Math266A-01F

Math 266A
Applied Ordinary Differential Equations

Lecture 1, Fall 2001 @ UCLA

This is the class homepage of math 266A, lecture 1. Instructor: Hailiang Liu.

Information:   course description, office hours, grading policy...

Syllabus:        tentative schedule of the lectures;

Homework:   homework exercises, guidelines for solving problems;

If you have any suggestions or comments, which you feel are helpful to the course, I would be very happy to hear from you. Email me at hliu@math.ucla.edu

Weekly Homework Assignments: Due each Tuesday on Discussion Section

HW SECTIONS/PROBLEMS DUE DATE&

1 Ch.1   p.9 #2;   (Deriving ODEs)
           p.13 #11, #12 (System of ODEs) Wed. Oct. 3

2 Ch.1   p.18 #2 (Vector Matrix)      p.20 #5   (Convergence);
          p.22 #8, #12 (Find solution)
          p27. #8,    p.29 #14 (Existence &Uniqueness) Wed. Oct.10

3 Ch.1   p. 32, #3 (Gronwall inequality)
Ch.2 p.39, #3;   (Existence for linear system)
           p. 41, #7; p.45, #17; (linear system) Tue. Oct. 16

4 Ch. 2 p.24, #49; p.27, #50 (Fundamental matrix);
            p.54, #5 (linear system with non-constant coefficients)
            p.71, #14 (linear system with constant coefficients) Tue. Oct.23

5 Ch. 2   p.83, #4 (Solution behavior);
             p.93, #8; p.95, #19 (phase plane analysis);         Tue.   Oct.30

6 Ch. 2   p.103, #1; p.104, #5 (Miscellaneous exercise);
            Oct. 31--- Midterm
Ch.3    p.110, #2; p. 111, #5 ; p137, #1 (Existence and Uniqueness revisited) Tue . Nov. 6

7 Ch.4   p. 149, #3(Global stability), p.150, #4(a)(c)(f) (Stability) ;
           p.158, #15* (Perturbed system); p.159, #17 (Time-dependent coefficient matrix);
           p. 164, #2 (asymptotic stability for linear system). Tue.    Nov.13

8 Ch. 4   p.182, #1; (Asymptotic Equivalence);
Ch. 5 p.190 #4 (Hamiltonian systems), p.200 #5 (Lyapunov's Method);
Tue.    Nov 20

9 Ch.5 p.201, #9 (Lyapunov's Method), p. 204, #11 (Asymptotic Stability)
         p.215, #2 (Invariant sets and Stability);

         p. 222, #5 (Region of asymptotic stability).
Tue.   Nov 27

10 Review: Dec. 3 --- general review;
                 Dec. 5 --- individual review, consult Ms. Kao at MS3905, 10:00am--11:00am.

                 Dec. 7 --- final at MS5118, 10:am--10:50am!

                            --- extra office hour at 7620D: 9:00am--10:00am
Fri. Dec. 7

HW	SECTIONS/PROBLEMS	DUE DATE&
1	Ch.1 p.9 #2; (Deriving ODEs) p.13 #11, #12 (System of ODEs)	Wed. Oct. 3
2	Ch.1 p.18 #2 (Vector Matrix) p.20 #5 (Convergence); p.22 #8, #12 (Find solution) p27. #8, p.29 #14 (Existence &Uniqueness)	Wed. Oct.10
3	Ch.1 p. 32, #3 (Gronwall inequality) Ch.2 p.39, #3; (Existence for linear system) p. 41, #7; p.45, #17; (linear system)	Tue. Oct. 16
4	Ch. 2 p.24, #49; p.27, #50 (Fundamental matrix); p.54, #5 (linear system with non-constant coefficients) p.71, #14 (linear system with constant coefficients)	Tue. Oct.23
5	Ch. 2 p.83, #4 (Solution behavior); p.93, #8; p.95, #19 (phase plane analysis);	Tue. Oct.30
6	Ch. 2 p.103, #1; p.104, #5 (Miscellaneous exercise); Oct. 31--- Midterm Ch.3 p.110, #2; p. 111, #5 ; p137, #1 (Existence and Uniqueness revisited)	Tue . Nov. 6
7	Ch.4 p. 149, #3(Global stability), p.150, #4(a)(c)(f) (Stability) ; p.158, #15* (Perturbed system); p.159, #17 (Time-dependent coefficient matrix); p. 164, #2 (asymptotic stability for linear system).	Tue. Nov.13
8	Ch. 4 p.182, #1; (Asymptotic Equivalence); Ch. 5 p.190 #4 (Hamiltonian systems), p.200 #5 (Lyapunov's Method);	Tue. Nov 20
9	Ch.5 p.201, #9 (Lyapunov's Method), p. 204, #11 (Asymptotic Stability) p.215, #2 (Invariant sets and Stability); p. 222, #5 (Region of asymptotic stability).	Tue. Nov 27
10	Review: Dec. 3 --- general review; Dec. 5 --- individual review, consult Ms. Kao at MS3905, 10:00am--11:00am. Dec. 7 --- final at MS5118, 10:am--10:50am! --- extra office hour at 7620D: 9:00am--10:00am	Fri. Dec. 7