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.
All exams will be open book, open notes,
|Midterm Exams (20 % each)
| Midterm I
||Tuesday, February 13
| Midterm II
||Tuesday, February 20
||Monday, May 7, 1:30-4:30
||ODEs and PDEs. Exponential ODE.
||Second-order linear ODEs. Oscillators
||Midterm I. Forced oscillators and
||Laplace transform. Delta functions.
Boundary value problems
||Linear algebra. Gauss method. Determinants.
||Linear Maps. Abstract vector spaces.
||Midterm II. Solving linear systems
by eigenvalue method.
||Computing matrix exp. Linear flows.
Variation of parameters.
||Nonlinear ODEs. Existence and uniqueness.
||Phase portraits. Equilibria and stability.
||Periodic orbits. 2D Hamiltonian ODEs.
||Forced pendulum. Lorentz equation.