Math 23
Differential Equations
Last updated June 25, 2009 14:49:14 EDT

## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures Sections in Text Brief Description
3/28 1.1 - 1.3 Direction fields, introduction to initial-value problems, introduction to computing, HW1 assigned. Matlab: http://math.rice.edu/~dfield/, intro.m
3/30 2.1,2.2 First order linear ODEs, separation of variables
4/2 2.4-2.6 Existence and uniqueness, exact equations, HW1 due, HW2 assigned
4/3 (x-hour) intro.m Formal introduction to matlab
4/4 2.7 Introduction to numerical methods, Euler's method, euler.m
4/6 2.3, 2.5 Modeling, population models
4/9 3.1 Second order linear homogrenous ODEs, the characteristic equation, HW2 due, HW3 assigned
4/10 (x-hour) handout Introduction to linear algebra for 2x2 matrices: question and answer
4/11 3.3 Wronskian, linear independence
4/13 3.4 Complex roots
4/16 3.5,3.6 Repeated roots, method of undetermined coefficients, HW3 due, HW4 assigned
4/18 3.7 Variation of parameters
4/20 3.8 Mechanical, electrical vibrations,resonance
4/23 3.9 Driven oscillators, resonance, HW4 due, HW5 assigned
4/24 (x-hour) MIDTERM EXAM In class portion of midterm exam, take home due tomorrow
4/25 5.1,5.2 Power series, series solutions, radius of convergence
4/27 5.3,5.4 Series solutions about ordinary points, Euler equations
4/30 7.1,7.2 Systems of first order equations, existence and uniqueness, HW5 due, HW6 assigned
5/2 7.3 Further topics in linear algebra
5/4 7.3 Eigenvalues and Eigenvectors
5/7 7.4,7.5 Homogeneous systems, HW6 due, HW7 assigned
5/9 7.6 Unusual eigenvalues
5/11 7.8,9.1 Phase portraits
5/14 9.2,9.3 Almost linear systems (e.g. pendulum), HW7 due, HW8 assigned
5/16 10.1 Boundary value problems
5/18 10.2,10.3 Fourier series, convergence
5/21 10.4 Even and odd functions, representations, HW8 due, HW9 assigned
5/23 10.5 Separation of variables, the heat equation
5/25 10.6 Wave equation
5/28 NO CLASS Memorial Day
5/29 (x-hour) 10.8 Laplace's equation
5/30   Course wrap up

Scott D. Pauls
Last updated June 25, 2009 14:49:14 EDT