The History and the Philosophy of this Site
I became interested in Internet-based instruction in 2001. I developed a set of videos which were used as the backbone of a course. Students viewed the videos at home but we met on campus as usual; however, class time was used exclusively for problem solving and discussion by students. I called it a "Now U-Try" course. 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 grades especially when 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.

To the Students:
We will make substantial use of Internet-based instruction; and, as it is with most technological breakthroughs, there are major benefits as well as risks associated with this new mode of instruction. Some of the risks of being online are related to psychological dependency, privacy, digital security, 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 compare it with your study time.

1. Resources:
   1. Prerequisite: Precalculus, 2311,2312
      PreCalculus Text 3rd ed, or 4th Beta version, by Carl Stitz and Jeff Zeager.
      The chapter 1 of any calculus book, for example Larson, Chapter 1.
      
   2. Calculus on Maxima (A Computer Algebra System is used to help with the concepts of calculus.)
   3. Asher Roberts Calculus videos.
   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.
      • Larson's CalcChat.com and CalcView.com have solutions to most of odd numbered problems of his texts.
      • Free tutoring services: (1) The Math Shop, Lucas 211 (2) STARS, Gray Library
      • Study in a group. Lucas L211 can be a good place to start a study group and it is the Math Shop.
      • Submit questions via WebAssign's "Ask Your Instructor".
      • Come to online/on-campus Office Hours.
   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. epsilon-delta definition of limits 1. (GeoGebra) Use a function with small slope to improve visiblity.
      3. epsilon-delta definition of limits 2, (GeoGebra)
      4. Visual differentiation 1. Slide the dot on x-axis to see tangent line move.
      5. Visual differentiation 2. Design a polynomial by moving the seven red dots. Then take its derivative.

   ---

   

   
    
   Calculus and Analytic Geometry II, MATH 2414
   Last update: Spring 2024.
   A YouTube channel for Stewart ETF9.
   List of visualization demos:
   
   Frequently used software
   
   • Desmos a graphing calculator, Usage Hints, User Guide, Help, YouTube Channel, Blog
     Desmos gives intersections to 3 digits, unless you apply steps explained in the Usage Hints, Item 2
   • Geogebra a graphing caculator (use x and y for variables) gives intersections to 14 digits
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

   ---

   

   
    
   Calculus III, Math 2415
   Last update: Fall 2021.
   Youtube PlayList
   The lectures review some of the end items, related to 3D space, from calculus II.
   
   Go to Blackboard for course policy.
   Visualization demos:
   Curves orthogonal to a family of curves Maesumi/Desmos. Directional derivatives and gradients. Larson, Calculus 7E, Section 13.6, Page 925, Example 6 and Problems 59,60. Application: heat seeking particle path.
   
   
   • Desmos a graphing calculator, Usage Hints, User Guide, Help, YouTube Channel, Blog
     Desmos gives intersections to 3 digits, unless you apply steps explained in the Usage Hints, Item 2
   • Geogebra a graphing caculator (use x and y for variables) gives intersections to 14 digits
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

   ---

    
   Linear Algebra, MATH 2318
   

   

   Last update: Scheduled Summer 2023 (online)
   YouTube PlayList Lecture videos for the course.
   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 (MHT file format. View on Edge with IE enabled.)
   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. Demos:
      1. 3D Cartesian Coordinates
      2. 3D Vector Operation Plotter
      3. Force diagram for block on inclined plane
      4. Visualization of the intersection of three planes Wolfram Mathematica, requires Wolfram CDF player , download file to run
      5. Matrix Multiplcation Demo, Wolfram Mathematica, requires Wolfram CDF player , download file to run.
      6. 2D Mapping, of a quadrilateral region, D.Q. Nykamp, University of Minnesota. (Interactive)
      7. 2D Mapping, of letter F, Wolfram Mathematica, requires Wolfram CDF player , download file to run.
      8. 2D Mapping, of letter z, P. Falstad. (Interactive).
      9. 3D Mapping of a Cube, D.Q. Nykamp, University of Minnesota. (Partially interactive)
      10. Determining Eigenvectors by Exploration, D.Q. Nykamp, University of Minnesota.
      11. 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).
      12. Spanning sets: Example of "Feasible Space" from other fields of science and engineering: Kinght Tour in Chess, Robotic Arm, and Ray tracing
          
      13. 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".
      14. 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.
   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. Homework is to be done on WebAssign. For syntax hints and dealing with errors check
         WebAssign Hints 1 and
         WebAssign Hints 2 and
         
   4. Software, webapps :
      1. Interactive Row Reduction M. Maesumi
      2. GaEl Gaussian Elimination M. Eiserman
      3. Row Reducer NClab , Requires registration

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
      Desmos gives intersections to 3 digits, unless you apply steps explained in the Usage Hints
   3. Geogebra a graphing caculator (use x and y for variables) gives intersections to 14 digits
   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. Or check section 8.5 of your calculus text.
   7. Differentiation and Integration Formulas, Review from Calculus I and II. You need to be comfortable with these formulas before you start this course.
   Graphical and Numerical Solution of ODEs
   8. Direction Field Plotter Ariel Barton, U Ark
      
   9. Direction Field Plotter for single and system of 2 equations, Darryl Nester, Bluffton University.
   10. Direction Field Plotter for 2nd order and a system of 2 1st order equations, Stefan Waner.
   11. GeoGebra Direction Field Plotter, DNghiem.
   12. Graphical Solution of equations on GeoGebra, how to solve f(x)=g(x)
   Demos
   
   13. 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,
   14. 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.
   15. Acoustics and waves Dan Russell, Penn State
   16. Beat Wolfram Mathematica, requires Wolfram CDF player .
   17. Beats YouTube SMU, Interference of two waves which have nearby frequencies causes beats. We will see this in section 3.7.
   18. A simple pendulum.
   19. Graphical solution of second order ODE Mathematica Widget.
   20. Physics Science Resource Center, Pearson Publications.
   21. Johann Bernoulli and The Cycloid MyPhysicsLab, Vsauce, MathCurve, MacTutor, 3Blue1brown, Desmos Maesumi
   22. Oscillations of a Single Spring, EriK Neumann.
   23. Forced Mechanical Oscillation, Wolfram Demonstration, requires Wolfram CDF player .
   24. Attenuated sinusoidal function Desmos/Maesumi
   Texts and other sources:
   25. Publisher's companion web site for the text by Boyce and DiPrima, 7th+BVP 8th ed, 9th ed, 9th+BVP, 10th+BVP, 11th ed, 11th+BVP,
   26. A rudimentary/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. See Blackboard for Syllabus.
   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. Check WebAssign Hints 1 and WebAssign Hints 2.
      

   4. ---

      Lecture 1a- Introduction to Ordinary Differential Equations
      Lecture 1b- Introduction to Ordinary Differential Equations
      A primary source of differential equations: Newton's Law F=ma
      Let t=time, u=position, u'=velocity, u''=acceleration
      Types of force F: External depends on time, Spring/Gravity depends on position, Drag/Magnetic depends on velocity
      F depends on t,u,u', acceleration is u'', so Newton's law is a relationship between t,u,u',u''.
      A differential equation is a relationship between a function and its variables.
      Spring force Hooke's Law F=-kx, k spring hardness constant x stretch
      Gravitational force Newton's Law F= G M1 M2/r^2, M1, M2 masses, r distance, G constant of gravity
      Drag force F=-cv, v velocity, c drag coefficient
      Electromagnetic force Lorentz law F=qE+qv❌B, q electric charge, E electric field, v velocity, B magnetic field
      
      Warm Up homework from Calculus 1
      

      ---

      Section 2.2 of textbook
      Lecture 2a- Separable Differential Equations
      Lecture 2b- Separable Differential Equations, Interval of Validity of Solution or Interval were solution exits/defined
      dy/dx = f(x)/ g(y) can be written as g(y) dy = f(x) dx, hence separated. Integration provides a solution G(y)=F(x)+C.
      Initial condition y(a)=b means point x=a and y=b is on the solution curve, hence it specifies C via G(b)=F(a)+C.
      The interval of validity of the solution contains the initial point and begins or ends at an x where x or y or y' or a function in the ODE become undefined/discontinuous/infinite.
      Homework OHW1
      

      ---

      Section 2.1 of textbook
      Lecture 3a- Integrating Factor Method
      Lecture 3b- Multiple Integration by Parts
      OHW2
      

      ---

      Examples of ODEs that can be solved by the v subtitution method
      Homogeneous Equations, y'=f(y/x), v= y/x, Section 2.2, Pages 49-51, Problems 29-38
      Bernoulli Equation, y'=a(x)y+b(x)y^n, v= y^(1-n), Section 2.4, Pages 77-78, Problems 27-31, applied in Drag force and Population modeling
      Brachistochrone Equation, (1+y'^2)y'=k^2, v= y^(1/2) / k, Section 2.3, Pages 67-68, Problems 32, applied in design of slides with shortest time, (not assigned in exercises)
      Read about Johann Bernoulli and The Cycloid in MyPhysicsLab, Vsauce, MathCurve, MacTutor, 3Blue1brown
      Desmos/Cycloid animation, use the "t" slider
      Gompertz Equation, Section 2.5, y'=(a-b ln y) y, v= ln y, Pages 89, Problems 16-17, applied for Population modeling, (not assigned)
      Lecture 4a- ODEs by Method of Substitution, Homogeneous Equations
      Lecture 4b- ODEs by Method of Substitution, Bernoulli Equation
      OHW3

      ---

      Section 1.1, 1.2 of textbook
      Lecture 5a- Direction Field
      Lecture 5b- Direction field, stability, Long-term behavior
      OHW4
      How to download the high quality direction field plotter software Dfield to your PC:
      (a) 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.
      (b) Go to Direction Field Plotter, John Polking, Rice University.
      Then tap on "dfield.jar" on above page and download to your computer.
      A Manual for Dfield by Nancy Chan, Harvard, 2004.
      Software also works on Unix-type operating systems.
      For MAC, I am toldsoftware 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.
      For online options to draw direction fields check above under "Graphical and Numerical Solution of ODEs"

   ---

   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
   

   ---

   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
   

   ---

   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
   

   ---

   Sections 3.3 in detail
   Lecture 9- Euler Formula
   OHW8
   

   ---

   Section 3.4 in detail
   Lecture 10- Method of Reduction
   OHW9
   

   ---

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

   ---

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

   ---

   Section 3.8 of textbook
   Lecture 13- Forced Mechanical Vibrations
   OHW13
   

   ---

   Laplace Transform, Chapter 6
   Section 6.1 of textbook
   Lecture 14a- Introduction to Laplace Transform
   OHW
   

1. Information:
   1. Approximate Test Dates: Monday June 19, Friday June 30, Monday July 10.
   2. Textbook: Collaborative Statistics, 2/e, Barbara Illowsky and Susan Dean (online version is free through Open Educational Resources).
      
   3. 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).
      
   4. Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2
   5. 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. 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. Against All Odds, Annenberg Learner.
         
      3. Descriptive Statistics, Khan Academy.
      4. Basic Probability, Khan Academy.
      5. SticiGui, Professor Philip B. Stark, University of California, Berkeley.
         
   4. Articles:
      1. Monty Hall problem
      2. Probability puzzles

1. Resources:
   Courses:
   
   1. Arizona State University Precalculus, archived, no longer avilable, on edX platform, uses Aleks, free or certificate versions.
   Videos:
   
   2. Maesumi/Aleks mini lectures also accessible from inside Aleks Learning Page.
   3. Maesumi hour-long live lectures from an on-campus class. local copy WMV format.
   4. John Turner Videos selected videos. full Playlist
   5. Dr. Sarah Eichhorn and Dr. Rachel Lehman, University of California, Irvine,
   6. Stitz-Zeager, based on quizzes related to their text, listed below.
   Texts:
   
   7. PreCalculus 3rd edition, by Carl Stitz and Jeff Zeager. Has solved examples for each homework problem. See Stitz Zeager Open Source
   8. PreCalculus 4th edition by Carl Stitz and Jeff Zeager. Beta version of the 4th edition.
   9. Trigonometric Delights, by Eli Maor.
2. Apps and Demos:
   Exponential Functions:
   
   1. Exponential growth, a process that multiplies in time, (YouTube)
      
   2. A Exponential Function Story 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
      
   Trigonometry:
   
   5. Angles on a Protractor 1, Angles on a Protractor 2
   6. Latitude and Longitude as a coordinate system on Earth (YouTube).
   7. GPS coordiantes an application of "degree, minute, second" or "DMS" convention.
   8. Wrapping the real number line on the unit circle (GeoGebra)
   9. Length and Area of a Sector (in radians) (GeoGebra)
   10. Area of a sector (in degrees) (GeoGebra)
   11. Graphs of Sine and Cosine (GeoGebra), radians
   12. Graph of Sine moving circle
   13. Graphs of Six Trig Functions Notation: y=af(bx+c)+d, where f is a trig function, x in radians (GeoGebra)
   14. Side-Side-Angle or SSA demo, Solving a triangle (the two-solutions or ambigious case)
   15. Graph of transformed sine function Notation: y=cf(ax+b)+d, x in radians (Desmos)
   Applications of Trigonometry:
   
   16. Oscillation vs Rotation UNSW, Australia
   Symmetry:
   
   17. 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
       
   18. 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
       
   19. Reflection in two lines (GeoGebra)
       A double reflection is equivalent to a rotation.
   20. Axis of symmetry of a vertical parabola (Desmos)
   21. Symmetry of a polyhedra requires Wolfram CDF player
   22. Symmetry of a chemical compound (choose a molecule from left menu, tap Operation on right menu)
       (Molecular Symmetry Wikipedia article)
   Conic Sections:
   
   23. Conic sections (GeoGebra animation)
   24. Conic sections (Shodor animation)
   25. Conic sections (YouTube video)
   Transformations:
   
   26. 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
       Multiple Actions
       11. y=-f(-x), reflect in origin, or {reflect in x-axis, reflect in y-axis}
       12. y=-3f(x), {3 times taller, reflect in x-axis}
       13. y=f(-3x), {3 times narrower, reflect in y-axis}
       14. y=f(2x+3), left by 3, then 2 times narrower
       15. y=f(2x+3), 2 times narrower then left by 3/2
       16. y=f(-2x+3), {reflect in y-axis, shrink horizontally by half}, move right by 3/2
       17. y=f(-2x+3), move left by 3, {reflect in y-axis, shrink horizontally by half}
       18. y=2f(x)+3, up by 3/2, then 2 times taller
       19. y=2f(x)+3, 2 times taller then up by 3
       20. y=-2f(x)+3, down by 3/2, then {2 times taller, reflect in x-axis}
       21. y=-2f(x)+3, {2 times taller, reflect in x-axis}, then up by 3
   27. Transformation of an Exponential function, graphing f(x)= a*2^b(x-h) +k
       
   28. Graph of transformed sine function Notation: y=cf(ax+b)+d, x in radians (Desmos)
   29. 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)
       
   Polar Graphing:
   
   30. Polar coordinate graphing, r=f(theta) (Desmos)
       
   
   

   ---

    
   

   Partial Differential Equations, MATH 4302/5325
   Last Update: Spring 2025
   

   Partial lecture notes from 2019, in MHT format. 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
   
   Basic skills needed for PDE
   1- Integration-by-parts problems, used in Fourier Series
   integrals of x^n cos (a x), and x^n sin (a x), for n=0,1,2,3,....
   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, for 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", for 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, for example
   series( sin (k*x) *sin(k*y)/k^2, k,1,5)
   no sliders or account memberships (so take a screenshot) but a has 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 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.
         Prepare for a large download of 10-20GB.
         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:
         partial derivatives
         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.
         physics basics
         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. Function Calculator by Xiao Gang
            
         3. Wolfram Alpha
            
         4. InstaCalc
            
         5. MathStudio
            
         6. CalcPlot3D, Paul Seeburger
            
         7. GeoGebra 3D
            
         8. 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.
            (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. Alt Link
         6. Maesumi, Introductions to Partial Differential Equations Old lecture site.
            
      2. Texts and notes:
         
         1. Physical Modeling in Matlab By Allen B. Downey
         2. Linear Partial Differential Equations Matthew J. Hancock, MIT.
            
         3. Partial Differential Equations Victor Ivrii, Unoversity of Toronto
         4. A First Course in Quasi-Linear Partial Differential EQuations for Physical Sciences and Engineering Marcel B Finan, Arkansas Tech.
            
         5. 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. NEP-Pack Nonlinear eignevalue problems, Julia package.
         2. FEAST Eigenvalue solver.
         3. preCICE Multiphysics software.
         4. BVPSuite Implicit singular boundary value ODE problems, Matlab-based.
   3. Information:
      1. 2020 Syllabus
      2. Prerequisiste: ODE MATH 2320 + Calculus III MATH 3415
         Preferred background: Recent and successful completion of : Calculus I,II,III, Linear Algebra, Ordinary Differential Equations, Physics I,II, and a programming course.
         
      3. ODE Project accounts for 20% of course grade for graduates and optional for undergraduates.
      4. 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

   

   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.
         












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.



---

 
Online General-Purpose and Specialized 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 odd roots of negatives, eg (-8)^(1/3), if so then use -(8^(1/3))
3D plotting:
     CalcPlot3D, Paul Seeburger
     GeoGebra 3D
     GraphyCalc 3D
     Type the formula in Google search
Online Direction Field Plotter
      D.K. Nester, Bluffon University
For using Wolfram/Mathematica Demostration Projects 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.




---

 
Computer Algebra/Numerical/Graphical/Display Software
Campus-wide licenses for Lamar students:
(requires download, installation and yearly verification, has a web-based version)

1. Matlab

Free software:

1. Direction Field Plotter, John Polking, Rice U. 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
   

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

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, The Game of Set, The Ultimate Tic Tac Toe, Entanglement, Nim, Peg, Reversi, 25, Sudoku, Towers of Hanoi,
Scratch-based games,
Visual Programming:
Google Doodle, Google Blockly, MIT Scratch, Alice, Apple Swift Playgrounds, Twinery,
Memory and speed tests:
memory and reaction speed tests, Halves,
Games in politics:
The Redestricting Game



---

 
Competitions
Putnam Competition
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 for personal PC
OverLeaf an online TeX editor



---

 
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. Direct online purchase from the publishing company of WebAssign is the safest and gives most user support.
There is a trial period for the code (if purchased directly from WebAssign), and after purchase you have a grace period (usually 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.

As of 2019, Cengage, the publisher of WebAssign, has a Cengage Unlimited Subscription Plan (CUSP).
In short you pay (2019 data) $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.


---

 
WebAssign Hints and Errors
Do a browser check first before attempting your assignment.
On university computers Microsoft Edge may have more up-to-date components than Chrome. Check all available browsers.
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 or has forgotten that a particular form is requested.
Note that WebAssign, like most computer programing languages, 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


Some common roots of errors:
1- Exact vs decimal answers, (if the WebAssign problem 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 )
2- Angles in radians vs angles in degrees (degree angles have a little circle as superscript)
3- 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)
, vs ' comma vs prime (especially after a fraction a comma is common, not to be confused with derivative of denominator)
* vs (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)
[] vs [[]]
[] vs [()] (do not double bracket or put a bracket in a bracket or a parantheses in a bracket, this is a common error when the answer is a vector)
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.

WebAssign System Requirements

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



---

 
Courses, Locations, Hours, Office, Tutoring, Lab, and Maps


Office Hours:
Spring 2025:
On campus Lucas Engineeing Building L206 (or Lab L209).
T 3:30-5:00, R 12:30-1:30, 3:30-4:00 Online W 2:00-3:00, notify by email.
Online M-F 9-3 by prior appointment.
Exceptions: In the following cases office hours may be canceled or limited, check in advance
During the finals or on the days when any class has an exam.
On days university issues an alert (e.g. due to inclement weather).

Students who are preparing for exams are encouraged to ask their questions prior to the exam week. Postponing questions to the day of exam is strongly discouraged.
Rules for online office hours: Use "Ask Your Instructor" button on WebAssign, or "Message Center" on Aleks, send PDF of image of work or use a phone/camera to show your notebook.
Rules for on-campus office hours: Prepapre your questions in advance, bring your laptop and notebook. No food, drinks, or phone in office.

Free Mathematics Tutoring (check all at the beginning of semester to see which works best for you)
The Math Shop Lucas 211, in person.
Stars Student Tutoring and Retention Services, assigns a tutor for you.
Brainfuse Online tutoring.

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 or have access to computers

Calendars, Courses, Catalog, Personnel:
Academic Calendar
Final Exam Schedule Spring 2024 for on-campus or synchronous courses
Courses Offered, Schedule, Finals
University Directory
University Course Catalog
Degree Course Requirements
Dashboard, student demographics and performance

Campus Maps:
Map, 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 again and try more advanced problems.
• Look up similar problems in the text.
• Check videos from prior years or from online resources to anticipate upcoming lectures.
• If you are using an online homework system, such as WebAssign or Aleks, 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.
• Check Lamar tutoring services (The Math Shop or Stars) early in the semester to see which one works best for you.
• Study in a group. Lucas L211 can be a good place to start a study group. Or use Blackboard.
• DO ask your questions in class or in online formats or come to office. Don't wait for the day before the test to ask.
• WebAssign has an "ask your instructor" button, suitable for small issues. For major questions send an image from your notebook.



---

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



---

 
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
Students are strongly urged to read through this section to avoid mis-communication issues.
In case students misses deadlines/exams etc because of not reading the email the student assumes full responsibility.

Communication problems arise due to:
(a) volume of junk mail
(b) volume of information
(c) multiple email addresses, message boards, and calendars
(d) low bandwidth of written text
(e) uncertainties and assumptions

A concerted effort is needed to overcome these obstacles. Here are some suggestions:
(A) Students are encouraged to separate personal email from Lamar email to avoid clutter.
(B) Turn on all notifications from software (Aleks or WebAssign) and merge various educational email sources to one place. Email from Banner, Blackboard, WebAssign, Aleks should be merged, if possible.
(C) You still need to check, daily, all calendars, message boards, or announcements on Blackboard and the software you use (WebAssign or Aleks) as well as all email sources that are not merged.
(D) Do not use "Reply" unless you are replying to a prior message. "Reply" buries your email, and makes it less noticeable. Send emails to maesumi at lamar dot edu .
(E) Avoid the negative mind-set of social media and spamming on school email.

In Addition please remember:
1- If an issue is not resolved by the second email exchange you had with me then make an appointment for a Blackboard Class Collaborate meeting. (This is like Zoom or FaceTime.) A follow up email exchanged may be required to make sure what was agreed upon.
2- In each email please include Last Name, First Name, Course Name, Section, Semester (as in: Doe, Jane, PreCalculus II, 48f, Fall 2020 first half semester)
3- Alternatively, you can make a "signature file" each semester that includes a list of all your current courses. This is preferred as it can be used with all faculty. To make a signature line on OutLook: You can go to Settings (wheel on top), All Settings (at the very bottom), Compose and Reply (second item, second column)
or visit MicroSoft.
4- On your Lamar Profile page (on Self Service Banner) use your Lamar email address as your Preferred address and update your Personal email address, if it is listed. You may miss many emails due to using an outdated Personal email address. You may have changed your email address since the first registration, or you may have entered parental email address for yourself, or mis-typed, etc. If you are not successful at changing/correcting the issue yourself, ask for help from IT, X-2222, ServiceDesk@lamar.edu .
5- 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 Banner system does not send any email to you!


---

 
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).
You are allowed to use system calculator (in Search box type calculator, choose scientific view, study usage in advance)



---

 
Grade 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 within one week of the closing of the particular assignment. At the time of the final test, and before final grades are given, send a summary email.



---

 
Late Homework
Occasional late homework, if accepted, has a penalty that starts at %20 and increases by length of delay so that by the final the penalty is 100% .
Documentation of excuse for late homework must be submitted. Student waives confidentiality with respect to verification of excuse. All homework is to be done before the final. 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 grade is not an acceptable conduct under any conditions as it is unfair to other students.




---

 
Privacy Issues
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 software used for a class or exam can be inspected and analyzed by the instructor.
During online exams you may be asked to activate multiple cameras (HonorLock on computer and additional streaming via Phone on Blackboard Class Collaborate or external webcam).
You may be asked for proof of city of residence .
If you use a homework software all activity on it is visible to the instructor and certain employees of the company.
If an extension is sought for a test a verifiable explanation must be submitted in a timely manner. Student waves his/her privacy rights with respect to verification of the claims made.
There may be a seating assignment in class.
Your notebooks, papers, calculators, phones and anything visible to the 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 scan your room for HonorLock or for Blackboard/Phone moitoring system.
If you violate the Test Code or class decorum rules you may get a public reminder in class or in online exams.



---

 
Course Evaluations is a homework
The university will send you a notification toward the end of each semester to evaluate your courses.
Your input counts, it helps us to improve future classes.
Once you are done with your evaluation an Acknowledgment Page shows up and an email is sent. Take a screen shot of this page showing all your courses and your name. Upload it to WebAssign or Blackboard as proof of your participation.
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. 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.
Once done with all evaluations please get a screen shot of the entire evaluation window acknowledgement page, showing all courses and your name.
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.
Students using WebAssign: Upload the screen shot to WebAssign under the assignment "Evaluation".
Aleks Student: upload the acknowledgement page to Blackboard.
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.
Once evaluation window closes there is NO way of participating, so your forefeit the bonus points.


---

 
Academic Integrity, 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 the board or attend an online meeting or come to office and explain your answers.
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:
If anyone other than the registered student enters Blackboard, HonorLock, Blackboard Collaborate, Aleks or Webassign the registered student may receive an F for the course. This is a very strict requirement and students need to pay close attention to it.
To prevent academic integrity violation students will be asked to go through mutiple levels of identification.
Your face should be visible to the instructor.
No obstruction of face by sunglasses, hair, hand, caps, darkness, etc.
No obstruction of ears by headsets, musical devices, ear muffs, hoodies.
Bring an official picture ID (Lamar or Driver License) 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. Visiting the homework pages of WebAssign or Aleks during exams is NOT authorized.

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 entire 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 or a Blackboard Ultra meeting and explaining it.
University Academic Honesty rules apply.



---

 
Student Profile
Students are to required to prepare a Profile.
Students who are taking a course that uses WebAssign will upload it there, to an assignment named "Profile"
Students who are taking a course that uses Aleks will upload to Blackboard.

Instructions:
Copy and paste this questionnaire (the text between the the two lines below) to a Word file,
Open a new line after each question and answer the question as well as you can
Make a blank line between successive questions
Save the file and Export it to PDF
Upload it

-------------------------------------------------------------------
I- Identity Information
You are being asked to identify yourself because you are accessing our network and getting credit for the work performed. All of this information is also collected during tests. Here you are confirming that information. If any of these change during the course (in particular if you are changing address, computer, ISP, etc) then you need to inform me, make an updated resume and submit that before any test. Incorrect or incomplete or late identity information has a penalty ranging up to an F for the course.
1- First name
2- Last name
3- Lamar University L number
4- Lamar email
5- Secondary email (optional)
6- City, State, Country, Zip code address of ALL computers you will use for this course. In case of travel update the info before using your computer.
7- Are you planning to travel during this course? 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- Two large clear undistorted ID-type picture (at least 6 by 4 inches or half a page) showing your face and profile but without hat or sunglasses. Like what you would take for an ID at DMV.

II- Education Information
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? Why this particular section? If this course is online, asynchronous, accelerated how do you plan to respond to the additional challenge?
14- How many hours of study are you planning to spend on this course each week?
15- What math classes, if any, are you planning 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 (5 Mbps upload), a webcam, a microphone, a smart phone, 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 or electricity 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 HonorLock tests 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. HonorLock will record all events. If the proctoring standards are not met student will be asked to attend a meeting. Penalty can range up to an F for the course.
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 to the satisfaction of Instructor I will attend a meeting with him. I understand penalty can range up to an F for the course."

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 three challenges: Online classes, Asynchronous classes, Accelerated classes (summer, half semester). If the course you are taking falls under any of these categorioes explain to me that you understand it and the steps you are taking to meet the challenge.
-------------------------------------------------------------------------------


---

 
Online Readiness / HonorLock

1- HonorLock is a software that proctors your tests and quizzes. It must be installed by the end of first day of class.
The day before each exam you are to
remove HonorLock extension.
update your OS, browsers, reboot modem and router.
reinstall the HonorLock extension.
in case of difficulty contact their online Support. A typical recommendation is to remove cache and cookies for all time.

2- Procedure: (a) We will use a "Gateway Test" to activate HonorLock and start screenshare.
(b) You will see a link at the top of Blackboard/Content. Follow the link to initiate your Gateway Test on Blackboard and start Honorlock.
(c) You will come to a Password Announcement Page (PAP) and get a password for your actual test.
(d) Let PAP to stay open, (do not click submit) and Open another tab to go to your actual test website (WebAssign or Aleks)
(e) Open the math test using the password you just picked, take the test (f) Once you are finished with your test come back to the PAP tab (g) Type "Submitted"in the submission box type
(h) Click Submit (i) Click "Stop Screen Share", now you are free to go!
Please note: There are separate instructions for the Blackboard Gateway Test and the WebAssign/Aleks test.
For example typically Blackboard says you have unlimited attempts. That referes to WiFi communications and set up, and not to the math questions. Aleks/WebAssign will usually allow only one or two attempts per question on exams.
Also, Blackboard might give a generous-looking 600 minutes for the test! That, again, is for the mechanics of setting your exam and contacting HonorLock in case you run into IT problems and need to reach out to Support. The actual test on Aleks/WebAssign is at most 2.5 hours, usually shorter.
3- Make sure your room is bright and well-lit but without glare. Your face and your ID should be visible.

4- If a "room scan" requested by the proctoring software or person the main thing to do is to slowly count from 1000 to 1020 and turn your webcam over your table showing the items on your table and around it. 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. Only software authorized by the instructor and listed on the exam may be used.
6- No: calculators, tablets, books, printed materials.
7- No: headsets, hats, sunglasses, smoking, vaping, eating, drinking, lying in a bed, music, noise, gum, dark room. Do not appear shirtless. Do not lie/roll on a bed. Your appearance has to be exactly as if you are in a classroom.
8- No: copying, pasting, downloading, browsing, communicating with unauthorized persons.
9- No: surfing in unauthorized sites or ebooks, files, Chat. The software homework pages other than exam page are also off limit. <10> 10- If HonorLock flags your exam the instructor will investigate. Penalty can be as high as an F for the course.

Computer Requirements
By taking this course you acknowledge that you are responsible for your own IT issues and you have a recent uptodate computer with the following capabilities:
Internet, Webcam, Microphone, Chrome browser, HonorLock, WiFi capable of 5 MBps upload.
Check speed, for example at SpeedNet
Min 8GB memory
Chrome browser (go to chrome://settings/help to update)
Webcam (independent webcam with base preferred), check compatibility with OS before purchase
Microphone (independent USB headset with wireless capability preferred)


---

 
Votes, Time Extensions
Occasionally we may take votes in class. In these cases we go by the vote of students who are present or participate by the given deadline. 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 on-campus 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 to the extension.



---

 
Absence
For excusable absence from an exam you need a written verifiable proof of emergency. At the instructor's discretion, a make up exam might be given. Please note that for a make up exam several issues cannot be guaranteed: date, time, a quiet room, level of difficulty, etc.
Occasionally 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. In case of sporadic attendance I may 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, 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 and attendance issues:
1- Students are strongly discouraged from late registration. Students are expected to be present on the first day of classes.
2- I do not allow "Late Add" without an extensive interview. Most excuses are not acceptable. That includes visa/adviser/GI-scholarship/ not being sure what course to take/SAT scores/financial or health issues etc.
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. The instructor is not under any obligations to restart the course for late comers.
5- If your registration is in limbo you are to continue attending classes as usual in so much as possible. For most courses (claculus, linear algebra, differential equations) lectures are on YouTube and homework is on WebAssign so students can access both without any Blackboard blocks. For Precalculus contact me.
6- For students with sporadic course activity the "last attend date" is the last date student had an overall passing score. This is of importance especially if you are on scholarship or probation or on visa etc and you are failing the course. To pass the 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.

ARC 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 EACH of 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- ARC students take the same quiz as all other students. There are no separate arrangements for quizzes. If necessary their quiz grades will be adjusted.