system of 2 1st order equations, Stefan Waner. This is web-based and does not require installation.
        4. Integrator.
        5. Fourier Series Numerical and graphical analysis.
        6. A simple pendulum.
        7. Solution of wave equation with a hat function as the starting value, on infinite domain.
        8. Making waves with different boundary conditions, PhET. Neumann and Dirichlet Boundary conditions.
        9. Heat Equation Solver for hand-drawn input. Luis Silvestre. University of Chicago.
      7. Demos:
        1. Forced Oscillation 1 demo of resonance and beat.
        2. Forced Oscillation 2.
        3. Forced Oscillation 3 requires Wolfram CDF player .
        4. Beat requires Wolfram CDF player .
        5. Fourier Series, describing Fourier Series similar to old model of planetary motion, Dr. Doga Kurkcuoglu, Georgia Tech .
        6. Mathematica code and resulting movies for solving PDEs Peter J. Olver, U Minnesota.
        7. Waves, Dan Russell, Penn State U. Collection of Acoustics and Vibration Animations.
        8. Types of Waves, Dan Russell, PSU. Longitudinal (spring, air, earthquake primary), Transverse (wire, earthquake secondary), water, Rayleigh (solid surface).
        9. Physical demo of a plucked string, Dan Russell.
        10. Standing waves in air, Walter Fendt. Neumann and Dirichlet Boundary conditions.
        11. Standing wave, Geogebra.
        12. Demo of solution of Wave Equation for a plucked string, MIT.
        13. Coupled oscillators: two masses and three springs or two pendulums connected by a spring,
        14. System Simulations, EriK Newmann
        15. Simulation of 2D pure-tone waves on the surface of a circular drum.
        16. Simulation of a 2D Wave on the surface of a circular drum.
        17. 2D waves on a rectangular membrance with damping.
    2. Next Steps: If you want to pursue the topic at a more advanced level there are many courses, texts and software available; in particular
      1. Courses:
        1. MIT 18.152, Jared Speck, Introductions to Partial Differential Equations class notes.
        2. MIT 18.152, Tobias Colding, Introductions to Partial Differential Equations class notes.
        3. MIT 18.303, Matthew Hancock, Linear Partial Differential Equations class notes.
        4. MIT 18.303, Steven G. Johnson, Linear Partial Differential Equations; Analysis and Numerics class notes + Introduction to Julia Language.
        5. Partial Diffferential Equations Videos by Chris Tisdell, University of New South Wales, Australia.
        6. Maesumi, Introductions to Partial Differential Equations Old lecture site.
      2. Texts and notes:
        1. Physical Modeling in Matlab By Allen B. Downey
        2. 1D Heat Equation Matthew J. Hancock, MIT.
        3. A First Course in Quasi-Linear Partial Differential EQuations for Physical Sciences and Engineering Marcel B Finan, Arkansas Tech.
        4. Publisher's companion web site for Boyce DiPrima's text, 8th ed, 9th ed, 9th ed, +BVP, 10th ed, +BVP, 11th ed,
      3. PDEs via standard software packages:
        1. Mathematica Wolfram
        2. Mathematica Wolfram DSolve
        3. Mathematica or Maple N. Abbasi
        4. Mathematica D. Garanin
        5. Maple Waterloo Maple
        6. Matlab MathWorks
        7. ScholarPedia matlab-based basic solvers
      4. PDEs via advanced software packages:
        1. OPM, Open Porous Media, simulation of porous media processes and flows.
        2. MFEM, Finite Element Methods.
        3. FEAtool Finite Element Analysis and MultiPhysics
        4. FEAtool MultiPhysics Python FEM and MultiPhysics Simulations with FeniCS and FEATool
        5. redbKIT, a matlab toolbox for finite element simulation.
        6. Deal.ii, a C++ FEM library
        7. Dune, a C++ Distributed and Unified Numerics Environment for PDEs
        8. K-Wave, a Matlab tool box for simulation of acoustic wave fields
        9. Trilinos, a multi-physics project
        10. HiFlow, A C++ Finite Element Method package
        11. hp-FEM, A C++ FEM solver
        12. Alberta, An adaptive finite element toolbox
        13. Overture, OO ttolkit for PDEs in complex geometries
        14. SINTEF/MRST, Matlab-based, Flow in porous media, secondary recovery
        15. GAMS Fortran-based PDEs
        16. OpenFoam Computational Fluid Dynamics
      5. Related Advanced software:
        1. BVPSuite Implicit singular boundary value ODE problems, Matlab-based.
        2. NEP-Pack Nonlinear eignevalue problems, Julia package.
        3. FEAST Eigenvalue solver.
        4. preCICE Multiphysics software.
    3. Information:
      1. Syllabus
      2. Prerequisiste: ODE 3301 + Calculus III 3415
        Preferred background: Recent and successful completion of : Calculus I,II,III, Linear Algebra, Ordinary Differential Equations, Physics I,II, and any programming course.
      3. Approximate Test Dates: Thursday February 13, March 12, April 16, Final May 7.
      4. Differential Equations Project accounts for 20% of grade for graduates and 10-20% for undergraduates.
      5. Recommended Texts:
        Advanced Engineering Mathematics, Sixth Edition, Dennis G. Zill
        The older editions were authored by Dennis G. Zill and Michael R. Cullen
        Elementary Applied Partial Differential Equations, Richard Haberman
        Elementary Differential Equations and Boundary Value Problems, William E. Boyce and Richard C. DiPrima
        Partial Differential Equations for Scientists and Engineers, Stanley J. Farlow


     
    Numerical Analysis, MATH 4315/5325

    Fractal

    1. Resources:
      1. MathWorks Tutorials
      2. MathWorks Matlab Academy Tutorials
      3. Introduction to MATLAB Yossi Farjoun, MIT/OCW.
      4. Physical Modeling in Matlab By Allen B. Downey
      5. An Introduction to Numerical Methods and Analysis by James E. Epperson.
        Basin of Newton Method is detailed in Chapter 5.
    2. Information
      1. Approximate Test Dates :












    3. General Information


      Learning how to learn
      A Coursera course on learning
      Some excerpts. Tips on how to study.
      A Ten Commandments List for Mathematics.
      How to build new healthy habits.


       
      General-Purpose and Specialized Online Calculators and Applets
      Desmos, User Guide, Help, YouTube Channel, Blog
      GeoGebra Graphing Calculator
      Function Calculator by Xiao Gang
      Wolfram Alpha
      InstaCalc
      MathStudio
      Note: many calculators do not do roots of negatives, eg (-8)^(1/3), if so then use -(8^(1/3))
      3D plotting:
           CalcPlot3D, Paul Seeburger
           GeoGebra
           GraphyCalc
           Type the formula in Google search
      Online Direction Field Plotter (download DField for offline work)
            D.K. Nester, Bluffon University
      For using Wolfram/Mathematica-based applets you need to download the following:
           Mathematica Computable Document Format (CDF) Player.
           For example, try the following demo
           Newton Law of Cooling. Download the CDF file and run it with the CDF-player. Compatibility list.

      Symbolic representation of decimal numbers: ISC/WayBack, REIS, WolframAlpha use command "closed form 1.4142135".
      Online Encyclopedia of Integer Sequences

      Software for Physics, Engineering, and the Sciences (STEM fields)
      Circuit Simulation, and Schematics with textbook.
      BrainBox Circuit Simulator.



       
      Computer Algebra/Numerical/Graphical/Display Software
      Campus-wide licenses for Lamar students:
      (these require download, installation and yearly verification, some have web-based version)
      1. Matlab
      2. Mathematica

      Free software:
      1. DField, PPlot, An ODE Direction Field and Phase Plotter, Dr. Polking, Rice U, manual. For MAC install using Mozilla or use Grapher
      2. Scilab, A numerical computation software, similar to Matlab
      3. Octave, A numerical computation software, similar to Matlab
      4. Sage, A comprehensive numerical computation software, to get Windows 64 bit Installer visit here
      5. Julia, A numerical computation software
      6. Maxima, A computer algebra system, Calculus on Maxima, a maxima-based calculus textbook
      7. GeoGebra, A geometry software
      8. Cinderella, A visual math and physics software
      9. R Project, A statistics software
      10. Mathematics 4.0, An advanced graphing calculator, Microsoft
      11. Runiter, A 3D Graphing Calculator

      The following (as well as 32 bit Sage) may require the instalation of a Virtual Machine:
      SAS Statistics Analysis System

      Packages with discounts for students:
      MATLAB A numerical computation software, Student Version
      Maple A comprehensive mathematics software, Student version
      Wolfram Mathematica A comprehensive computer algebra system, Student version

      Viewers:
      Wolfram Player Replaces, CDF / Computable Document Format Viewer Wolfram Mathematica
      Maple Viewer Waterloo Maple
      Flash Player Adobe (open Task Manager and search and close ALL instances of your browser to install. Heads up: Some "Offers" are included in download)
      ShockWave Player Adobe

      Lists:
      Comparison of Computer Algebra Systems, Wikipedia.
      Report of work in progress on SouthForge.
      Comparison of Interactive Geometry Systems, Wikipedia.


       
      OnLine Course Repositories
      edX, Stanford, Harvard, MIT, Yale, Coursera, Academic Earth, Khan Academy.
      Udacity fee-based and free courses



      Games
      Chess,
      WIMS20, Pegs, The Game of Set, The Ultimate Tic Tac Toe, Entanglement, Nim 1, Towers of Hanoi,
      Scratch-based games,
      Use IE or update Flash first for these:Catlan, Nim 2,
      Visual Programming:
      Google Doodle, Google Blockly, MIT Scratch, Alice, Apple Swift Playgrounds, Twinery,
      Human speed tests:
      memory and reaction speed tests
      Games in politics:
      The Redestricting Game


       
      Competitions
      Putnam Competition
      Internet Olympiad
      International Collegiate Programming Contest
      AMC - American Mathematics Competitions
      Wikipedia List of Math Competitions
      Wikipedia List of Programming Competitions


       
      TeX
      Students who are in senior level classes or above are expected to type their homework and papers.
      WORD or Matlab Publisher are two common choices.
      Students who are in MS program or contemplating entering one, and more so those who wish to get a PhD, should learn TeX.
      Expect to spend as much time as a course for learning TeX. So you want to start early and gradually improve your skill.
      Here are some resources among many:
      TeX Tutorial
      TeX commands
      MiKTeX Distribution


       
      Desmos, User Guide, Help, YouTube Channel, Blog

      Usage Hints for Desmos
      1. Piecewise-defined and Step functions
        Example: In Desmos type y(x)= { -2< x< 0 : x+2, 0< x < 2 : 2-x}
        Syntax: y={ simple inequality 1 : formula 1 , simple inequality 2 : formula 2 , simple inequality 3 : formula 3 }
        Note the usage of braces, colons, and commas.

        To define the unit step function use
        u(t)= { t < 0 : 0 , t > 0 :1}
        Then instead of u_c(t) use u(t-c)

        Here is an example showing how to enter lengthy functions
        The step function: u(t)= { t < 0 : 0 , t > 0 :1}
        Function 1: f(t)= t/(1+t^2)
        Function 2: g(t)= 7sin(3t)
        Function 3: h(t)= 5cos(2t)
        A combination of above with various delays:
        y(t)=f(t)+u(t-3)*g(t-3)+u(t-5)*h(t-5)

        Here is an extended example: modeling the solution of a wave equation

      2. Numbers of digits of accuracy
        Desmos, by default, provides 3 digits.
        In order to get five digits when solving f(x)=g(x) follow these steps.
        1. Graph y=f(x) and then y=g(x) on the same screen. Find the point of intersection and record it.
        2. Graph y=f(x/100) and g=(x/100) (simply replace x by x/100 on existing screen).
        3. Use the wrench icon to modify the x window. For example if in step (a) the root of interest was 2.1 now make sure the window includes 210=2.1*100.
          There is an inequality like -10 < x < 10 when you click on the wrench, change it to 205 < x < 215, play with window or the zoom to clearly see the intersection.
          Now Desmos shows the root to 5 digits. Record this root and divide it by 100.

      3. Summing up to term N. An example of a "slider"
        To plot y = sum of sin (n pi x) / n^2 for N terms type the following
        1. y= sum
        2. A capital sigma shows up with a lower and an upper limit.
        3. In the lower limit you enter the starting value of n, probably 1.
        4. In the upper limit you can enter N, to indicate that you want to add up N terms.
        5. Then you enter your formula , in terms of x and n, e.g. sin (n pi x) / n^2
        6. A slider shows up labeled as N. You can move it over the indicated range.
        7. As default, the range is -10 < N < 10. You can click on "-10" or "10" to change the limits and the increment, for example to 1 and 30.

      4. Labeling
        Type a coordinate (a,b), a menu comes up, you can also put TeX commands in a back quote as in `y=\cos x`
        How to put Labels

      5. Animation
        You can use a slider for parameters. When you use a slider for a time variable you can make an animation.
        For a comet effect use a format as
        (cos(2t),sin(3t) {t < a} )
        (cos(2a),sin(3a))


       
      Access Code
      Most introductory courses require an access code. This provides homework sets, instant checking of answers, and may come with additional resources such as e-book and instructional videos. Access codes are for a limited time use by one person during one semester (unless the course is designated as a multi-semester course, such as Calculus I,II,III, in this case the access code is for three semesters). Once an access code is registered for a course it cannot be used for another person even if it was not used.
      Sometimes an unregistered access code can be used for a course other than the one you bought it for. Ot it can be bought from third party sites. If you have an access code or want to buy one and want to make sure it applies to a text check the following site page for WebAssign Prefix list. Direct online purchase from the publishing company of WebAssign is the safest and gives most user support but costs more.
      There is a two-week trial period for the code (if purchased directly from WebAssign), and after purchase you have two weeks to get a refund if you drop a course. Therefore there is no excuse not to get started with homework right away at the start of semester.

      Cengage, the publisher of WebAssign, has a Cengage Unlimited Subscription Plan (CUSP).
      In short you pay $120 per semester, or $180 per year, or $240 per two years, and you get Cengage digital textbook library, digital online homework system (WebAssign, MindTap, ...), printed text rental at $8/semester. To see if it makes sense for you to use a subscription check here.
      Only books published by Cengage are included in the rental agreement. However WebAssign usually includes the ebook.
      Starting with 2019 we will adopt Larson, Calculus Early Transcendental, 7th edition, which will be in CUSP and in the rental plan. Also Poole's Introduction to Linear Algebra is a Cengage book and in the rental plan.

      Running Adobe Flash Player.
      WebAssign needs to run Flash. To activate it see How to activate Flash


       
      WebAssign Hints and Errors
      Do a browser check first before attempting your assignment.
      On university computers Internet Explorer has more up-to-date components than Chrome.
      WebAssign errors are rare but occasionally they do occur. If you see one let me know.
      More often than not it is the student who has not paid attention to syntax issues or has a typo.
      Note that webassign like most computer programs is case sensitive, so B and b are different. Not only that, font matters too so B is also differnt from B and b. And if that was not enough, you also have β (Greek beta). It is good to be familiar with Greek Letters.
      Also read How to enter exponents, subscripts, roots, functions, etc
      And how to use CalcPad to enter formulas


      Please pay attention to the following and most of your problems will go away!
      Do not mix up:
      Exact vs decimal answers, (if it does not tell you to give the answer to say 2 or 3 or 4 decimal places then it wants the exact answer, e.g. cos-1 (2/ 13  ) vs 56.3099 degrees )
      angles in radians vs angles in degrees (degree angles have a little circle as superscript)
      Ordinary font e.g. F for scalars vs bold fonts e.g. F for vectors
      Here are some characters you might have difficulty with:
      a, A, A, α (alpha)
      b, B, B, β (beta)
      d, D, D, δ, Δ (delta)
      t, T, T, τ (tau)
      w, ω (double-u and omega)
      1,l (one and ell)
      0,o (zero and oh)
      ,' comma vs prime (especially after a fraction a comma is common, not to be confused with derivative of denominator)
      *,(blank) (missing a multiplication sign or using a blank space in its place in a formula, xy is not understood as x*y)
      [],(),{},<> (different fences or delimiters, each book may have a different style)
      [] , [[]] (do not double bracket or put a bracket in a bracket)
      Keep a record of typical errors in your notebook to remind yourself. For more info read WebAssign Syntax Hints

      To have WebAssign work properly, configure the following settings in your Web browser:
      * Allow cookies and pop-up windows from webassign.net.
      * Accept third-party cookies when accessing WebAssign from BlackBoard.
      * Do not allow your browser to store your password.
      * Enable Adobe Flash Player.

      SYSTEM REQUIREMENTS: WebAssign is tested and supported for the following web browsers:
      * Mozilla Firefox (38+) Windows, macOS, Linux
      * Internet Explorer / Microsoft Edge (11+) Windows
      * Google Chrome (44+) Windows, macOS Apple
      * Safari (8+) macOS, iOS 8 or later on iPad

      If you need help with WebAssign view the following or search on YouTube
      WebAssign Registration
      Completing Assignments
      Entering Math Answers on WebAssign


       
      Office Hours, Schedules for Exams, Tutoring, Computer Lab 209, and Maps
      Summer II, 2020, July 7 - August 10.


      Office Hours:
      Online by prior appointment
      Students who are preparing for exams are encouraged to ask their questions in the classes prior to the exam day. Postponing questions to day of exam is discouraged.
      Office hours on exam and final days are by appointment only, and they are usually restricted and could be cancelled.
      Rules for office hours: No food, drinks, or texting in office. Bring your homework/lecture notebook and laptop.

      Teaching and Exam Schedule:
      Ordinary Diffential Equations, Math 3301-07 online
      Tentative Test Days: Mondays, July 13,20,27,August 3, Cumulative Final Monday August 10, 6:00-9:00 pm.
      (STEM) Precalculus II, MATH 2312-07 online
      Tentative test days: (See Aleks), July 20, August 1, August 10


      On Campus Mathematics Tutoring
      The Math Shop, Lucas Engineering Building, Room L211

      Online Tutoring
      Lamar has partnered with SmarThinking to offer tutoring for online/distance education courses.
      To login, user name is your Lamar email address.
      Password example: Assuming your name, birth date and SSN are
      John Doe, January 25, 1981, Social Security Number 1234567890
      then password is 810125&DJ7890
      i.e. YYMMDD & Last Initial First Initial Last 4 SSN
      More info

      Lab L209
      Lucas Engineering Mathematics Computer Lab L209 is usually open to all students when there is no class there
      The Lab is useful in the following cases:
          you want to see me concerning a homework that is on computer and you don't have your laptop, or
          you want to see me as a group, or
          you want to get together as a study group and you want to be able to reach me or the Math Shop

      Calendars, Courses, Personnel:
      Academic Calendar
      Final Exam Schedule Spring 2020
      Courses Offered, Important Dates
      University Directory
      University Course Catalog

      Campus Maps:
      Map 1, interactive/html
      Map 2, building and parking map, PDF
      Map 3, PDF
      Map 4, Google


       
      Help with homework and lectures
      • Read your text. Preferrably read it before the lecture, and try some of the simpler problems. Then read it after the lecture.
      • Look up similar problems in the text.
      • If you are using an online homework system, such as WebAssign, check to see if it gives a chance to see a solution to a similar problem.
      • WebAssign may have a video for you to watch.
      • Most texts have a companion site, for example Larson Calculus has CalcChat.com which presents solutions to most odd numbered problems of the text.
      • Lectures from prior years may be available here, for example Calculus I.
      • Mathematics department runs free tutoring in Lucas L211, suitable for introductory classes. Check Tutoing Schedule.
      • Study in a group. Lucas L211 can be a good place to start a study group.
      • DO ask your questions in class. Don't wait for the day before the test to ask.
      • Submit questions via WebAssign.
      • Come to Office.


       
      Handbooks
      NIST Digital Library of Mathematical Functions National Institute of Standards and Technology
      Handbook of Mathemtical Functions Abramowitz and Stegun


       
      Java-based applets error messages
      Many Internet-based mathematical demos used to use Java. However due to security concerns you have to take certain extra steps to be able to use them.
      The accepted practice is to move away from such software.
      However if you attempt to use them it is very likely that you get one of the following error messages if and when you try to access Java-based apps:
      A) Java applications are blocked by your security settings.
      B) Missing Application-Name manifest attribute.
      C) Missing required Permissions manifest attribute in main jar.
      You need to upgrade JAVA frequently, and remove your older versions,
      then close and open your browser,
      then include the trusted math site in your Java seucity exemptions file,
      then give permission to your browser to run the app.
      Read the instructions in the following pages for additional information (and use at your own risk)
      Java Security Warning and Solutions. Here is more info.


       
      The Cost of Math/Engineering Errors
      (Or what can happen to you if your teacher gives partial credit to the person sitting next to you!
      Or if we hesitate to withhold credit from a "master".)
      A nutjob
      Pounds vs kilograms
      Another pounds vs kilograms story
      1/2 or 2/1? That is the question!
      How many decimal places you said!?
      What not to learn from a "master"
      One-Time Excusable Errors:
      How not to make waves
      Why not to square the circle


       
        Policies


      Student Email Address
      Check your profile page under Self Service Banner and make sure your data is up-to-date.
      In particular one of your emails should be designated as "The Prefered Email" address and visible to your professors on Self Service Banner.
      Otherwise the system does not send any email to you!

      A test email will be sent to all students at the beginning of semester.
      The email addresses will be taken from "Email List" for each class as provided by Lamar University Self-Service Banner website.
      If you do get it there is nothing to do (no need to confirm by sending a reply).
      If you do not get the email you need to check if
      0) you did not specify your preferred email address correctly during registration (most common mistake)
      1) you typed your email incorrectly during registration
      2) you entered a parent's email for yourself during registration
      3) you changed your email
      4) you requested your email not to show on a web page during registration
      5) your guardian typed your email incorrectly
      6) etc.
      You need to make a corrective action so that your correct email shows on Lamar's "Email List" for each class.
      You must have an email address that you check nightly.
      You should turn on ALL notifications from any homework software (WebAssign/Aleks/etc) we use. You should not opt out of notifications.
      You should also register with your email on WebAssign (if required) and accept to be notified when and if there is new homework.
      If you are concerened with privacy issues you can use lamar.edu for school related topics and keep your private email account separate from your lamar email account.
      Instructor will not take any extra actions to reach you after the 12th class day.
      "I did not know/I do not get your emails / I do not get WebAssign emails, etc" will not be an acceptable excuse if majority of class knew! Attend classes and check email and webassign daily.


       
      Instructor's Email
      1) To contact me use emails: "maesumi at lamar dor edu".
      2) Include your full name, course name and section number on EACH email.
      3) Please do not use REPLY when your email topic is not related to the previous email.
      4) If you do not get a reply to your email after 12 hours re-send the email.
      5) All issues that potentially affect your grade need to be summarized and acknowledged in an email.


       
      Calculators
      Precalculus class Students: You are only allowed to use Aleks calculator which shows up on screen for certain problems.
      All others:
      You are allowed to have a basic scientific calculator on any test. These calculators typically cost about $15 new. They do not have graphing or computer algebra or wireless capabilities. The ones with "natural textbook display" are easier to use. They show formulas similar to how they are printed in texts. Examples are
      Texas Instrument TI-30XS or TI030X IIS or TI-36X Pro,
      Sharp EL-W516BSL556 or EL-W516XBSL,
      Casio FX-991EX or FX-115ES ,
      Cannon F-792SGA.
      Here is how natural textbook display looks like.

      Note:
      You are not allowed to have a phone calculator.
      You are not allowed to share a calculator.
      You are not allowed to use an advanced graphing calculators (as in TI84 etc).


       
      Appeals and Student Data
      In case you want your exam to be reviewed and re-graded you need to notify me within one week from the day grades are given. Two weeks after the final exam your course grade data will be discarded, unless you make a written request during the semester. All issues that may influence your grade should be documented in an email from you to me and acknowledged in an email from me to you. At the time of the final test, and before final grades are given, send a summary email.


       
      Late Homework
      Late homework, if accepted, has a penalty that starts at %20 and increases with the length of delay.
      Homework from beginning of semester loses much of its value by the end of semester.
      Here is how the late penalty will accrue: [17+3*(x-y)] percent, here x is the current homework number and y is the homework number you want to do late.
      So if we are doing homework 16 and you want to redo homework 2 the late penalty is 17+3*(16-2)=59%.
      You may be asked to come to my office and show your handwritten solutions of such late homeworks and explain them.
      During the pandemic you may be asked to attend a Zoom-type meeting.
      All homework is to be done BEFORE the final. Deadline Extensions, do not have any validity past the day of final.
      Students are reminded that waiting for end of semester to see what minimum work is needed to get a particular passing grade is not an acceptable conduct.


       
      Privacy
      Please read the Lamar login prompt before you log to university network. It states that you should not expect any privacy.
      All activity on a computer during class or exam time can be inspected and analyzed by the instructor.
      If you use a homework software all activity on it is visible to the instructor and certain employees of the company.
      There may be a seating assignment in class.
      Your notebooks, papers, calculators, phones and anything visible to instructor may be inspected by the instructor during tests.
      Put all private items in your backpack and keep it closed during tests.
      You may be asked to change your seat during a test.
      You may be asked to attend a Zoom-type meeting, or take your exam on Zoom.
      If you violate the Test Code or class decorum rules you may get a public reminder in class.


       
      Course Evaluations
      The university will send you a notification toward the end of semester to evaluate your courses.
      Your input counts, it helps to improve future classes.
      Your answers will be private. I do not know who evalauted the course. I get a summary after grades are submitted.
      Certain number of points will be added to your last test as a bonus for completing the survey.
      If participation rate is over 90% then bonus points will increase substantially. So encourage your classmates to participate!
      Evaluation period depends on the type of course you take. It is best to do the evaluation as soon as it is available.

      Go to LUConnect, then Go to Course Evals and complete the survey.
      Once done with all evaluations please get a screen shot of the entire evaluation window acknowledgement page, showing all courses and your name. Also print the acknowledgement page to prove that you completed the task.
      The acknowledgement page may take many forms, for example this . This is a page that lists all of your current courses and says you finished evaluating them.

      Write your name clearly on the paper you just printed.
      Write your course name/section on it.
      Students using WebAssign: Upload the screen shot to WebAssign under the assignment "Evaluation".
      Aleks Student: email the acknowledgement page.
      If you are taking multiple classes from me do the survey and upload one sheet per each class.
      Please: Do not print/submit your private answers! only the acknowledgement page!
      If you have technical problems with doing the survey contact Mr. Rossi at X-7143.

       
      Honor Code
      The Golden Rule : You should be able to repoduce, all by yourself, and without any additional help, whatever you write on an assignment or exam or project.
      That means I am within my rights to ask you to go to board or attend a Zoom-type meeting and redo whatever you wrote.
      I am also within my rights to ask you to take a test again if the result of above meeting is unsatisfactory.

      To avoid misunderstanding during an exam pay attention to the following common sense rules:
      Do not look sideways, you are to look at your own papers or screen and protect them from others.
      Follow the guidelines for a Proctorio-based test.
      Your face should be visible to the instructor.
      No obstruction of face by sunglasses, hair, hand, caps, etc.
      No obstruction of ears by musical devices, ear muffs, hoodies.
      Bring an official picture ID (Lamar or DL) to all tests.
      Use of printed sheets, cell phones, advanced calculators, shared calculators or loose paper is forbidden on tests.
      Use of unauthorized websites and communication with others is not acceptable during tests and may result in a grade of F for the course.
      All authorized sites will be listed on the exam, any other is unauthorized. Use of homework pages of WebAssign is NOT authorized.
      Do not give your WebAssign passwords to any other person for any reason.
      Unauthorized logins to WebAssign may result in a grade of F for the course for you.

      Fair Use Policy: (or how to get help and not be in trouble with plagiarism rules):
      Students are encouraged to try do the homework problems and projects without seeking help.
      But it is OK to consult other students and resources to learn how to solve homework problems or take-home projects or papers.
      If you want to seek help on a problem the acceptable process is the following:
      (a) Throw away whatever you have written on that problem so far.
      (b) Consult with as many resources as you wish, make sure you understand what you read or hear or see.
      (c) Write the solution of the problem all by yourself without listening to or looking at any other source. Your new writing must be from scratch and from the beginning.
      (d) If you get stuck again go back to step (a).
      At the end you should be able to reproduce and justify the steps of the solution you submit. For example by coming to the board and explaining it.
      See the penalty schedule for cost of infractions. University Academic Honesty rules apply.


       
      Student Profile
      Students are to required to prepare a profile/resume specific to their course.
      You will upload it to a WebAssign homework assignment labeled "Resume or Profile", there you will see a simple problem. you are to upload the resume under "Show My Work".
      If you attend two of my classes upload one for each.

      Copy this questionnaire to a Word file, answer each question, make a blank line between successive questions. If an item is not applicable to you just write "not applicable" and explain. convert the final copy PDF and upload it to WebAssign

      I- Identity Information
      You are being asked to identify yourself because you are accessing our network and getting credit for work performed. All of this information is collected during tests. Here you are confirming that information. If any of these change during the course (such as changing address, computer, ISP, etc) then you need to make an updated resume and submit that before any test.
      1- First name
      2- Last name
      3- Lamar University L number
      4- Lamar email
      5- Secondary email (optional)
      6- Public IP address ((IPv4) of your computers (go to What Is My IP Address to see your address)
      7- Your postal/physical address (choose the address where your computers is located)
      8- A clear copy of Lamar ID (If there is a credit card number on it you MUST cover it up)
      9- A clear copy of another official Picture ID, for example a Driver License. (You just need to show your name and your picture, you should cover up all the other items.)
      10- A large clear ID-type picture (about 4 by 6 inches) showing your face but without hat or sunglasses. Like what you would take for an ID at DMV.

      II- Education Information (optional)
      11- Declared fields of study, (major/minor)
      12- Details of the last three math classes you have taken (where, when, how well did you do, was it online?)
      13- Why are you taking this course?
      14- How many hours of study are you planning to spend on this course each week?
      15- What math classes, if any, will you take after this class?
      16- What other classes are you taking at this time?

      III- Other Info
      17- Do you have a solid computer, good online connectivity, a webcam, a microphone, and an uncluttered study area? An independent quality webcam with base/tripod is preferred. Here is an example of a good setup. Tablets, phones, custom-made computers, etc, may not be compatible. Do a system check on the first day.
      18- What is your back-up computer system in case your main computer or wifi or Internet are disabled?
      19- During tests you will be asked to use the webcam to show your ID, your face, your table, and your surroundings to ensure that standards of Proctorio test are met. This will require some practice. We apologize in advance for the intrusion and the inconvenience, but there is no other way of taking a secure test. Proctorio will record all events. If the proctoring standards are not met student will be asked to take another test. Do you agree with this requirement? In your resume you do need to type the following "I do agree with the requirements of proctored tests. If the standards are not met, my instructor, at his sole discretion, may ask me to take another test."

      IV- Voluntary Information
      20- As a part of your resume you may include optional items and information to let me know you, your educational goals, your career goals, responsibilities, current employment, what you expect from this course, and any details that you think might help what we intend to do in the course. If you have not done well in math classes before, let me know what steps you are willing to take, from the first day, to make sure you succeed this time. Pay close attention to the fact that summer courses are more than three times as fast as the long semester courses. There is really no time for a second engagement. So you need to put your absolute best effort forward.


       
      Online Readiness / Proctorio

      1- Proctorio is a software that proctors your tests and quizzes. It must be installed by the end of first day of class.
      2- On Blackboard enable Secure Exam Proctor. To do this go to BlackBoard, go to Course Resources/Tools. Search for Secure Exam Proctor (an icon resembeling an old-style webcam), and make sure it is enabled.
      3- Procedure: We will use a "container or gateway test" to employ Proctorio.
      This means that you initiate your test on Blackboard where you get a password for your test. You let Blackboard test stay open. Then you go to actual homework/test website (WebAssign or Aleks), (directly using browser's address line and opening a new tab), and, once there, open the test using the password you just picked. Once you are finished with your test you submit it there, then you head back to Blackboard and submit the container test there in order to terminate Proctorio.
      Proctorio has some strict standards that you need to adhere to. Otherwise you will be asked to take another test. Or you might be asked to take a live test via a software such as Zoom. We will practice using Proctorio on a quiz to make sure you are familiar with the steps. Therefore make sure you do not skip quizzes. Here are some videos that explains its use. These videos are from other universities, so your experience can be somewhat different: Proctorio Description 1 and Proctorio Description 2.
      Please note: There are separate instructions for the Blackboard container test and the Aleks test.
      For example typically Blackboard says you have multiple or unlimited attempts but the your homework software might says you have limited attempts. The first one just means if you are disconnected you can get back into the test, while the second one says you can only submit one answer per question.


      Problems with getting into Blackboard Gateway Test
      If you attempt to get into Blackboard Gateway Test and you see a page asking you for a password, similar to the photo below, then that indicates an error message

      Password on Blackboard

      and you need to
      1- Make sure you enabled Secure Exam Proctor on Blackboard as mentioned above.
      2- If that does not solve the problem then follow the instructions mentioned here to remove cause of error.
      3- If you still need help contact Proctorio Customer Support.

      Basics of a proctored test using Proctorio
      0- Install it long in advance of tests, to make sure it runs on your computer. Waiting until the first test to discover that it does not work for you does not reflect well on you.
      1- Your environment and your appearance has to be exactly as if you are in a classroom.
      1- To repeat: Your environment and your appearance has to be exactly as if you are in a classroom.
      2- Turn the light on! make sure your room is bright and well-lit. Otherwise your face and your ID will not be visible.
      3- Hold the ID so that your face appears in natural position. (Don't turn it sideways even if Proctorio's box suggests it.) Look at how your ID appears in image, make sure it is not blurry.
      4- When Proctorio says "room scan" the main thing to do is to scan your table. Count from 1000 to 1020 and slowly turn your webcam over your table showing the items on your table. For privacy you may use a sheet hung behind you. Or sit such that a wall is behind you.
      5-On Aleks, if a question needs a calculator then Aleks will show one on screen. That is the only calculator you will use.
      On WebAssign you are allowed a basic scientific calculator. Other software, as mentioned at the top of WebAssign test, may be allowed as well.
      6- No: phones, calculators, tablets, books, printed materials, secondary computers or monitors is allowed on your tableJ.
      7- No: headsets, hats, sunglasses, smoking, vaping, eating, drinking, lying in a bed, music, noise, dark room.
      8- No: copying, pasting, downloading, browsing, communicating with unauthorized persons.
      9- No: surfing in unauthorized sites or ebooks or files. Software homework pages other than exam page are also off limit.

      Computer Requirements
      By taking this course you acknowledge that you have a computer with the following capabilities:
      Internet, Webcam, Microphone, Chrome, Proctorio. Otherwise students should not attempt these courses.
      Students who take online courses will need a computer with the following capabilities and the most recent version of applicable software:
      High Speed (Broadband) Internet access (minimum 25 Mbps, check at a facility similar to SpeedNet
      Computer with at least 4 gigabytes of memory (8GB preferred)
      Chrome browser (go to chrome://settings/help to update)
      Webcam (independent webcam with base preferred)
      Microphone (independent USB headset with wireless capability preferred)
      Proctorio Extension must be installed on Chrome by the first day. Must be operational by the second quiz.

      My Blackboard course videos won't play. What should I do?
      The first step is to make sure you are using the latest version of your browser. Try all. Next make sure your Adobe Flash Player is up to date. You need to check the Task Manager to make sure no browser is open while you are installing. Decline “Offers” during download. Next try clearing your browser cache. Instructions for doing so can be found by searching “Clear Chrome cache” or "Clear FireFox cache", etc. Blackboard Contact:
      blackboard@lamar.edu
      409-880-2222
      Toll Free: 1-866-585-1738


       
      Votes, Time Extensions
      Occasionally we may have votes in class. In these cases we go by the vote of students who are present in class. As a courtesy to all students, and at instructor's discretion, the vote might be conducted via an email. Students will have 24 hours to respond. Failure to respond indicates the student will accept the vote already cast.
      Time Extensions: On some tests you may be given a time extension. The extensions will be given in increments of 5 minutes. So long as it does not conflict with the next class, and students in attendance do not object.


       
      Absence
      For excusable absence from an exam you need a written verifiable proof of emergency. In case of early contact, and at instructor's discretion, a make up exam might be give. Please note that for a make up exam several issues cannot be guaranteed: date, time, a quiet room, level of difficulty, etc.
      At instructor's discretion, in case of a justifiable absence, an adjusted mix of your other exam grades may substitute the missing grade.
      To reduce the negative impact of absence from classes please have a "buddy system" to provide you with missing notes, latest news, coverage report, etc. Students with excessive unjustified absence may not use office hours for homework help.

      Last date of attendance:
      For a failing students the instructor has to report the last date of attendance. I will enter the last date at which the student had a passing grade. Therefore it is important for students who are on probation, due to scholarship, loan, visa, GPA deficiency, etc, or who need to prove attendance for attendance, to submit all homework and attend all classes. Sporadic presence in tests or classes will not be considered a proof of attendance.
      There is a university-wide audit of attendance near the beinning of the semester. For census audit your last date of attendance will be the last date at which you had a homework grade of 70% or above.
      If you want your physical presence to be counted as attendance then sign a paper with your name and class name and give it to me in each class.


       
      Recommendations
      For a significant recommendation letter (other than for an on campus job) students need to choose a project, early in the semester, in consultation with the instructor, visit the instructor multiple times to show the progress made, write a report, and give an oral presentation.
      Interested students need to come and see me with a resume, a transcript, sample of related work, and a list of topics of interest at the beginning of the semester.
      I need to see how you process mathematics, and as such, homework and take home exams or projects cannot be a basis for a recommendation letter.


       
      ForOfficeUse
      If you come across an assignment with a title/name of "ForOfficeUse" ignore it unless you have specific instructions. Any grades or anomalies with respect to such assignments will disappear within a week.


       
      More FAQs

      Registration issues:
      1- Students are strongly discouraged from late registration. Students are expected to be present on the first day of classes.
      2- No "Late Add" is allowed.
      3- It is the student's responsibility to become familiar with class rules even if they missed the first few classes for whatever reason.
      4- If student registers late then he/she is responsible for catching up to the rest of class and he/she is to take the exams at the scheduled dates. All missed homework and exams of my course/section may be assigned a grade of zero.
      5- If your registration is in limbo you are to continue attending classes as usual.
      6- The "last attend date" is defined as the last date student had an overall passing score. This is of importance especially if you are on scholarship or probation or on visa. To pass university audit at the beginning of semester you must attend classes, participate in quizzes, and have a passing homework score. If you want your physical presence to be counted as attendance then sign a paper with your name and class name and give it to me in each class.

      DRC issues:
      1- Students who are considering to use DRC are to consult with me at the earliest possible time and have DRC send the notification at least one week in advance of any test.
      2- It is the students responsibility to arrange for their test well in advance.
      3- It is responsibility of the student to make sure, well in advance of any test, that the computer they will use has all the software we use in class.
      4- DRC students take the same quiz as all other students. There are no separate arrangements for quizzes. If necessary their quiz grades will be adjusted.