Instructor: Daniel Tataru
Lectures: TuTh 12:30-14:00 am, 4 EVANS
Course Control Number: 54847
Office: 841 Evans, e-mail: tataru@math.berkeley.edu
Office Hours: Monday 1:00-2:00 or by appointment
Prerequisites: Math. 104
Textbook Hirsch, Smale and Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos
Syllabus: The course provides a more elementary yet rigorous introduction to Ordinary Differential Equations. We begin with linear systems of equations, first in the plane and then in higher dimension. Then we move on to nonlinear systems and study the existence and uniqueness of solitions, equilibrium and stability, as well as the Poincare-Bendixson theorem. Finally we consider some applications to biology and mechanics. Additional topics will be covered as time permits.
Grading: 40% homeworks, 20% midterm, 40% final.
Homework: Homework for each week will be assigned on the web, and due every Tuesday. The two lowest homework grades will be dropped.
Midterm: Tuesday October 16
Homework assignments:
| No: |
Due Date: |
Problems: |
| 1. |
4/9 |
p.16: 2,3,5,9,11,12 |
| 2. |
11/9 |
p.38: 1,2,6,7,8,10 |
| 3. |
18/9 |
p.57: 1,2(i)(ii)(iv),4,6,8,9,13 |
| 4. |
25/9 |
p.72:1,2,5,6,7 |
| 5. |
2/10 |
p.104: 2(c,e),3,5(c,g),8(b),11 |
| 6. |
9/10 |
p.135, 1(a,c,f),3,6,8,9,10 |
| 7. |
30/10 |
p.156: 1 a,b,d, 2 p. 404: 4 abce, 5 |
| 8. |
6/11 |
p.184: 1,2 |
| 9. |
13/11 |
p.185: 4,5,6,9 |
| 10. |
20/11 |
p. 211: 1(c), 4,5,6 |
| 11. |
4/12 |
p. 231:1ad,2,7,8 |