Syllabus for Math 2574H --- Spring 2001



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


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.


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

All exams will be open book, open notes, calculators allowed.

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.