MATH3310 Computational and Applied Mathematics, 2012-2013

Announcement

• Homework 1 has been posted. It is due on October 3, Wednesday, before 6pm.
• Question 2 and 4 in Homework 1 has been updated ( 25 - 9 - 2012 )
• Midterm exam will be on October 26, 9:30am-11am (in class, LT2)
• Homework 2 has been posted. It is due on October 19, Friday, before 6pm.
• Your homework 1 has been corrected and can be available above the mail box.(57 received, 54 returned. 3 of you must pick your HW in Rui's office - LSB 101. Check it out yourself)
• A hint has been added to Question 4(a) at Homework 2
• The due date of HW 2 is postponed to October 22 (Monday).
• Chapter 2 supplementary notes has been updated (21-10-2012)
• Homework 3 has been posted. It is due on November 12, Monday, before 6pm.(Please print your code and results with your paper HW )
• Here are some remarks about HW2 [Download file]
• HW2 has been corrected and can be available above the mail box.(57 received, 49 returned,1 name missed. 8 of you must pick your HW in Rui's office - LSB 101.)
• Homework 4 has been updated. It is due on November 26, Monday, before 6pm.
• HW3 has been corrected and can be available above the mail box.(55 received, 55 returned)
• HW4 has been corrected and can be available above the mail box.(58 received, 58 returned)
• HW5 has been corrected and can be available above the mail box.(56 received, 56 returned)
• The list of students with missing HW(s) available. If you want to argue with your record, please bring your ORIGINAL copy of HW(s) to 101 LSB.(email Rui firstly to make sure you can find him) [Download file]

General Information

Course Description

This course introduces the general techniques frequently used in computational and applied mathematics. Applications can be found in different areas such as physics, engineering, imaging sciences and so on. In real situation, practical problems can usually be formulated or modeled by differential Equations, linear or nonlinear system of equations. Developing effective methods to solve and analyze these equations is therefore very important. In this course, we aim to give a brief introduction of the methods frequently used in applied mathematics to solve and analyze these problems. In particular, both analytical and numerical approaches will be introduced.

The outline of the course is summarized as follows:

1. Introduction: (a) Motivation of the course; (b) Physical modeling and PDE;

2. Analytic approach: (a) Simple cases: Separation of variable, Initial value problem, Boundary value problem; (c) Laplace method; (d) Fourier method and Fast Fourier Transform;

3. Numerical approach: Spectral method

4. Numerical approach: Iterative method for solving linear system; (a) Motivation of solving linear system by finite difference method; (b) Gaussian elimiation revision; (c) Iterative method for solving very large linear system; (d) Convergence;

4. Eigenvalue problem

5. Least-square method

6. Conformal mapping: dealing with complicated domains.

Textbooks

• The course will be solely based on my lecture note, which will be posted on the course website.

Lecture Notes

• Chapter 1: Introduction
• Chapter 2: Analytical Methods(Last update: 17-9-2012)
• Chapter 2: Supplymentary materials(Last update: 21-10-2012)
• Chapter 3: Spectral Methods
• Chapter 4: Iterative methods for Linear system(Last update: 3-12-2012)
• Chapter 5: Eigenvalues Problems(Last update: 3-12-2012)
• Chapter 5-2: Eigenvalues Problems(Last update: 17-12-2012)
• Chapter 6: Conformal Mappings(Last update: 17-12-2012)
• Practice exercises(Last update: 12-10-2012)

Tutorial Notes

• Tutorial 1
• Tutorial 2
• Tutorial 3
• Tutorial 4

Assignments

• Homework 1 (Due on October 3, Wed, before 6pm) (Updated : 25-9-2012)
• Homework 2 (Due on October 22, Mon, before 6pm) (Updated : 15-10-2012)
• Homework 3 (Due on November 12, Mon, before 6pm) (Updated : 29-10-2012)
• Homework 4 (Due on November 26, Mon, before 6pm) (Updated : 18-11-2012)
• Homework 5 (Due on December 10, Mon, before 6pm) (Updated : 29-11-2012)

Quizzes and Exams

• Solution of Mid-Term

Solutions

• Solution of HW1 (Written by TA, for reference only) (Updated: 10-10-2012 )
• Solution of HW2 (Written by TA, for reference only) (Updated: 11-1-2012 )
• Solution of HW3 (Written by TA, for reference only) (Updated: 11-21-2012 )
• Solution of HW4 (Written by TA, for reference only) (Updated: 12-4-2012 )
• Solution of HW5 (Written by TA, for reference only) (Updated: 12-24-2012 )

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.