Math 290A - Methods in Applied Mathematics

Class is scheduled for MWF 10:00-10:50am in RH 440R.
Office Hours: To be announced, Rowland Hall 410F.

Course Information
This class is an introduction to continuous flows and dynamical systems generated by ordinary differential equations. Linear systems will be considered first as the basis for the local nonlinear theory around equilibria and periodic orbits. Some elements of global nonlinear theory will also be touched upon as well as material from bifurcation theory.

Assignments
Homework numbers refer to problems in Perko's book.
Problem Set 1 (due Mo, Oct 3): Problems 2,3,4 on p. 15, 6 on p. 19, and 9 on p. 27.
Problem Set 2 (due Mo, Oct 10): Problems 2d, 3d on p. 37, 3,4 on p. 47, and 2,3,6 on p. 56.
Problem Set 3 (due We, Oct 19): Problems 3 of Sec. 2.1, 3,4 of Sec. 2.2, and 5,6 of Sec. 2.3.
Problem Set 4 (due Fr, Oct 28): Problems 3 of Sec. 2.4, 6,7 of Sec. 2.5, and 2,3 of Sec. 2.6.
Problem Set 5 (due Mo, Nov 7): Problems 4,5,6,7 of Sec. 2.7 and 1 of Sec. 2.8.
Problem Set 6 (due Mo, Nov 14): Problems 4,5,6 of Sec. 2.9 and 1 of Sec. 2.10.
Problem Set 7 (due We, Nov 23): Problems 1,2 of Sec. 2.12 and 1,2,11 of Sec. 2.14.

Take Home Final: Read the notes about bifurcation which I handed out in class and the solve the relative problem set.

Grading and Exam Policy
Grading will be based on active participation, homework, and a take home exam.

Textbooks
G. Iooss & D. D. Joseph, Elementary Stability and Bifurcation Theory, Springer 1990.
L. Perko, Differential Equations and Dynamical Systems, Springer 2001.