# Math 462/512. Introduction to Ordinary Differential Equations. Fall 2016.

## Book:

Section 002. TR 11:00-12:15. Room: DSH 328. Syllabus for Math 462/512-002 (57728/57752). 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 (Steven J. Leon) and the direct link to the recommended PDF.

## Office hours:

TR 14:00-15:15. Room: SMLC 220.

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 Quiz 04 (Thursday, December 1st). (Solution published) Topic: Limit sets.
Training problem from HW for Poincare-Bendixon's theory.
Take home Quiz 05 (Thursday, December 8th).. Topic: Poincare-Bendixon's theory. Scan of the solution is due: 12pm on Friday, December 9th.
Take home Exam 2. (Solution published) (will be published on Friday, December 9th, 2016, scan is enough).
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 9th, 2016, 2pm.
(You can send me a scan of the HW)
10 Quiz 03 (Tuesday, November 22nd). (Solution published) Topic: Hamiltonian and gradient systems. Lyapunov stability theory.
Take home Exam 1. Published on Friday, November 4th. (Solution published) (due Tuesday, November 8th, 2016).
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 22nd, 2016, 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 8th, 2016, class time.
6-8 Quiz 02 (Tuesday, October 18th). (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 18th, 2016, class time.
5 LP Section 1.9 (p. 57): 2(b,d);
LP Section 1.10 (p.61): 3.
October 4th, 2016, class time.
1-4 Quiz 01 (Tuesday, September 20th). (Solution published) Topics: Jordan canonical form of a matrix.