## Lecture materials

I will post reading assignments here both before and after
class. Even before the first class, review background calculus
material in chapter 0 (Preliminaries) of Coddington.

### 1. (Sept 4th) Intro and first-order ODEs

Based on sections 1-3 of chapter 1 of Coddington. First
assignment posted also.

### 2. (Sept 6th) First and second-order ODEs

Finish all sections of chapter 1 and sections 1 and 2 of
chapter 2.

### 3. (Sept 11th) Constant-coefficient second-order ODEs

Chapter 2 of Coddington, sections 1, 2, first half of 3, 4,
and 6. The sections on higher-order equations will not be
covered. Second assignment posted.

### 4. (Sept 13th) Variable-coefficient second-order ODEs

Chapter 3 of Coddington, sections 1, first part of 2, 5, and
6, and generalization/review of results for
constant-coefficient equations. We will focus on second-order
equations unlike the book.

### 5. (Sept 18th) Euler's equation

Explan use of complex numbers at end of section 2.2. Solve
Euler's equation including use of complex numbers, section 4.2
in book. We will return to ch 4 and the rest of ch 3 later on.

### 6+7. (Sept 25th and 27th) Separable and exact nonlinear
ODEs

Chapter 5 of Coddington, sections 1, 2 and 3, and a little bit
on existence/uniqueness.

### 8. (Oct 2nd) Analytical series solutions

Chapter 3, section 7.

### 9. (Oct 4th) Existence and uniqueness

Proof of existence/uniqueness (not on midterm, more advanced).

### 10. (Oct 9th) Review

Review for midterm.

### 11. (Oct 11th) Midterm

Problems will be similar to homework problems, nothing tricky,
just a check that you are not falling behind.

### 12. (Oct 18th) Review of Linear Algebra

We will review briefly key concepts from Linear Algebra and
start discussing systems of linear first-order ODEs. Here are
some

lecture notes since
this is not covered well in either book. The corresponding
chapter in Miller & Michel is sections 3.1-3.3, but they
are at an advanced level. My notes are mostly based on "The
Qualitative Theory of ODEs: An Introduction" by Fred Brauer
and John A. Nohel.

Here is a summary

Review of Linear Systems.

The next few lectures will focus on phase-space analysis of
the qualitative behavior of the solutions to systems of ODEs.
I will rely mostly on lecture notes posted here, based in part
on the (optional) book by Fred Brauer and John A. Nohel. In
the book by Miller & Michel, the material is in Section
5.6.

I will rely mostly on lecture notes posted here, based in part
on the (optional) book by Fred Brauer and John A. Nohel. In
the book by Miller & Michel, the material is in Sections
5.1-5.5.

In the book by Miller & Michel, the material is in
Sections 6.1-6.2.

Based on Sections 5.1 and 5.2 (optional) book by Fred Brauer
and John A. Nohel.

### 20. (Nov 27th) Fun with ODEs: Fibonacci sequence

Guest lecture by Prof. Jonathan Goodman

Guest lecture by Prof. Jonathan Goodman. Here are the Matlab
codes (download them into one directory and then run 'matlab'
and execute command 'ssim', Ctrl+C to stop the animation):

fsim.m,

ssim.m
### 22. (Dec 4th) Solving ODEs using Maple

Here is a Maple script (execute 'xmaple

ODE_Maple.mw'). Here is a

PDF and an

html version.

### 23. (Dec 6th) Solving ODEs using Matlab

And here is a related Matlab script

ODE_Matlab.m
which solves the pendulum equation using Euler's method. And
here is the script

PredatorPrey.m
to solve the Lotka-Volterra equations from Travis Askham's
recitation.

### 24. (Dec 11th) Chaotic Dynamics (+review)

### 26. (Dec 18th) Final Exam (10am-12pm)

###