﻿ MAT 665, Professor Swift

# MAT 665, Ordinary Differential Equations

## Prof. Swift, Fall 2017

syllabus. Here are the math department policies and the university policies that are technically part of the syllabus.

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

Section 2.4. Notebook for Example 3.

Section 2.2. This pdf shows a function that is not a contraction, even though two points always get closer together.

Exam 1, on Chapter 1, will be Friday, Oct. 27 in class.

Section 1.8: Jordan Canonical Form algorithm. Here are some scanned Examples From Perko.

Section 1.8 in class exercises: example 4, example 5.
Here are checks of the calculation: one solution to example 4, and one solution to example 5.

Section 1.8: Notebook showing Jordan Canonical Form dynamics with a size 3 Joran block with real eigenvalue.
The general solution for a 4x4 matrix with repeated complex conjugate eigenvalues.

In class on 10/4, I forgot the "det A" in the formula for the inverse using the cofactor matrix. There is a link about halfway down this wiki page.

More on Section 1.6: Here's a notebook for checking the solutions and computing the eAt matrix.
Here is a photo and Mathematica notebook for a calculation with 1 real and 2 complex conjugate eigenvalues.

Section 1.6: Error on white board from 9/22, and here is the correction.
Here are animations or two logarithmic spirals, the nautilus and the Fibonnaci. Are they zooming in or rotating? Here's the Mathematica notebook used to make those animations.
Mathematica notebook for Complex Eigenvalues Phase Portrait.
General solution and phase portrait for an example where A has complex eigenvalues. (This uses books notation that eigenvector is w = u + i v, whereas I use v = vR + i vI.)

Section 1.3: Here is a proof of Corollary 4 that is different from the book.

Section 1.1: Here are some examples of three-dimensional phase portraits of uncoupled linear systems in R3. I notice that the homeqork on section 1.1 doesn't need this type of phase portraits. I'll need to write my own problem next time.