Syllabus for Math 2574H --- Spring 2001

Description:

This is a one-semester introduction to differential equations and linear algebra. Unlike most books, I will try to give a fairly modern presentation.

Text:

The presentation will be somewhat unconventional so there is no really good textbook. The multivariable calculus text from last semester, Multivariable Mathematics, by Trotter and Williamson is a good reference for the more standard topics. Some other books will be put on reserve in the Math Library. The lectures will be your most reliable source; you should take notes in class.

Grades:

Homework / Quizzes	20 %
Midterm Exams (20 % each)	40 %
Final Exam	40 %

Exam Dates:

Midterm I	Tuesday, February 13
Midterm II	Tuesday, February 20
Final	Monday, May 7, 1:30-4:30

Approximate Schedule:

Week	Topics
1/17-1/19	ODEs and PDEs. Exponential ODE.
1/22-1/26	Complex Exponentials
1/29-2/2	Matrix Exponentials
2/5-2/9	Second-order linear ODEs. Oscillators
2/12-2/16	Midterm I. Forced oscillators and resonance.
2/19-2/23	Laplace transform. Delta functions. Boundary value problems
2/26-3/2	Linear algebra. Gauss method. Determinants.
3/5-3/9	Eigenvalues. Diagonalization.
3/12-3/16	Linear Maps. Abstract vector spaces.
3/19-3/23	Midterm II. Solving linear systems by eigenvalue method.
3/26-3/30	Spring Break.
4/2-4/6	Computing matrix exp. Linear flows. Variation of parameters.
4/9-4/13	Nonlinear ODEs. Existence and uniqueness.
4/16-4/20	Phase portraits. Equilibria and stability.
4/23-4/27	Periodic orbits. 2D Hamiltonian ODEs. Numerics.
4/30-5/4	Forced pendulum. Lorentz equation.