MATH3310 - Computational and Applied Mathematics - 2020/21

Course Name: 
Computational and Applied Mathematics
Teacher: 
Prof. Ronald Lok Ming LUI
Course Year: 
2020/21
Term: 
2

Announcement

  • Announcement of onine lectures & tutorial sessions

    •  To reduce the risk of spreading the novel coronavirus, lectures and tutorial sessions will be conducted online via ZOOM. 
  • There will be no tutorial classes in the first week.
  • Homework 1 has been posted. It will be due on Feb 5 before 11:59PM. Please write or type your solution. Scan it as a pdf and upload it to Blackboard.
  • Hint for Q6b for HW1 has been added. Please download the updated pdf.
  • Midterm examination will be held on March 12 (Friday) online. Details will be announced.
  • Homework 2 has been posted. It will be due on Feb 22 before 11:59PM. Please submit your solution through the Blackboard system.

  • Arrangment of midterm examination

    Until now, the possibility of resuming face-to-face lectures is still unknown. As such, we need to make suitable arrangements for our midterm examination as follows:

     
    1. Midterm exam will be held on March 12, 2021 (Friday).
    2. Midterm exam will be conducted online using "Blackboard" as a "take-home exam" with 24 hours limit. It will be available on March 12, 2021 at 10:00am and deadline for submission (via "Blackboard") is March 13 at 10:00am. It is expected that the paper can be finished within 3 hours. As such, the 24-hour limit should allow enough flexibility. LATE SUBMISSION WILL NOT BE ACCEPTED.
    3. Midterm exam will cover materials from Lecture 1 to Lecture 12.
    4. Your submitted solution will be checked carefully to avoid plagiarism. Discussions amongst classmates are strictly prohibited. Related to this, please kindly be reminded of the following regulations enforced by the university:
    "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:  http://www.cuhk.edu.hk/policy/academichonesty/ and thereby help avoid any practice that would not be acceptable."
    5. Arrangement of final examination will be announced later.
  • Homework 2 has been posted. It will be due on Mar 15 before 11:59PM. Please submit your solution through the Blackboard system.
  • Homework 3 has been posted.
  • Midterm exam question paper has been posted. It will be due on March 13 before 10AM. Please submit your solution through Blackboard. Late submission will not be accepted.

  • Clarifications on Q2, Q5 and Q6a. 

    For Q2. The equation should be: d^2 y/ dt^2 = c^2 d^2 y /dx^2
     
    In other words, it should be second derivatives both on the left hand side and right hand side.
     
    For Q5, as usual, we assume the iterative scheme is trying to solve the linear system (I-G)x = b. As such, we assume I-G is invertible.
     
    For Q6a, C is tridiagonal as well.
  • The deadline of homework 3 is postponed to March 17 before 1159PM.
  • Homework 4 has been posted.

  • Arrangment of the final examination

    • The online final examination will be held on May 7 (Friday) at 8:30pm and due on May 8 before 8:30pm.
    • It is s a 24-hour examination. I will post the question paper (on Blackboard & course website) on May 7 at 8:30pm.
    • The exam can be finished within 3-4 hours. The 24-hour limit is just set to allow enough flexibility.
    • The coverage of the examination will be all the course materials after the midterm examination.
  • Homework 5 has been posted.
  • Practice final exam and its solution have been uploaded.
  • Final examination paper has been uploaded.

  • Typo in Q1b of the final exam

    There is a typo in Q1b of the final exam. \mu should be the minimal eigenvalue of A in magnitude.

     

    Q2 in the final exam

    The exact definition of g(x) is: g(x) = x_l, where l is the smallest index such that |x_l| = ||x||_{infty}

     

    Please refer to the updated version of the pdf.

     

  • In Q4, x^(k) and x_k refer to the same vector. Please refer to the updated pdf.

General Information

Lecturer

  • Ronald Lok Ming LUI
    • Office: LSB 207
    • Tel: 39437975
    • Email:

Teaching Assistant

  • Zhipeng ZHU (Tutorial)
    • Office: LSB 222B
    • Tel: 39437963
    • Email:
  • Ling DAI (Grader)
    • Office: LSB 222A
    • Email:

Time and Venue

  • Lecture: Mon 2:30PM - 4:15PM; Wed 4:30PM - 5:15PM (Conducted online via ZOOM)
  • Tutorial: Wed 5:30PM - 6:15PM (Conducted online via ZOOM)

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. Real world problems can usually be formulated by mathematical equations (e.g. differential, linear or nonlinear equations). Developing effective methods to solve and analyze the solutions is therefore important. In this course, we aim to give a brief introduction of the methods frequently used in applied mathematics to solve these problems.

The outline of the course is summarized as follows:

1. Introduction: (a) Motivation of the course; (b) Mathematical modelling of real world problems;

2. Brief introduction on some commonly used analytical approaches: (a) Initial value problem & Boundary value problem; (b) Analytic spectral (Fourier) method;

3. Numerical approach: Numerical spectral method, iterative method for solving large linear system (Jacobi, Gauss-Seidel, SOR, (preconditioned) conjugate gradient etc), Multigrid method;

4. Eigenvalue problem

5. Energy minimization problems

6. Conformal mapping: dealing with complicated domains.


Lecture Notes


Class Notes


Tutorial Notes


Assignments


Quizzes and Exams


Solutions


Assessment Scheme

Homework 15%
Midterm exam (March 12, Friday conducted online) 35%
Final exam (May 7, 8:30pm) 50%

Useful Links


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:

http://www.cuhk.edu.hk/policy/academichonesty/

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

Assessment Policy

Last updated: May 08, 2021 10:59:15