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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 Internetbased 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 UTry" 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 labbased and collaborative.
Elaborate prerequisite 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 wellarranged and searchable; with index, table of contents, page numbers,
definitions, theorems, graphs, methods, tables, examples, computer programs and workedout examples.
To the Students:
We will make substantial use of Internetbased 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 proactively guard against such risks.
You may also want to find your screen time and read an article regarding effects of exposure to
radiofrequency radiation.
Potpourri:
A.
Nature by Numbers, Cristóbal Vila's fanciful tribute to the world of Fibonacci numbers, 2010.
B.
A homework from 3800 years ago, calculate
√ 2
to six decimal places!
C.
She is a, ... computer, the stories of Charlote, 1920, and
Katherine
D.
Richard Feynman,
The Messenger Series, 1964, seven 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, B. Polster;
3Blue1Brown, G. Sanderson;
Numberphile, MSRI;
Up and Atom, J. TanHolems;
J. Dry water and Hot ice:
Physics Girl, D. Cowern;
Steve Mould,SM.
K. Numbers and our world:
One,
Two,
Three,
Four,
Five,
Six,
Seven,
Eight,
Nine,
Ten,
CV0,
CV1,
CV2,
CV3,
CV4,
CV5,
...
L. Mathematics in Movies.
Kids going to school



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 
Calculus II, 2414 
Games 
Class Regulations Sheet 
Calculus III, 2415 
Access Code 
Honor Code 
Statistics, 1342 
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 
G. Ordinary Differential Equarions, 5308 
TeX 
Evaluations 
. 
Competitions 
Late Registration/DRC 
COURSES
Calculus and Analytical Geometry I, Math 2413
Last update: Fall 2023.
A YouTube PlayList based on Stewart, ETF.
 Resources:

Prerequisite: Precalculus, 2311,2312
PreCalculus Text 3rd ed, or
4th Beta version,
by Carl Stitz and Jeff Zeager.
A short summary appears in
First chapter of the Calculus text by Larson.

Calculus on Maxima (A Computer Algebra System is used to help with concept of calculus.)

Asher Roberts Calculus videos.
 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/oncampus Office Hours.

Homework is to be done on WebAssign. Check WebAssign Hints 1
and WebAssign Hints 2
 Apps and demos
 Apps for Calculus I Marc Renault, Shippensburg University. GeoGebrabased.
 epsilondelta definition of limits 1. (GeoGebra) Use a function with small slope to improve visiblity.
 epsilondelta definition of limits 2, (GeoGebra)
 Visual differentiation 1. Slide the dot on xaxis to see tangent line move.
 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
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.
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, GaussJordan 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, GaussJordan 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: Evalues, Evectors, Espaces, 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

Demos:
 3D Cartesian Coordinates
 3D Vector Operation Plotter
 Force diagram for block on inclined plane
 Visualization of the intersection of three planes Wolfram Mathematica,
requires Wolfram CDF player , download file to run
 Matrix Multiplcation Demo, Wolfram Mathematica,
requires Wolfram CDF player , download file to run.
 2D Mapping, of a quadrilateral region, D.Q. Nykamp, University of Minnesota. (Interactive)
 2D Mapping, of letter F, Wolfram Mathematica,
requires Wolfram CDF player , download file to run.
 2D Mapping, of letter z, P. Falstad. (Interactive).
 3D Mapping of a Cube, D.Q. Nykamp, University of Minnesota. (Partially interactive)
 Determining Eigenvectors by Exploration, D.Q. Nykamp, University of Minnesota.

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).

Spanning sets: Example of "Feasible Space" from other fields of science and engineering:
Kinght Tour in Chess,
Robotic Arm, and
Ray tracing

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".

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.

Next Steps:
If you are interested in a more advanced treatment there are many online resources for linear algebra. Here is a sample:

18.06 Linear Algebra, Dr. Strang, MIT, archived course.

18.06 Linear Algebra, Most recent class, MIT.

Linear Algebra: Foundations to Frontiers, Course, Robert van de Geijn, Dr. Maggie Myers, The University of Texas at Austin.

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.

Essense of Linear Algebra, Grant Sanderson

A First Course in Linear Algebra, textbook by Robert A. Beezer.

Linear Algebra, textbook by Jim Heffereon.

Introduction to Matrix Algebra, textbook by Autar Kaw.

Elementary Linear Algebra, Lecture Notes, Keith Matthews.

Vector Algebra, Interactive text by Duane Q. Nykamp, University of Minnesota.

Information:

Homework is to be done on WebAssign. For syntax hints and dealing with errors check
WebAssign Hints 1 and
WebAssign Hints 2 and

Software, webapps :

Interactive Row Reduction M. Maesumi

GaEl Gaussian Elimination M. Eiserman

Row Reducer NClab , Requires registration
Graduate Ordinary Differential Equations, MATH 5308
Last Update: Fall 2022
Recommended texts and courses:
Texts:
1 A Second Course in Differential Equations: Dynamical Systems and Boundary Value Problems
by Russell L. Herman
PDF version ,
LibreText version
2 Second Course in Elementary Differential Equations, by Paul Waltman, Dover Publications. (older copy publication by John Wiley)
used copies ,
Google Books
3 Gardner's class notes based on the text by Waltman PDF by section
4 The ODE Project T.W. Judson, sfasu
5 Two Species Model S. Baigent
6 Models for Systems of ODEs G. Gustafson
7 Advanced Engineering Mathematics D. Zill
8 Elementary Differential Equations and Boundary Value Problems, William E. Boyce and Richard C. DiPrima
7th+BVP,
8th+BVP
9th+BVP,
10th+BVP,
11th+BVP,
12th+BVP
Courses:
1 Computational Methods Course MIT 16.90, Karen Wilcox, Qiqi Wang
2 MIT 18.03, Haynes Miller, Arthur Mattuck.
Notes,
3 (not offered now) Differential Equations: 2 by 2 Systems MIT 18.032 on edX platform
Demos:
1 Lorentz attractor Malin Christersson
2 Nbody massspring system D.A. Russell
3 Triple spring Matthew Collett
4 Double pendulum Walter Fendt
5 Predatorprey Stephen Wilkerson
6 Determining Eigenvectors by Exploration, D. Q. Nykamp
7 Linear Phase Portraits, Cursor Entry in terms of Trace and Determinant. H. Miller, MIT.
8 Linear Phase Portraits, Matrix Entry in terms of Trace and Determinant. H. Miller, MIT.
Projects:
1 Aircraft wing design
MIT 16.90
2 Nbody solar systems
Natalie Orozco ,
S.M.F. Rabbi ,
3 SpringMass sytems
A. Svirin,
R. Fitzpatrik ,
D. Morin ,
L. S. Anres ,
4 Properties of certain trajectories in the phase plane of a system of ODEs,
Maesumi,
Homework:
HW2,
HW3,
HW4,
HW5,
HW6,
HW7,
HW8,
HW9,
HW10,
HW11,
HW12,
HW13,
HW14,
HW15,
HW16,
HW17,
HW18,
HW19,
HW20,
HW21,
HW22,
HW23,
Frequently used software:
Graphing Calculators:
1
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
2
Geogebra a graphing caculator (use x and y for variables) gives intersections to 14 digits
3
Graphical Solution of equations on GeoGebra, how to solve f(x)=g(x)
4 3D Plotter
Field Plotters:
1
Direction Field and Phase Plane Plotters, John Polking, Rice University.
You need to install JAVA/JRE first.
Then tap on "dfield.jar" on above page and download to your computer, then "pplane.jar".
(There is concern with security of JAVA. So this is a runatyourownrisk 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 webbased directionfield plotters that do not require installation and do not use JAVA.
However they are not as fullfeatured as this one.)
A
manual of DField by Nancy Chan, Harvard, 2004.
Software also works on Unixtype 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
Direction Field Plotter Ariel Barton.
3
Direction Field Plotter for single and system of 2 equations, Darryl Nester.
4
Direction Field Plotter for 2nd order and a system of 2 1st order equations, Stefan Waner.
5
GeoGebra Direction Field Plotter, DNghiem.
Matlab:
Lamar stuednts can download and use it. Renew license each September.
Start from here.
Ordinary Differential Equations, MATH 2320 (old 3301)
Last Update: Fall 2023
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 notes 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 Dan Gries, Flash program is disabled, 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 Quasifrequency, Quasiperiod, 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 MultipleIntegrationbyParts 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, 9:1011:00.
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(tc)u(tc), example discon. force
23 05/04/2020 Last class
Fall 2019:
Section2.2SeparableDifferentialEquations
Section2.1IntegratingFactorMethod
Section1.1DirectionFields
Section1.1StabilityandDirectionFields
Section1.12.3Modeling1stOrderODES
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, piecewisedefined functions, L[f(tc) U_c(t)], inverse examples .
05/02/2019
Laplace Transforms, Part 6, Periodic functions .

Resources:
Frequently Used Software

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 runatyourownrisk 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 webbased directionfield plotters that do not require installation and do not use JAVA.
However they are not as fullfeatured as this one.)
A
manual of DField by Nancy Chan, Harvard, 2004.
Software also works on Unixtype 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.

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

Geogebra a graphing caculator (use x and y for variables) gives intersections to 14 digits
Review of some calculus concepts

Multiple Integration by Parts, YouTube, example of Tableau method

Multiple Integration by Parts, a short cut similar to the ladder tableau method.

Partial Fraction Decomposition, Dr Dawkins. Or check section 8.5 of your calculus text.

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

Direction Field Plotter Ariel Barton, U Ark

Direction Field Plotter for single and system of 2 equations, Darryl Nester, Bluffton University.

Direction Field Plotter for 2nd order and a system of 2 1st order equations, Stefan Waner.

GeoGebra Direction Field Plotter, DNghiem.

Graphical Solution of equations on GeoGebra, how to solve f(x)=g(x)
Demos
 Examples of fields:
Velocity Field in Hurricane Sandy,
Magnetic Field 1,
Magnetic Field 2,
Electric Field +,
Gravitational Field EarthMoon,
Image of Saturn's Polar Hexagonal Vortex,
and the article,

Coupled Oscillators triple spring or
double pendulum.
Understanding this phenomena requires concepts from this course (modeling of physical systems as ODEs) and linear algebra.
NSpring.

Acoustics and waves Dan Russell, Penn State

Beat Wolfram Mathematica,
requires Wolfram CDF player .

Beats YouTube SMU,
Interference of two waves which have nearby frequencies causes beats.
We will see this in section 3.7.

A simple pendulum.

Graphical solution of second order ODE Mathematica Widget.

Physics Science Resource Center, Pearson Publications.

Johann Bernoulli and The Cycloid
MyPhysicsLab,
Vsauce,
MathCurve,
MacTutor,
3Blue1brown,
Desmos Maesumi

Oscillations of a Single Spring, EriK Neumann.

Forced Mechanical Oscillation, Wolfram Demonstration,
requires Wolfram CDF player .

Attenuated sinusoidal function Desmos/Maesumi
Texts and other sources:

Publisher's companion web site for the text,
7th+BVP
8th ed,
9th ed,
9th+BVP,
10th+BVP,
11th ed,
11th+BVP,

ODE Videos by Maesumi Win, HTML + WMV or
Mac/Win HTML + MOV from 2006.

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 cloudbased version or download a copy to your own computer.
Once you have opened Matlab copypaste 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.

Next Steps:
If you are interested in a more advanced treatment there are many online resources for ODEs. Here are a few:

ODE at MIT,
Video of lectures given by Arthur Mattuck and Haynes Miller, mathlets
by Huber Hohn. Includes videos,
transcript, tools, exams, etc.

Differential Equations in Action,
Instructor: Jorn Loviscach, Course Developer: Miriam Swords Kalk.

Differential Equations, course by KhanAcademy.

Elementary Differential Equations with Boundary Value Problems, textbook by William E. Trench.

Introduction to Differential Equations, textbook by Jeffrey R. Chasnov.

Introduction to Differential Equations, MIT 18.031, archived on EdX.

Information:
 See Blackboard for Syllabus.

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.

ODE Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2.
 If you buy WebAssign from thirdparty sellers or students make sure it is unused and check its prefix with
WebAssign.
(this is a gray area so proceed cautiously)

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 4951, Problems 2938
Bernoulli Equation, y'=a(x)y+b(x)y^n, v= y^(1n), Section 2.4, Pages 7778, Problems 2731, applied in Drag force and Population modeling
Brachistochrone Equation, (1+y'^2)y'=k^2, v= y^(1/2) / k, Section 2.3, Pages 6768, 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'=(ab ln y) y, v= ln y, Pages 89, Problems 1617, 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, Longterm 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 Unixtype 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 firstorder ODEs, Mixing Problem
Lecture 6b Modeling with firstorder ODEs, Finance Problem
Lecture 6c Modeling with firstorder ODEs, Population forecasting
Lecture 6X1 Modeling with firstorder 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
Statistics, MATH 1342
Last Update: Summer I, 2017

Information:

Approximate Test Dates: Monday June 19, Friday June 30, Monday July 10.

Textbook:
Collaborative Statistics, 2/e,
Barbara Illowsky and Susan Dean (online version is free through Open Educational Resources).

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).

Homework is to be done on WebAssign. Check WebAssign Hints 1 and WebAssign Hints 2

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.

Resources:

Statistical Apps:

Interactive calculators:

Standard deviation calculator separate your data by commas .

Grouped data calculator.

Central tendency calculator, mean,mode,median, quartile,etc.

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 0.51.5, 1.52.5, 2.53.5 etc so that midpoints are the actual data.

Binomial Distribution Calculator.
Matt Bognar, University of Iowa.

Binomial and Cumulative Binomial Distribution App, David Irland, DI Management.

Normal Distribution Calculator.
Matt Bognar, University of Iowa.

Normal Distribution Calculator, at the bottom of page. Give a,b, μ and σ get P(a < X < b) for a normal distribution.

T Distribution Calculator, Matt Bognar, University of Iowa.

Demos:

PDF of Rolling a dice Kyle Siegrist, University of Alabama.

Galton Board /Binomial Experiment, YouTube, marbles falling through pegs.

Central Limit Theorem for Means, Distribution of averages from an arbitrary distribution approaches a normal distribution.

Z vs tdistributions, (JAVA, use IE), As df increases they become same.

Collections:

Statistics Calculators, MathPortal.

Statistical Apps,
Matt Bognar, University of Iowa.

Statistics Online Computational Resource (SOCR), University of California, Los Angeles.

WISE,(Java, use IE), Web Interface for Statistics Education, Claremont Graduate University.

Rice Virtual Lab in Statistics (Java, use IE), David Lane, Rice University.

Random, Kyle Siegrist, University of Alabama.

GapMinder, statistical information about the world.

Statistical Tables:

Cumulative Binomial Distribution Table, Xander Faber, University of Hawaii.

Z Distribution Table, area from left, listed from middle.

Z Distribution Table, area from left, listed from left to middle.

Z Distribution Table, area from center, 5 digits, National Institute of Standards and Technology, NIST.

T Distribution Table, NIST.

Table of random numbers.

Video Courses:

Collaborative Statistics, YouTube videos by Illowsky (also available on iTunes for free, search for ``collaborative statistics'').

Against All Odds, Annenberg Learner.

Descriptive Statistics, Khan Academy.

Basic Probability, Khan Academy.

SticiGui, Professor Philip B. Stark, University of California, Berkeley.

Articles:

Monty Hall problem

Probability puzzles
STEM PreCalculus II, MATH 2312
Last Update Dall 2024.
For final details see Blackboard.
Approximate time requirement:
Summer version 40 hours per week
Halfsemester version 20 hours per week
Fullsemester version 10 hours perweek
The halfsemeter version is designed for students who want to take Precalculus I and II in one semester.
It is recommended for students who have seen the material recently in high school and are in need of a higher level refresher.
Course software is called Aleks. In case you are using it 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 2nd edition, by
Julie Miller and Donna Gerken, published by McGraw Hill Education. The ebook of this text is part of ALEKS subscription,
which must be purchased by the student and be valid for a period at least as long as the length of the semester.

Resources:
Courses:

Arizona State University Precalculus, on edX platform, uses Aleks, free or certificate versions.
Videos:

Maesumi/Aleks mini lectures also accessible from inside Aleks Learning Page.

Maesumi hourlong live lectures from an oncampus class.
local copy
WMV format.

John Turner Videos selected videos.
full Playlist

Dr. Sarah Eichhorn and Dr. Rachel Lehman, University of California, Irvine,

StitzZeager, based on quizzes related to their text, listed below.
Texts:
 PreCalculus 3rd edition, by Carl Stitz and Jeff Zeager.
Has solved examples for each homework problem. See Stitz Zeager Open Source

PreCalculus 4th edition by Carl Stitz and Jeff Zeager. Beta version of the 4th edition.

Trigonometric Delights, by Eli Maor.

Apps and Demos:
Exponential Functions:

Exponential growth, a process that multiplies in time, (YouTube)

A Exponential Function Story Wheat and Chessboard Problem

Exponential function b^x vs its rate of growth, introducing e the base of natural log

Transformation of an Exponential function, graphing f(x)= a*2^b(xh) +k
Trigonometry:

Angles on a Protractor 1, Angles on a Protractor 2

Latitude and Longitude as a coordinate system on Earth (YouTube).

GPS coordiantes an application of "degree, minute, second" or "DMS" convention.

Wrapping the real number line on the unit circle (GeoGebra)

Length and Area of a Sector (in radians) (GeoGebra)

Area of a sector (in degrees) (GeoGebra)

Graphs of Sine and Cosine (GeoGebra), radians

Graph of Sine moving circle

Graphs of Six Trig Functions Notation: y=af(bx+c)+d, where f is a trig function, x in radians (GeoGebra)

SideSideAngle or SSA demo, Solving a triangle (the twosolutions or ambigious case)

Graph of transformed sine function Notation: y=cf(ax+b)+d, x in radians (Desmos)
Applications of Trigonometry:

Oscillation vs Rotation UNSW, Australia
Symmetry:

Reflection with respect to a line (GeoGebra)
Choose/type the equation of a line
x=0, i.e. yaxis, changing (x,y) to (x,y) in an equation will reflect its graph in the yaxis, mirror or reflection line is x=0
y=0, i.e. xaxis, changing (x,y) to (x,y) in an equation will reflect its graph in the xaxis, mirror or reflection line is y=0
y=x, i.e. 45degree 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. 45degree line, changing (x,y) to (y,x) in an equation will reflect its graph in the 45 degree line y=x

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 xaxis and a second time in yaxis, or a roation of 180 degrees

Reflection in two lines (GeoGebra)
A double reflection is equivalent to a rotation.

Axis of symmetry of a vertical parabola (Desmos)

Symmetry of a polyhedra
requires Wolfram CDF player

Symmetry of a chemical compound (choose a molecule from left menu, tap Operation on right menu)
(Molecular Symmetry Wikipedia article)
Conic Sections:

Conic sections (GeoGebra animation)

Conic sections (Shodor animation)

Conic sections (YouTube video)
Transformations:

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 (zb)/a or z/ab/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
 y=f(x)+3, up by 3
 y=f(x)3, down by 3
 y=3f(x), 3 times taller
 y=(1/3)f(x), 3 times shorter
 y=f(x+3), left by 3
 y=f(x3), right by 3
 y=f(3x), 3 times faster or 3 times narrower
 y=f(x/3), 3 times slower or 3 times wider
 y=f(x), reflect left/right, in yaxis
 y=f(x), reflect up/down, in xaxis
Multiple Actions
 y=f(x), reflect in origin, or {reflect in xaxis, reflect in yaxis}
 y=3f(x), {3 times taller, reflect in xaxis}
 y=f(3x), {3 times narrower, reflect in yaxis}
 y=f(2x+3), left by 3, then 2 times narrower
 y=f(2x+3), 2 times narrower then left by 3/2
 y=f(2x+3), {reflect in yaxis, shrink horizontally by half}, move right by 3/2
 y=f(2x+3), move left by 3, {reflect in yaxis, shrink horizontally by half}
 y=2f(x)+3, up by 3/2, then 2 times taller
 y=2f(x)+3, 2 times taller then up by 3
 y=2f(x)+3, down by 3/2, then {2 times taller, reflect in xaxis}
 y=2f(x)+3, {2 times taller, reflect in xaxis}, then up by 3

Transformation of an Exponential function, graphing f(x)= a*2^b(xh) +k

Graph of transformed sine function Notation: y=cf(ax+b)+d, x in radians (Desmos)

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:

Polar coordinate graphing, r=f(theta) (Desmos)
Partial Differential Equations, MATH 4302/5325
Last Update: Spring 2023
Location and Time: Lucas L209, TR 2:003:20
Exams:
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 Integrationbyparts 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, 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 kth 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

Resources:

Campuswide 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.

Learning Matlab:

MatTV, Charles F. Van Loan and K.Y. Daisy Fan, Cornell University

MathWorks Tutorials

MathWorks MatLab Academy Tutorials

Introduction to MatLab, Yossi Farjoun, MIT/OCW.

MatLab Publish Tab, How to use MatLab to prepare a report or homework

First MatLab homework:
A basic Euler solver for y'=f(x,y), To run it:
Open Matlab, open the Editor Window.
Copypaste 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.

Solving a basic PDE/heat equation using MatLab:
A basic solver for u_t=u_xx,

Learning Mathematica:

Mathematica for Applied DEs , V. Dobrushkin

Review of Prerequisite Topics:

Partial Derivatives, Khan Academy

Multiple Integration by Parts, a short cut similar to the ladder tableau method.

Partial Derivatives Demo, GeoGebra, S. Phelps.

Partial Derivative as Slope, GeoGebra, A.S. Alberca.

Derectional Derivative, GeoGebra, A.S. Alberca.

Specific Heat Capaity, Wikipedia.

Thermal Conductivity, Wikipedia.

Thermal Diffusivity, Wikipedia.

Graphing/calculators:

Desmos,
User Guide,
Help,
YouTube Channel,
Blog

Function Calculator by Xiao Gang

Wolfram Alpha

InstaCalc

MathStudio

CalcPlot3D, Paul Seeburger

GeoGebra 3D

GraphyCalc 3D

3D plotting on WolframAlpha accepts expressions such as "sum (sin(n pi x/4) sinh(n pi y/10)) n=1:3"

Interactive Apps:

Direction Field Plotter, John Polking, Rice University.
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 Unixtype 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.

Direction Field Plotter for single and system of 2 equations, Darryl Nester, Bluffton University. This is webbased and does not require installation.

Direction Field Plotter for 2nd order and a system of 2 1st order equations, Stefan Waner. This is webbased and does not require installation.

Integrator.

Fourier Series Numerical and graphical analysis.

A simple pendulum.

Solution of wave equation with a hat function as the starting value, on infinite domain.

Making waves with different boundary conditions, PhET. Neumann and Dirichlet Boundary conditions.

Heat Equation Solver for handdrawn input. Luis Silvestre. University of Chicago.

Demos:

Forced Oscillation 1 demo of resonance and beat.

Forced Oscillation 2.

Forced Oscillation 3 requires Wolfram CDF player .

Beat requires Wolfram CDF player .

Fourier Series, describing Fourier Series similar to old model of planetary motion, Dr. Doga Kurkcuoglu, Georgia Tech .

Mathematica code and resulting movies for solving PDEs Peter J. Olver, U Minnesota.

Waves, Dan Russell, Penn State U. Collection of Acoustics and Vibration Animations.

Types of Waves, Dan Russell, PSU. Longitudinal (spring, air, earthquake primary), Transverse (wire, earthquake secondary), water, Rayleigh (solid surface).

Physical demo of a plucked string, Dan Russell.

Standing waves in air, Walter Fendt. Neumann and Dirichlet Boundary conditions.

Standing wave, Geogebra.

Demo of solution of Wave Equation for a plucked string, MIT.

Coupled oscillators: two masses and three springs or
two pendulums connected by a spring,

System Simulations, EriK Newmann

Simulation of 2D puretone waves on the surface of a circular drum.

Simulation of a 2D Wave on the surface of a circular drum.

2D waves on a rectangular membrance with damping.

Next Steps:
If you want to pursue the topic at a more advanced level there are many courses, texts and software available; in particular

Courses:

MIT 18.152, Jared Speck, Introductions to Partial Differential Equations class notes.

MIT 18.152, Tobias Colding, Introductions to Partial Differential Equations class notes.

MIT 18.303, Matthew Hancock, Linear Partial Differential Equations class notes.

MIT 18.303, Steven G. Johnson, Linear Partial Differential Equations; Analysis and Numerics class notes + Introduction to
Julia Language.

Partial Diffferential Equations Videos by Chris Tisdell, University of New South Wales, Australia.

Maesumi, Introductions to Partial Differential Equations Old lecture site.

Texts and notes:

Physical Modeling in Matlab By Allen B. Downey

1D Heat Equation Matthew J. Hancock, MIT.

A First Course in QuasiLinear Partial Differential EQuations for Physical Sciences and Engineering Marcel B Finan, Arkansas Tech.

Publisher's companion web site for Boyce DiPrima's text,
8th ed,
9th ed,
9th ed, +BVP,
10th ed, +BVP,
11th ed,

PDEs via standard software packages:

Mathematica Wolfram

Mathematica Wolfram DSolve

Mathematica or Maple N. Abbasi

Mathematica D. Garanin

Maple Waterloo Maple

Matlab MathWorks

ScholarPedia matlabbased basic solvers

PDEs via advanced software packages:

OPM, Open Porous Media, simulation of porous media processes and flows.

MFEM, Finite Element Methods.

FEAtool Finite Element Analysis and MultiPhysics

FEAtool MultiPhysics
Python FEM and MultiPhysics Simulations with FeniCS and FEATool

redbKIT, a matlab toolbox for finite element simulation.

Deal.ii, a C++ FEM library

Dune, a C++ Distributed and Unified Numerics Environment for PDEs

KWave, a Matlab tool box for simulation of acoustic wave fields

Trilinos, a multiphysics project

HiFlow, A C++ Finite Element Method package

hpFEM, A C++ FEM solver

Alberta, An adaptive finite element toolbox

Overture, OO ttolkit for PDEs in complex geometries

SINTEF/MRST, Matlabbased, Flow in porous media, secondary recovery

GAMS Fortranbased PDEs

OpenFoam Computational Fluid Dynamics

Related Advanced software:

BVPSuite Implicit singular boundary value ODE problems, Matlabbased.

NEPPack Nonlinear eignevalue problems, Julia package.

FEAST Eigenvalue solver.

preCICE Multiphysics software.

Information:

Syllabus

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.

Approximate Test Dates: Thursday February 13, March 12, April 16, Final May 7.

Differential Equations Project accounts for 20% of grade for graduates and 1020% for undergraduates.

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

Resources:

MathWorks Tutorials

MathWorks Matlab Academy Tutorials

Introduction to MATLAB Yossi Farjoun, MIT/OCW.

Physical Modeling in Matlab By Allen B. Downey

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 GeneralPurpose 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 CDFplayer. 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
Campuswide licenses for Lamar students:
(requires download, installation and yearly verification, has a webbased version)

Matlab
Free software:

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

Scilab, A numerical computation software, similar to Matlab

Octave, A numerical computation software, similar to Matlab

Sage, A comprehensive numerical computation software,
to get Windows 64 bit Installer visit here

Julia, A numerical computation software

Maxima, A computer algebra system, Calculus on Maxima, a maximabased calculus textbook

GeoGebra, A geometry software

Cinderella, A visual math and physics software

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 feebased and free courses
Games
Chess,
WIMS20,
The Game of Set,
The Ultimate Tic Tac Toe,
Entanglement,
Nim,
Peg,
Reversi,
25,
Sudoku,
Towers of Hanoi,
Scratchbased 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

Piecewisedefined and Step functions
Example: In Desmos type y(x)= { 2< x< 0 : x+2, 0< x < 2 : 2x}
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(tc)
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(t3)*g(t3)+u(t5)*h(t5)
Here is an extended example: modeling the solution of a wave equation

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.

Graph y=f(x) and then y=g(x) on the same screen. Find the point of intersection and record it.

Graph y=f(x/100) and g=(x/100) (simply replace x by x/100 on existing screen).

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.

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

y= sum

A capital sigma shows up with a lower and an upper limit.

In the lower limit you enter the starting value of n, probably 1.

In the upper limit you can enter N, to indicate that you want to add up N terms.

Then you enter your formula , in terms of x and n, e.g. sin (n pi x) / n^2

A slider shows up labeled as N. You can move it over the indicated range.

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.

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

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 ebook and instructional videos. Access
codes are for a limited time use by one person during one
semester (unless the course is designated as a multisemester 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 twoweek 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.
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.
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.
WebAssign Hints and Errors
Do a browser check first before attempting your assignment.
On university computers Microsoft Edge may have more uptodate 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 (doubleu 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 popup windows from WebAssign.net.
* Accept thirdparty 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
Spring 2024:
Full semester: January 11 May 9
Math 3301 Ordinary Differential Equations.
Math 2414 Calculus II.
Math 2312 Precalculus.
Office Hours:
By prior appointment.
On campus Lucas Building L209/L206 MW 3:154;15.
Online TRF 83.
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.
Typically there are no office hours available during the finals or on the days when any class has an exam.
Rules for online office hours:
Use "Ask Your Instructor" button on WebAssign, or "Message Center" on Aleks, send homework problem number or PDF image of work or use a phone/camera to show your notebook.
Rules for oncampus office hours: Prepapre your questions in advance, bring your laptop and notebook. No food, drinks, or phone in office.
Mathematics Tutoring
The Math Shop Lucas 211.
Stars Student Tutoring and Retention Services.
Lab L209
Lucas Engineering Mathematics Computer Lab L209 is usually open to all students when there is no class there
(During nonpandemic times) 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 oncampus or synchronous courses
Courses Offered, Schedule, Finals
University Directory
University Course Catalog
Degree Course Requirements
Dashboard, student demographics and performance
Campus Maps:
Map 3, 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 all Lamar tutoring services 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"
OneTime 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 miscommunication 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 mindset 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 mistyped, etc.
If you are not successful at changing/correcting the issue yourself, ask for help from IT, X2222, ServiceDesk@lamar.edu .
5 Check your profile page under Self Service Banner and make sure your data is uptodate.
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 resend 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 TI30XS or TI030X IIS or TI36X Pro,
Sharp ELW516BSL556 or ELW516XBSL,
Casio FX991EX or FX115ES ,
Cannon F792SGA.
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 regraded 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. 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
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.
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 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.
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
X7143.
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 board or attend an online meeting 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 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, 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 takehome 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.
See the penalty schedule for cost of infractions. 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 IDtype 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, custommade computers, etc, may not be compatible. Do a system check on the first day.
18 What is your backup 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:
We will use a "Gateway Test" to activate HonorLock and start screenshare.
You will see a link at the top of Blackboard/Content. Follow the link to
initiate your Gateway Test on Blackboard where you start Honorlock. There you get a password for your actual test. You may be directed to Private Chat to get your password.
You let Blackboard test stay open (do NOT close or submit anything).
Then you go to your actual test website (WebAssign or Aleks),
and, once there, open the math test using the password you just picked.
Once you are finished with your test you submit WebAssign or Aleks,
then you head back to Blackboard and submit the Gateway Test in order to terminate HonorLock.
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 the math questions.
Aleks/WebAssign will usually allow only one or two attempts per question on exams.
Also, Blackboard might give a generouslooking 10 hours for the test!
That again is for the mechanics of setting your exam and HonorLock in case you run into IT problems and need to reach out to Support.
The actual test on Aleks/WebAssign is typically 12 hours.
3 Make sure your room is bright and welllit 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.
5On 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, secondary computers or monitors is allowed.
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, HonorLock. In addition Smart phone, wifi,
Otherwise students should drop the course.
High Speed (Broadband) Internet access is required
(minimum 5 Mbps upload speed, 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.
Read Troubleshooting guide on Blackboard.
My Blackboard course videos won't play. What should I do?
Contact Blackboard Support:
blackboard@lamar.edu
4098802222
Toll Free: 18665851738
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 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 oncampus 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.
Email it to me, and depending on the software used for the course you will be instructed on how to upload it.
For WebAssign courses upload under the Documentation assignment.
For Aleks courses upload to Blackboard under Documentation assignment.
At the 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.
Or 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 universitywide 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/GIscholarship/ 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.
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 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 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.