﻿ MAT 661, Professor Swift

# MAT 661, Applied Mathematics

## Prof. Swift, Fall 2018

Syllabus for our class. Master syllabus for MAT 661. Here are the math department policies and the university policies that are technically part of the syllabus.

My office hours are M 4-5, Tu 10:30-11:30, W 4-5, Th 10-11, 2-3. You can always send me e-mail, drop in, or make an appointment if these times aren't convenient. Here is my weekly schedule.

You can follow this link to sign up for Mathematica on your personal machine. The program is installed the lab computers in the math building. (How about Engineering?)
This is a great webcast introducing you to Mathematica. I suggest you look at it even if you know about Mathematica.

Here are some graphical resources for differential equations:
Slope Field and Vector Field applet by Darryl Nester of Bluffton University.
Vector Field applet written by Ariel Barton of the University of Arkansas.

External chaos web sites.

### Figures and Help in reverse Chronological Order

Dec. 7: Mathematica notebook to illustrate the Poisson Kernel.

Nov. 30: Picture of the white board after Wednesday's lecture, as a pdf and as a jpg. The sketch of the eta = constant lines was corrected after class. This Mathematica notebook can plot various solutions to problem 6.2(c).

Nov. 28: Office hour moved to 12:30-1:30 today

Nov. 19: Exam 2

Nov. 9: Notebook to check 1st integral in problem III 2.1(a).

Nov. 2: Slick version of the notebook, IVPconservationLawsNew.nb

Oct. 31: Examples of existence, non-existence, and non-uniqueness of solutions.
Mathematica notebook IVPconservationLaws.nb

Oct. 24: Initial Value Problem for Burgers' Equation: BurgersEquationIVP.nb.

Oct. 19: Plotting general integrals of Quasi-linear PDEs: general-integral.nb.

Oct. 8: Here are Comments on problem 1.9 in Chapter 2.

Oct. 5: Here is a corrected proof of theorem 4.2, as well as some help on the homwork due Monday. Here is a Mathematica notebook Cat's Eyes.

Oct. 3: Mathematica file for the Integral Surface Through a Curve. Here is the statement of Theoerem 4.2 from the white board, and here is the botched proof I gave in class. A correct proof will appear here soon!

Sept. 26: Here is a figure of Two First Integrals from the white board.

Sept. 21: Here is a mathematicat notebook for showing intersection of level surfaces of two first integrals: surfacesManipulate.nb.

Sept. 17: My office hour today is shifted one hour earlier. It will be 3:00-4:00 today.
Here is a link to the Reynolds number in fluid mechanics, and link directly to the section on the derivation of the Reynolds number via non-dimensionalizing the Navier-Stokes equations.
Here is a page about the Millenium problem associated with the Navier-Stokes equations.

Sept. 12: Mathematica notebook ElectromagneticWave.nb and the animated gif it produced, linearlyPolarizedLight.gif.

Sept. 7: Mathematica notebook for plotting surfaces and curves.

Sept. 5: Mathematica notebook with Homework 1 help. Wikipedia page on the Implicit Function Theorem.

Aug. 29: Web pages on Maxwell's Equations, and the Nonlinear Schroedinger Equation.