Math 130A - Ordinary Differential Equations     Winter 2009

When is the final exam? Friday 8-11am
Where is the final exam?
If your family name begins with A-M go to APM B402A.
If your family name begins with N-Z go to WLH 2111.
What topics are on the final exam?
1. Phase lines and phase portraits.
2. Writing a second order equation as a first order system.
3. Solving any 2x2 linear system, determining the type and the long time behavior.
4. Solving any 3x3 linear system, determiing the long time behavior.
5. Taking a 2 or 3 dimensional non-linear system, determining the equilibrium points, finding the linearization close to the equilibrium point, solving the linearized equation and determining whether the non-linear system is conjugate to the linear one close to the equilibrium point, and using this to deduce the behavior of the non-linear system if possible.

Instructor:   Kate Okikiolu     okikiolu@math.ucsd.edu

Lectures: MWF 10-10:50am, WLH 2111

Office Hours: W 1-2pm in APM 7426 (There will be an office hour 3/18/09.)

Teaching Assistant: Christopher Tiee     ctiee@math.ucsd.edu    

Section: W 5pm, 6pm, in HSS 2150.

TA Office Hours: M 2-4pm and Tu 12-2pm in APM 6434.    Exam week office hour is Wednesday March 18, 5-7pm.

Homework: The solutions are thanks to your TA Chris Tiee.

 wk  Due Wednesday  Homework Assignment
  1  1/7  Chapter 1.   # 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13.
  2  1/21  Chapter 2.   # 2, 3, 4, 6, 7, 8, 9, 11, 12, 14.
  3  1/28  Chapter 3.   # 1, 2, 3, 4, 5, 7, 9, 10, 14, 16.
  4  2/4  Chapter 4.   # 1, 2, 3, 4, 5, 6.
  5  2/11  Chapter 5.   # 3, 4, 5, 6, 8, 9.   Chapter 6.   # 1.
  6  2/18   Problems  
  7  2/25  Chapter 5.   # 10.   Chapter 6.   # 2, 3, 4, 5, 6, 7, 8, 9, 10.
  8  3/4  Chapter 5.   # 15.   Chapter 6.   # 11, 12, 13, 15.    H1
  9  3/11  Chapter 7.   # 1, 5, 6.   Chapter 8.   # 1, 2.
  

Text: "Differential Equations, Dynamical Systems and an Introduction to Chaos" by Robert L. Devaney, Morris Hirsch, Stephen Smale, Academic Press.

Other texts:
Syllabus: 130A. Ordinary Differential Equations (4) Linear and nonlinear systems of differential equations. Stability theory, perturbation theory. Applications and introduction to numerical solutions.

Prerequisites: Prerequisites: Math. 20D/21D and 20F.

Exams:
Midterm 1New: Midterm 1, 2009   
Midterm 2:   Practice midterm from 2003   New: Midterm 2, 2009
Final:   Practice final from 2003      Read me: One solution from the practice final from 2003

Grading: Homework: 20%,   2 midterm exams: 15% each,   final exam: 50%. (The lowest homework score will not be counted. Missed exams will count zero.)

Approximate Lecture Schedule (may be updated during the course): The day after each lecture, I might write a lecture summary which can be obtained by clicking the relevant section number.

 wk  date  Monday  Wednesday  Friday
  1  1/5  First order equations  Phase Line  Bifurcation
  2  1/12  Poincare map  Periodic harvesting  Linear systems
  3  1/19  Holiday  2.5-2.7  linear algebra
  4  1/26   phase portraits   Examples   Exam
  5  2/2      3-d systems
  6  2/9  3-d systems  4.2  
  7  2/16  Holiday    
  8  2/23   3x3 systems     Exam
  9  3/2      
 10  3/9      
 11  3/17        Final 8-11am