# Math 462/512. Introduction to Ordinary Differential Equations. Fall 2014.

## Book:

Section 001. TR 14:00-15:15. Room: CTLB 130. Syllabus for Math 462/512-001 (18741/18801). Differential Equations and Dynamical Systems 3rd Ed.
Lawrence Perko, 553 pp., Hardcover, Springer, 2001
ISBN: 978-0-387-95116-4.

Additional chapters of Linear Algebra (Jordan blocks): Site of the author (Steve J. Leon) and the direct link to the recommended PDF.

## Office hours:

Wednesday 12:45-14:00, Tuesday 11:00-12:15. Room: SMLC 220.

## How grades are assigned?

All homeworks: 100 points.
Two midterm exams: 100 points each (100+100 points).
In class quizes: 50 points.
Final exam: 200 points.
Total: 550 points.
Lowest thresholds for grades (not higher than):
A = 495, B = 440, C = 380, D = 330.

Week # Homework problems Due date
- Final Exam (10am, Tuesday, December 9th, 2014). -
11-12 Take home Quiz 03. (Solution published) (due date: Tuesday, December 2nd, scan is enough). Topic: Limit sets.
Take home Quiz 04. (Solution published) (due date: Thursday, December 4th, scan is enough). Topic: Floquet theory.
Training problem from HW for Poincare-Bendixon's theory.
Take home Quiz 05 (due date: Friday, December 5th, 5pm, scan is enough). Topic: Poincare-Bendixon's theory.
Take home Exam 2 (Solution published) (due 12pm, Monday, December 10th, 2014, scan is enough).
Additional reading on Floquet method.
Qualifier from August, 2013.
Solution of the first two problems from Qualifier of August, 2013.
LP Section 3.2: 1;
LP Section 3.3: 4;
LP Section 3.7: 2;
LP Section 3.9: 3;
LP Section 3.5: 1,2.
Friday, December 5th, 2014, 2pm.
(You can send me a scan of the HW)
10 Take home Exam 1. (Solution published) (due Tuesday, November 11th, 2014).
LP Section 2.11: 2 (d,f), 3 (b,f);
LP Section 2.12: 2, 7;
LP Section 2.13: 2, 5;
LP Section 2.14: 8, 11, 12.
November 20th, 2014, class time.
9 LP Section 2.7: 4, 5, 7;
LP Section 2.9: 2, 4, 5 (a,c), 6;
LP Section 2.10: 1 (a,b,c), 4 (a,b,c,f).
November 6th, 2014, class time.
6-8 Quiz 02 (Thursday, October 30th). (Solution published) Topic: Linearization.
LP Section 2.2 (p.75): 4;
LP Section 2.3 (p.83): 4, 5, 6;
LP Section 2.4 (p.92): 2(b), 3;
LP Section 2.5 (p. 100): 6, 7;
LP Section 2.6 (p. 104): 2, 3.
October 30th, 2014, class time.
5 Quiz 01 (Tuesday, October 7th). (Solution published) Topics: Jordan canonical form of a matrix.
LP Section 1.9 (p. 57): 2(b,d);
LP Section 1.10 (p.61): 3.
October 7th, 2014, class time.
1-4 Additional chapters in Linear Algebra (see link above):
p. 13: 4, 5, 7;
p. 22: 3(a,c,e);
Find:
(a) (det[exp(At)] = det[Phi(t)];
(b) a differential equation satisfied by det[exp(At)];
(c) Given det[Phi(0)] = 1; find det[Phi(t)];
LP Section 1.5 (p. 26): 1, 3;
LP Section 1.6 (p. 31): 2, 4;
LP Section 1.7 (p. 37-38): 1(a,c), 2(c), 3(d);
LP Section 1.8 (p. 47-49): 2(c), 6(f,g), 7, 10.
September 16th, 2014, class time.