NEW

The final week: The final is on June 5, Friday, from 7:00pm-9:00pm. Room 380 380F. Part of the final will be on periodic solution and Poincare maps; part of the final will be on topics learned this quarter. (Preparing Final pdf)

Preparing Final pdf, Preparing midterm-2 PDF, Preparing midterm PDF,

Assignment VIII, due Tu. 6/2, 5pm, to office 383Z

Solutions: Set I, Set II, Set III, Set IV, Set V

Information

Reference: Differential equations, dynamical systems, and an introduction to chaos, M. Hirsch, S. Smale and R. Devancy

Past assignments Set I, Set II, Set III, Set IV, Set V, Set VI, Set VII,

Course description

This course covers the basic theory of ordinary differential equations. We will begin with a discussion of linear differential equations, and develop the necessary tools from linear algebra for solving such systems. Moreover, we will analyze the asymptotic properties of their solutions. We will then develop the general nonlinear theory. Nonlinear systems of differential equations can not usually be solved in closed form. Instead, we will discuss existence and uniqueness theorems and analyze the qualitative behavior of solutions. In parsssssssicular, we will study the behavior of the solutions near an equilibrium point. Time permitting, we will discuss boundary value problems for second order equations and Sturm-Liouville theory. This is a proof-oriented course. If you are interested in a "cookbook"-style course on ordinary differential equations, you may want to consider taking Mathematics 53. (Prerequisites: Mathematics 51H and 52H, or equivalent)

Course Logistic

• Lectures: MTWTh, 2:15-3:05PM;
• Review/Discussion Fri, 2:15-3:05PM
• Location: Building 380-380W;
• Text Book: Ordinary Differential Equations, by Simon Brendle (Text book (reader) should be available in bookstore before the quarter begins. If you have any questions, please contact course assistant Michail msavvas@stanford.edu)

Contact Information

• Office: 380-383Z,
• Office Phone: 723-4508
• E-mail: jli@math.stanford.edu
• Office Hours: Mon. 11-12:30, 3:15-4:00; Tu. 3:15-4:00, or by appointment.

Course assistant

• Michail Savvas,
• Office: 380-381N; email: msavvas@stanford.edu
• Office hours: Mon. 12-2, and Tu. 10:30-11:30.

Exam and Course grade

There will be one in-class (first) midterm exam; one take-home (second) midterm exam, and an in-class final exam.
Course grade: homework 25%, midterm one 25%, midterm two 25%, final 25%

Assignments

Homework will usually be assigned once a week, and will be due the following Tuesday. While you may discuss the homework problems with your peers, what you hand in must be your own work and not a joint project of several people. Please deliver weekly assignments by 5PM, to my office. (Do not leave the assignments in my mailbox.) No late assignment will be accepted unless pre-approved.

Further help and Advice

• Confused about the material? Your first resource should be the office hours offered by the teaching assistants and me. Office hours are also a good time to give me feedback on the class.
• Please write neat and complete solutions to the problem sets. "Neat" means well structured, not only esthetically, but also logically. "Complete" means that the grader will need to see a sufficient amount of explanations and details to give you full credit, even if the question only asks for a numerical answer.