Apps and Demos:
Exponential Functions:

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

A Exponential Function Story
(Wikipedia,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

Simple Harmonic Motion (SHM) demo by D. M. Harrison. Requires SWF Player.
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 2020
Location and Time: Lucas L209, TR 3:505:10
Exams: Thursdays February 13, March 12, April 23, Cumulative Final May 12, 57:30
If possible, I will put class lecture notes here while the classes are shifted online due to chronovirus.
These are easier to view on Edge.
Solution for exam 1 Spring 2020
Wave 1
Wave 2
Heat Eq, Dirichlet/Neumann
Derivation of Wave Equation for a spring
Derivation of Wave Equation
Laplace/Potential Equation
Polar form of Laplace/Potential Equation 1
Polar Laplace 2
PDE Review
Essential skills needed for PDE
1 Most introductory problems in Fourier Series depend on the following integrals, it is best to make a table for these
integral of x^n cos (a x), and x^n sin (a x), for n=0,1,2,3,4.
View the following video and read the write up to refresh your calculus integration skills:
Multiple Integration by Parts, YouTube, example of Tableau method
Multiple Integration by Parts, Maesumi, an inline version of the ladder/tableau method.
2 Graphing hints
For graphing we have several choices, make an account in each to be able to send URL of your solutions
a for 2d graphs:
Desmos, practice adjusting graph and slider range to improve presentation
b for 3d cases:
b1 WolframAlpha, good for sums in rectangular domain x,y, but no sliders, no joystick, example type
plot ( sum ( sin(k*x) * sin(k*y))/k^2 ,k,1,5 ), y=0..2 , x=0..2
b2 GeoGebra 3D, has sliders and joystick, but to avoid equation editor issues type somewhere else and use CTRL V to paste, use ALT p to get pi, ALT t for theta, && for ^ , this sympbol stands for "and", example type
If(0 < x < 1 & & 0 < y < 1 , Sum(Sequence( sin(n*x) * sin(n*y)/n^2 , n,1,N) ))
N is the main slider
b3 CalcPlot 3D,
in the box in front of z= type the 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

GeoGebra Graphing Calculator

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, 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.

Information

Approximate Test Dates :
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.
GeneralPurpose and Specialized Online Calculators and Applets
Desmos,
User Guide,
Help,
YouTube Channel,
Blog
GeoGebra Graphing Calculator
Function Calculator by Xiao Gang
Wolfram Alpha
InstaCalc
MathStudio
Note: many calculators do not do roots of negatives, eg (8)^(1/3), if so then use (8^(1/3))
3D plotting:
CalcPlot3D, Paul Seeburger
GeoGebra
GraphyCalc
Type the formula in Google search
Online Direction Field Plotter (download DField for offline work)
D.K. Nester, Bluffon University
For using
Wolfram/Mathematicabased applets you need to download the following:
Mathematica Computable Document Format (CDF) Player.
For example, try the following demo
Newton Law of Cooling.
Download the CDF file and run it with the 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.
BrainBox Circuit Simulator.
Computer Algebra/Numerical/Graphical/Display Software
Campuswide licenses for Lamar students:
(these require download, installation and yearly verification, some have webbased version)

Matlab

Mathematica
Free software:

DField, PPlot, 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

Mathematics 4.0, An advanced graphing calculator, Microsoft

Runiter, A 3D Graphing Calculator
The following (as well as 32 bit Sage) may require the instalation of a Virtual Machine:
SAS Statistics Analysis System
Packages with discounts for students:
MATLAB A numerical computation software,
Student Version
Maple A comprehensive mathematics software,
Student version
Wolfram Mathematica A comprehensive computer algebra system,
Student version
Viewers:
Wolfram Player Replaces, CDF / Computable Document Format Viewer Wolfram Mathematica
Maple Viewer Waterloo Maple
Flash Player Adobe (open Task Manager and search and close ALL instances of your browser to install. Heads up: Some "Offers" are included in download)
ShockWave Player Adobe
Lists:
Comparison of Computer Algebra Systems, Wikipedia.
Report of work in progress on SouthForge.
Comparison of Interactive Geometry Systems, Wikipedia.
OnLine Course Repositories
edX,
Stanford,
Harvard,
MIT,
Yale,
Coursera,
Academic Earth,
Khan Academy.
Udacity feebased and free courses
Games
Chess,
WIMS20,
Pegs,
The Game of Set,
The Ultimate Tic Tac Toe,
Entanglement,
Nim 1,
Towers of Hanoi,
Scratchbased games,
Use IE or update Flash first for these:Catlan, Nim 2,
Visual Programming:
Google Doodle,
Google Blockly,
MIT Scratch,
Alice,
Apple Swift Playgrounds,
Twinery,
Human speed tests:
memory and reaction speed tests
Games in politics:
The Redestricting Game
Competitions
Putnam Competition
Internet Olympiad
International Collegiate Programming Contest
AMC  American Mathematics Competitions
Wikipedia List of Math Competitions
Wikipedia List of Programming Competitions
TeX
Students who are in senior level classes or above are expected to type their homework and papers.
WORD or Matlab Publisher are two common choices.
Students who are in MS program or contemplating entering one, and more so those who wish to get a PhD, should learn TeX.
Expect to spend as much time as a course for learning TeX. So you want to start early and gradually improve your skill.
Here are some resources among many:
TeX Tutorial
TeX commands
MiKTeX Distribution
Desmos,
User Guide,
Help,
YouTube Channel,
Blog
Usage Hints for Desmos

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.
Cengage, the publisher of WebAssign, has a
Cengage Unlimited Subscription Plan (CUSP).
In short you pay $120 per semester, or $180 per year, or $240 per two years, and you get Cengage digital textbook library, digital online homework system (WebAssign, MindTap, ...), printed text rental at $8/semester.
To see if it makes sense for you to use a subscription
check here.
Only books published by Cengage are included in the rental agreement. However WebAssign usually includes the ebook.
Starting with 2019 we will adopt Larson, Calculus Early Transcendental, 7th edition, which will be in CUSP and in the rental plan. Also Poole's Introduction to Linear Algebra is a Cengage book and in the rental plan.
Running Adobe Flash Player.
WebAssign needs to run Flash. To activate it see How to activate Flash
WebAssign Hints and Errors
Do a browser check first before attempting your assignment.
On university computers Internet Explorer has more uptodate components than Chrome.
WebAssign errors are rare but occasionally they do occur. If you see one let me know.
More often than not it is the student who has not paid attention to syntax issues or has a typo.
Note that webassign like most computer programs is case sensitive, so B and b are different.
Not only that, font matters too so B is also differnt from B and b. And if that was not enough, you also have β (Greek beta).
It is good to be familiar with Greek Letters.
Also read How to enter exponents, subscripts, roots, functions, etc
And how to use CalcPad to enter formulas
Please pay attention to the following and most of your problems will go away!
Do not mix up:
Exact vs decimal answers, (if it does not tell you to give the answer to say 2 or 3 or 4 decimal places then it wants the exact answer, e.g. cos^{1} (2/
√ 13
) vs 56.3099 degrees )
angles in radians vs angles in degrees (degree angles have a little circle as superscript)
Ordinary font e.g. F for scalars vs bold fonts e.g. F for vectors
Here are some characters you might have difficulty with:
a, A, A, α (alpha)
b, B, B, β (beta)
d, D, D, δ, Δ (delta)
t, T, T, τ (tau)
w, ω (doubleu and omega)
1,l (one and ell)
0,o (zero and oh)
,' comma vs prime (especially after a fraction a comma is common, not to be confused with derivative of denominator)
*,(blank) (missing a multiplication sign or using a blank space in its place in a formula, xy is not understood as x*y)
[],(),{},<> (different fences or delimiters, each book may have a different style)
[] , [[]] (do not double bracket or put a bracket in a bracket)
Keep a record of typical errors in your notebook to remind yourself.
For more info read WebAssign Syntax Hints
To have WebAssign work properly, configure the following settings in your Web browser:
* Allow cookies and popup windows from webassign.net.
* Accept thirdparty cookies when accessing WebAssign from BlackBoard.
* Do not allow your browser to store your password.
* Enable Adobe Flash Player.
SYSTEM REQUIREMENTS: WebAssign is tested and supported for the following web browsers:
* Mozilla Firefox (38+) Windows, macOS, Linux
* Internet Explorer / Microsoft Edge (11+) Windows
* Google Chrome (44+) Windows, macOS Apple
* Safari (8+) macOS, iOS 8 or later on iPad
If you need help with WebAssign view the following or search on YouTube
WebAssign Registration
Completing Assignments
Entering Math Answers on WebAssign
Office Hours, Schedules for Exams, Tutoring, Computer Lab 209, and Maps
Summer II, 2020, July 7  August 10.
Office Hours:
Online by prior appointment
Students who are preparing for exams are encouraged to ask their questions in the classes prior to the exam day. Postponing questions to day of exam is discouraged.
Office hours on exam and final days are by appointment only, and they are usually restricted and could be cancelled.
Rules for office hours: No food, drinks, or texting in office. Bring your homework/lecture notebook and laptop.
Teaching and Exam Schedule:
Ordinary Diffential Equations, Math 330107 online
Tentative Test Days: Mondays, July 13,20,27,August 3,
Cumulative Final Monday August 10, 6:009:00 pm.
(STEM) Precalculus II, MATH 231207 online
Tentative test days: (See Aleks), July 20, August 1, August 10
On Campus Mathematics Tutoring
The Math Shop, Lucas Engineering Building, Room L211
Online Tutoring
Lamar has partnered with SmarThinking
to offer tutoring for online/distance education courses.
To login, user name is your Lamar email address.
Password example: Assuming your name, birth date and SSN are
John Doe, January 25, 1981, Social Security Number 1234567890
then password is 810125&DJ7890
i.e. YYMMDD & Last Initial First Initial Last 4 SSN
More info
Lab L209
Lucas Engineering Mathematics Computer Lab L209 is usually open to all students when there is no class there
The Lab is useful in the following cases:
you want to see me concerning a homework that is on computer and you don't have your laptop, or
you want to see me as a group, or
you want to get together as a study group and you want to be able to reach me or the Math Shop
Calendars, Courses, Personnel:
Academic Calendar
Final Exam Schedule Spring 2020
Courses Offered, Important Dates
University Directory
University Course Catalog
Campus Maps:
Map 1, interactive/html
Map 2, building and parking map, PDF
Map 3, PDF
Map 4, Google
Help with homework and lectures
 Read your text. Preferrably read it before the lecture, and try some of the simpler problems. Then read it after the lecture.
 Look up similar problems in the text.
 If you are using an online homework system, such as WebAssign, check to see if it gives a chance to see a solution to a similar problem.
 WebAssign may have a video for you to watch.
 Most texts have a companion site, for example Larson Calculus has CalcChat.com which presents solutions to most odd numbered problems of the text.
 Lectures from prior years may be available here, for example Calculus I.
 Mathematics department runs free tutoring in Lucas L211, suitable for introductory classes. Check Tutoing Schedule.
 Study in a group. Lucas L211 can be a good place to start a study group.
 DO ask your questions in class. Don't wait for the day before the test to ask.
 Submit questions via WebAssign.
 Come to Office.
Handbooks
NIST Digital Library of Mathematical Functions National Institute of Standards and Technology
Handbook of Mathemtical Functions Abramowitz and Stegun
Javabased applets error messages
Many Internetbased mathematical demos used to use Java. However due to security concerns you have to take certain extra steps to be able to use them.
The accepted practice is to move away from such software.
However if you attempt to use them it is very likely that you get one of the following error messages if and when you try to access Javabased apps:
A) Java applications are blocked by your security settings.
B) Missing ApplicationName manifest attribute.
C) Missing required Permissions manifest attribute in main jar.
You need to upgrade JAVA frequently, and remove your older versions,
then close and open your browser,
then include the trusted math site in your
Java seucity exemptions file,
then give permission to your browser to run the app.
Read the instructions in the following pages for additional information (and use at your own risk)
Java Security Warning and Solutions.
Here is more info.
The Cost of Math/Engineering Errors
(Or what can happen to you if your teacher gives partial credit to the person sitting next to you!
Or if we hesitate to withhold credit from a "master".)
A nutjob
Pounds vs kilograms
Another pounds vs kilograms story
1/2 or 2/1? That is the question!
How many decimal places you said!?
What not to learn from a "master"
OneTime Excusable Errors:
How not to make waves
Why not to square the circle
Policies
Student Email Address
Check your profile page under Self Service Banner and make sure your data is 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 system does not send any email to you!
A test email will be sent to all students at the beginning of semester.
The email addresses will be taken from "Email List" for each class as provided by
Lamar University SelfService Banner website.
If you do get it there is nothing to do (no need to confirm by sending a reply).
If you do not get the email you need to check if
0) you did not specify your preferred email address correctly during registration (most common mistake)
1) you typed your email incorrectly during registration
2) you entered a parent's email for yourself during registration
3) you changed your email
4) you requested your email not to show on a web page during registration
5) your guardian typed your email incorrectly
6) etc.
You need to make a corrective action so that your correct
email shows on Lamar's "Email List" for each class.
You must have an email address that you check nightly.
You should turn on ALL notifications from any homework software (WebAssign/Aleks/etc) we use. You should not opt out of notifications.
You should also register with your email on WebAssign (if required) and accept to be notified when and if there is new homework.
If you are concerened with privacy issues you can use lamar.edu for school related topics and keep your private email account separate from your lamar email account.
Instructor will not
take any extra actions to reach you after the 12th class day.
"I did not know/I do not get your emails / I do not get WebAssign emails, etc" will not be an acceptable excuse if majority of class knew! Attend classes and check email and webassign daily.
Instructor's Email
1) To contact me use
emails: "maesumi at lamar dor edu".
2) Include your full name, course name and section number on EACH email.
3) Please do not use REPLY when your email topic is not related to the previous email.
4) If you do not get a reply to your email after 12 hours 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).
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 and acknowledged in an email from me to you.
At the time of the final test, and before final grades are given, send a summary email.
Late Homework
Late homework, if accepted, has a penalty that starts at %20 and increases with the length of delay.
Homework from beginning of semester loses much of its value by the end of semester.
Here is how the late penalty will accrue: [17+3*(xy)] percent, here x is the current homework number and y is the homework number you want to do late.
So if we are doing homework 16 and you want to redo homework 2 the late penalty is 17+3*(162)=59%.
You may be asked to come to my office and show your handwritten solutions of such late homeworks and explain them.
During the pandemic you may be asked to attend a Zoomtype meeting.
All homework is to be done BEFORE the final. Deadline Extensions, do not have any validity past the day of final.
Students are reminded that waiting for end of semester to see what minimum work is needed to get a particular passing grade is not an acceptable conduct.
Privacy
Please read the Lamar login prompt before you log to university network. It states that you should not expect any privacy.
All activity on a computer during class or exam time can be inspected and analyzed by the instructor.
If you use a homework software all activity on it is visible to the instructor and certain employees of the company.
There may be a seating assignment in class.
Your notebooks, papers, calculators, phones and anything visible to instructor may be inspected by the instructor during tests.
Put all private items in your backpack and keep it closed during tests.
You may be asked to change your seat during a test.
You may be asked to attend a Zoomtype meeting, or take your exam on Zoom.
If you violate the Test Code or class decorum rules you may get a public reminder in class.
Course Evaluations
The university will send you a notification toward the end of semester to evaluate your courses.
Your input counts, it helps to improve future classes.
Your answers will be private. I do not know who evalauted the course. I get a summary after grades are submitted.
Certain number of points will be added to your last test as a bonus for completing the survey.
If participation rate is over 90% then bonus points will increase substantially.
So encourage your classmates to participate!
Evaluation period depends on the type of course you take. It is best to do the evaluation as soon as it is available.
Go to LUConnect, then Go to Course Evals and complete the survey.
Once done with all evaluations please get a screen shot of the entire evaluation window acknowledgement page,
showing all courses and your name.
Also print the acknowledgement page
to prove that you completed the task.
The acknowledgement page may take many forms, for example
this .
This is a page that lists all of your current courses and says you finished evaluating them.
Write your name clearly on the paper you just printed.
Write your course name/section on it.
Students using WebAssign: Upload the screen shot to WebAssign under the assignment "Evaluation".
Aleks Student: email the acknowledgement page.
If you are taking multiple classes from me do the survey and upload one sheet per each class.
Please: Do not print/submit your private answers! only the acknowledgement page!
If you have technical problems with doing the survey contact Mr. Rossi at
X7143.
Honor Code
The Golden Rule : You should be able to repoduce, all by yourself, and without any additional help, whatever you write on an assignment or exam or project.
That means I am within my rights to ask you to go to board or attend a Zoomtype meeting and redo whatever you wrote.
I am also within my rights to ask you to take a test again if the result of above meeting is unsatisfactory.
To avoid misunderstanding during an exam pay attention to the following common sense rules:
Do not look sideways, you are to look at your own papers or screen and protect them from others.
Follow the guidelines for a Proctoriobased test.
Your face should be visible to the instructor.
No obstruction of face by sunglasses, hair, hand, caps, etc.
No obstruction of ears by musical devices, ear muffs, hoodies.
Bring an official picture ID (Lamar or DL) to all tests.
Use of printed sheets, cell phones, advanced calculators, shared calculators or loose paper is forbidden on tests.
Use of unauthorized websites and communication with others is not acceptable during tests and may result in a grade of F for the course.
All authorized sites will be listed on the exam, any other is unauthorized. Use of homework pages of WebAssign is NOT authorized.
Do not give your WebAssign passwords to any other person for any reason.
Unauthorized logins to WebAssign may result in a grade of F for the course for you.
Fair Use Policy: (or how to get help and not be in trouble with plagiarism rules):
Students are encouraged to try do the homework problems and projects without seeking help.
But it is OK to consult other students and resources to learn how to solve homework problems or 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 solution of the problem all by yourself without listening to or looking at any other source. Your new writing must be from scratch and from the beginning.
(d) If you get stuck again go back to step (a).
At the end you should be able to reproduce and justify the steps of the solution you submit. For example by coming to the board and explaining it.
See the penalty schedule for cost of infractions. University Academic Honesty rules apply.
Student Profile
Students are to required to prepare a profile/resume specific to their course.
You will upload it to a WebAssign homework assignment labeled "Resume or Profile", there you will see a simple problem.
you are to upload the resume under "Show My Work".
If you attend two of my classes upload one for each.
Copy this questionnaire to a Word file, answer each question, make a blank line between successive questions.
If an item is not applicable to you just write "not applicable" and explain. convert the final copy PDF and upload it to WebAssign
I Identity Information
You are being asked to identify yourself because you are accessing our network and getting credit for work performed.
All of this information is collected during tests. Here you are confirming that information.
If any of these change during the course (such as changing address, computer, ISP, etc)
then you need to make an updated resume and submit that before any test.
1 First name
2 Last name
3 Lamar University L number
4 Lamar email
5 Secondary email (optional)
6 Public IP address ((IPv4) of your computers (go to What Is My IP Address to see your address)
7 Your postal/physical address (choose the address where your computers is located)
8 A clear copy of Lamar ID (If there is a credit card number on it you MUST cover it up)
9 A clear copy of another official Picture ID, for example a Driver License.
(You just need to show your name and your picture, you should cover up all the other items.)
10 A large clear IDtype picture (about 4 by 6 inches) showing your face but without hat or sunglasses.
Like what you would take for an ID at DMV.
II Education Information (optional)
11 Declared fields of study, (major/minor)
12 Details of the last three math classes you have taken (where, when, how well did you do, was it online?)
13 Why are you taking this course?
14 How many hours of study are you planning to spend on this course each week?
15 What math classes, if any, will you take after this class?
16 What other classes are you taking at this time?
III Other Info
17 Do you have a solid computer, good online connectivity, a webcam, a microphone, and an uncluttered study area?
An independent quality webcam with base/tripod is preferred.
Here is an example of a good setup.
Tablets, phones, 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 are disabled?
19 During tests you will be asked to use the webcam to show your ID, your face, your table,
and your surroundings to ensure that standards of Proctorio test are met.
This will require some practice.
We apologize in advance for the intrusion and the inconvenience, but there is no other way of taking a secure test.
Proctorio will record all events. If the proctoring standards are not met student
will be asked to take another test.
Do you agree with this requirement?
In your resume you do need to type the following "I do agree with the requirements of proctored tests.
If the standards are not met, my instructor, at his sole discretion, may ask me to take another test."
IV Voluntary Information
20 As a part of your resume you may include optional items and information to let me know
you, your educational goals, your career goals, responsibilities, current employment, what you expect from this course,
and any details that you think might help what we intend to do in the course.
If you have not done well in math classes before, let me know what steps you are willing to take, from the first day,
to make sure you succeed this time.
Pay close attention to the fact that summer courses are more than three times as fast as the long semester courses.
There is really no time for a second engagement.
So you need to put your absolute best effort forward.
Online Readiness / Proctorio
1 Proctorio is a software that proctors your tests and quizzes.
It must be installed by the end of first day of class.
2 On Blackboard enable Secure Exam Proctor.
To do this go to BlackBoard, go to Course Resources/Tools.
Search for Secure Exam Proctor (an icon resembeling an oldstyle webcam), and make sure it is enabled.
3 Procedure: We will use a "container or gateway test" to employ Proctorio.
This means that you initiate your test on Blackboard where you get a password for your test.
You let Blackboard test stay open. Then you go to actual homework/test website (WebAssign or Aleks),
(directly using browser's address line and opening a new tab),
and, once there, open the test using the password you just picked.
Once you are finished with your test you submit it there,
then you head back to Blackboard and submit the container test there in order to terminate Proctorio.
Proctorio has some strict standards that you need to adhere to.
Otherwise you will be asked to take another test.
Or you might be asked to take a live test via a software such as Zoom.
We will practice using Proctorio on a quiz to make sure you are familiar with the steps.
Therefore make sure you do not skip quizzes.
Here are some videos that explains its use. These videos are from other universities,
so your experience can be somewhat different:
Proctorio Description 1 and
Proctorio Description 2.
Please note: There are separate instructions for the Blackboard container test and the Aleks test.
For example typically Blackboard says you have multiple or unlimited attempts but the your homework software might says you have limited attempts.
The first one just means if you are disconnected you can get back into the test,
while the second one says you can only submit one answer per question.
Problems with getting into Blackboard Gateway Test
If you attempt to get into Blackboard Gateway Test
and you see a page asking you for a password, similar to the photo below, then that indicates an error message
and you need to
1 Make sure you enabled Secure Exam Proctor on Blackboard as mentioned above.
2 If that does not solve the problem then follow the instructions mentioned here to remove cause of error.
3 If you still need help contact Proctorio Customer Support.
Basics of a proctored test using Proctorio
0 Install it long in advance of tests, to make sure it runs on your computer.
Waiting until the first test to discover that it does not work for you does not reflect well on you.
1 Your environment and your appearance has to be exactly as if you are in a classroom.
1 To repeat: Your environment and your appearance has to be exactly as if you are in a classroom.
2 Turn the light on! make sure your room is bright and welllit. Otherwise your face and your ID will not be visible.
3 Hold the ID so that your face appears in natural position.
(Don't turn it sideways even if Proctorio's box suggests it.) Look at how your ID appears in image, make sure it is not blurry.
4 When Proctorio says "room scan" the main thing to do is to scan your table.
Count from 1000 to 1020 and slowly turn your webcam over your table showing the items on your table.
For privacy you may use a sheet hung behind you. Or sit such that a wall is behind you.
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.
Other software, as mentioned at the top of WebAssign test, may be allowed as well.
6 No: phones, calculators, tablets, books, printed materials, secondary computers or monitors is allowed on your tableJ.
7 No: headsets, hats, sunglasses, smoking, vaping, eating, drinking, lying in a bed, music, noise, dark room.
8 No: copying, pasting, downloading, browsing, communicating with unauthorized persons.
9 No: surfing in unauthorized sites or ebooks or files. Software homework pages other than exam page are also off limit.
Computer Requirements
By taking this course you acknowledge that you have a computer with the following capabilities:
Internet, Webcam, Microphone, Chrome, Proctorio.
Otherwise students should not attempt these courses.
Students who take online courses will need a computer with the following capabilities
and the most recent version of applicable software:
High Speed (Broadband) Internet access
(minimum 25 Mbps, check at a facility similar to SpeedNet
Computer with at least 4 gigabytes of memory (8GB preferred)
Chrome browser (go to chrome://settings/help to update)
Webcam (independent webcam with base preferred)
Microphone (independent USB headset with wireless capability preferred)
Proctorio Extension must be installed on Chrome by the first day.
Must be operational by the second quiz.
My Blackboard course videos won't play. What should I do?
The first step is to make sure you are using the latest version of your browser. Try all.
Next make sure your Adobe Flash Player is up to date. You need to check the Task Manager to make sure no browser is open while you are installing. Decline “Offers” during download.
Next try clearing your browser cache. Instructions for doing so can be found by searching “Clear Chrome cache” or "Clear FireFox cache", etc.
Blackboard Contact:
blackboard@lamar.edu
4098802222
Toll Free: 18665851738
Votes, Time Extensions
Occasionally we may have votes in class.
In these cases we go by the vote of students who are present in class.
As a courtesy to all students, and at instructor's discretion, the vote might be conducted via an email. Students will have 24 hours to respond.
Failure to respond indicates the student will accept the vote already cast.
Time Extensions: On some tests you may be given a time extension.
The extensions will be given in increments of 5 minutes. So long as it does not conflict with the next class, and students in attendance do not object.
Absence
For excusable absence from an exam you need a written verifiable proof of emergency.
In case of early contact, and at instructor's discretion, a make up exam might be give.
Please note that for a make up exam several issues cannot be guaranteed: date, time, a quiet room, level of difficulty, etc.
At instructor's discretion, in case of a justifiable absence, an adjusted mix of your other exam grades may substitute the missing grade.
To reduce the negative impact of absence from classes please have a "buddy system" to provide you with missing notes, latest news, coverage report, etc.
Students with excessive unjustified absence may not use office hours for homework help.
Last date of attendance:
For a failing students the instructor has to report the last date of attendance. I will enter the last date at which the student had a passing grade.
Therefore it is important for students who are on probation, due to scholarship, loan, visa, GPA deficiency, etc, or who need to prove attendance for attendance,
to submit all homework and attend all classes.
Sporadic presence in tests or classes will not be considered a proof of attendance.
There is a 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 issues:
1 Students are strongly discouraged from late registration. Students are expected to be present on the first day of classes.
2 No "Late Add" is allowed.
3 It is the student's responsibility to become familiar with class rules even if they missed the first few classes for whatever reason.
4 If student registers late then he/she is responsible for catching up to the rest of class and he/she is to take the exams at the scheduled dates. All missed homework and exams of my course/section may be assigned a grade of zero.
5 If your registration is in limbo you are to continue attending classes as usual.
6 The "last attend date" is defined as the last date student had an overall passing score. This is of importance especially if you are on scholarship or probation or on visa.
To pass university audit at the beginning of semester you must attend classes, participate in quizzes, and have a passing homework score.
If you want your physical presence to be counted as attendance then sign a paper with your name and class name and give it to me in each class.
DRC issues:
1 Students who are considering to use DRC are to consult with me at the earliest possible time and have DRC send the notification at least one week in advance of any test.
2 It is the students responsibility to arrange for their test well in advance.
3 It is responsibility of the student to make sure, well in advance of any test, that the computer they will use has all the software we use in class.
4 DRC students take the same quiz as all other students. There are no separate arrangements for quizzes. If necessary their quiz grades will be adjusted.