MATH3240 Numerical Methods for Differential Equations, 2012-13

Announcement

• (Jan 12) Lecture notes can be downloaded from this website.
• (Jan 31) First assignment has been uploaded. Please note the due date and no late submission is accepted.
• (Feb 21) Second assignment has been uploaded. Please note the due date and no late submission is accepted.
• (Mar 05) You can get back your assignment 1 from assignment box. You are strongly recommended to read the comments as well. [Download file]
• (Mar 07) Special review session: March 11, 6:30-7:30pm, LSB C1
• (Mar 11) Second assignment has been corrected and you can get back from assignment box. Solution has also been uploaded. [Download file]
• (Mar 11) Since the mid-term exam, there will be no tutorial class on Mar 13th.
• (Mar 29) Problem 2(a) of Assignment 3 is revised.
• (Apr 10) New due date of Assignment 3 is April 18
• (Apr 16) In question 3(d)(e) of assignment 3, "value of x(t) with respect to t" means the values of x(t) by the approximation .
  You are NOT supposed to graph the exact solution x(t).
• (Apr 25) Assignment 3 has been corrected. You can get back your work from the assignment box.

General Information

Course Description

Overview:

This course is an introduction to numerical methods for differential equations. Differential equations are common mathematical models of many realistic applications from physics, biology, finance and engineering. In order to quantitatively study these problems, one needs to find the solutions of the differential equations under consideration. However, analytical solutions to these differential equations are typically very difficult to compute. It is therefore important to design some methods to obtain approximate solutions in an efficient way. The focus of this course is to present some basic numerical methods for solving differential equations. We will consider both ordinary and partial differential equations.

Requirement:

In addition to the derivation of the methods, we will also prove stability and convergence theorems. A solid background in analysis and differential equations (ODE and PDE) is thus a very important prerequisite for this course. Moreover, there are some computational assignments, and some knowledge in MATLAB or C is needed.

Outline:

1. One step methods for ODE

2. Runge-Kutta methods for ODE

3. Multi-step methods for ODE

4. Systems of ODEs

5. Stiff problems

6. Boundary value problems

7. Finite difference methods for parabolic PDEs

8. Finite element methods for elliptic PDEs

Textbooks

• Numerical Mathematics and Computing, by Cheney and Kincaid. (7th Edition)

References

• An Introduction to Numerical Analysis, by Suli and Mayers.

Lecture Notes

• Lecture notes written by Prof. Jun Zou

Tutorial Notes

• Introduction of MATLAB
• Tutorial notes on 23/01/2012
• Tutorial notes on 30/01/2012
• Tutorial notes on 06/02/2012
• Tutorial notes on 20/02/2012
• Tutorial notes on 27/02/2012
• Tutorial notes on 06/03/2012
• Tutorial notes on 20/03/2012
• Tutorial notes on 27/03/2012
• Tutorial notes on 03/04/2012
• Tutorial notes on 10/04/2012
• Tutorial notes on 17/04/2012

Assignments

• Assignment 1 (due: Feb 20)
• Assignment 2 (due: Mar 7)
• Assignment 3 (due: Apr 18)

Quizzes and Exams

• Sample midterm problems
• Questions for the mid-term exam
• Sample final problems

Solutions

• Solution to Assignment 1
• Comment on Assignment 1
• Solution to Assignment 2
• Solution to Assignment 3

Assessment Scheme

Honesty in Academic Work

The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:

and thereby help avoid any practice that would not be acceptable.