## MATH 130A, Ordinary Differential Equations, Fall 2006:

Office hours:M:4:30-5:30 WF 2-3

Office: APM 5256, tel. 534-2734

Email: hwenzl@ucsd.edu

Teaching assistant: Ananda Leininger, office: APM 6432, office hours: Thursday 1-3. email: aleining@math.ucsd.edu

Computation of grade: homework: 20%, midterm: 30%, final 50%.

Dates of exams: No make-up exams!

Midterm: 11/3 in class

Final: December 6, 3-6

Course material: We will use the book "Differential Equations, Dynamical Systems, and an Introduction to Chaos", by Hirsh, Smale and Devaney.

Homework assignments Unless further notice, homework is to be turned in BY NOON on or before the date posted in section. There will be a drop box on the 6th floor of APM, marked for our course (turn right leaving the elevator).

Disclaimer: I will try to get the homework assignment on the net in time. Due to time and other limitations, this may not always be possible. The fact that there is no assignment posted for a particular date does therefore NOT necessarily mean that no homework is due.

Homework Solutions: Selected solutions will be posted at the TA's website:

for 9/29: p. 16: 2bce, 5

for 10/6: p. 18: 10, p. 37: 2(d), 3

for 10/13: p. 57: 1ac (i.e. you only need to identify the phase portraits (I called them flow diagrams in class) for the matrices in a and c), do 2abcd for matrix in (iii), 11, 3(a)

for 10/20: p. 135: 1(c),(d)(if you can't do (d) right away, wait until Monday's lecture), 3, 7

for 10/27: p. 138: 12abf, 13, p. 156: 1bcd, 6

no homework due this week: a few review problems for midterm: p. 58: 6, p. 105: 5(CHANGE: two of the entries of the matrix are equal to b. Change ONE of them to -b; otherwise this problem is not very interesting). Also: Calculate the flow and the Poincare map for the X'=AX, with A as on page 52. Here the Poincare' map P is defined as P(X_0)= X(1), where X(t) is the solution of the differential equation with X(0)=X_0. See below for further info about the midterm. You can also already look at problems p. 72: 4, 5a

for 11/10: p. 72: 4, 5a, p. 184: 1(i),(iii) (for answering part (c), read the first few lines of Section 8.2, p. 165/166)

for 11/17: p.185: 4(you need not prove your answer), 5, 7(look at example on p.180; solve the two differential equations qualitatively by drawing flow diagrams and deduce from this the qualitative behavior of the solutions).

for 12/1: p 211: 1(b), 4(basin of attraction: points from which the solution goes to the equilibrium point), 6, 7bc

Midterm: The midterm takes place on Friday, 11/3 in class. You are allowed to use one hand-written cheat sheet, but NO CALCULATORS, NO BOOKS. The problems will be similar, or at least related to homework problems or review problems (except for the problems on page 72, which you can ignore for the test). As for nonlinear differential equations, you need not worry about what we did this week. But some of the things we did last week (Picard iteration, existence and uniqueness questions) may conceivably be on the test.

Final: The final takes place on Wednesday, December 6, 3-6pm in class. You are allowed to use one hand-written cheat sheet, can be both sides, but NO CALCULATORS, NO BOOKS. The problems will be similar, or at least related to homework problems or review problems. Problems will go over the whole course, with an emphasis on problems after the midterm. There is a practice midterm on my colleague's webpage, a link of which is given below. Corrections/Hints: In the practice final, please remove the z^2 in Problem 3 (it is only a 2-dimensional problem). For problem 5, replace the second equation by y'=-x-2y). For problem 1, you may pick any matrix A which has the given eigenvalues, so pick one which is easy to work with. Check back later, I may give a few more practice problems/info.

Office hours in finals week: Monday 4-5, Tuesday 2-3

the following webpage of the same course given by a colleague of mine, based on a previous version of our book.