MATH3310  Computational and Applied Mathematics  2020/21
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.
 ZOOM link for lectures: https://cuhk.zoom.us/j/97007613919(Lecture time: Mon 2:30PM  4:15PM; Wed 4:30PM  5:15PM)
 ZOOM link for tutorial classes: https://cuhk.zoom.us/j/99678118705 (Tutorial time: Wed 5:30PM  6:15PM)
 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 facetoface 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 "takehome 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 24hour 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^2In 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 (IG)x = b. As such, we assume IG 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 24hour examination. I will post the question paper (on Blackboard & course website) on May 7 at 8:30pm.
 The exam can be finished within 34 hours. The 24hour 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, GaussSeidel, SOR, (preconditioned) conjugate gradient etc), Multigrid method;
4. Eigenvalue problem
5. Energy minimization problems
6. Conformal mapping: dealing with complicated domains.
Lecture Notes
 Lecture 1
 Lecture 2
 Lecture 3
 Lecture 4
 Lecture 5
 Lecture 6
 Lecture 7
 Lecture 8
 Lecture 9
 Lecture 10
 Lecture 11
 Lecture 12
 Lecture 13
 Lecture 14
 Lecture 15
 Lecture 16
 Lecture 17
 Lecture 18
 Lecture 19
 Lecture 20
 Lecture 21
 Lecture 22
 Lecture 23
 Lecture 24
Class Notes
 Extra references on "Mathematical modelling of real world problems"
 Extra references on "Analytic spectral method"
Tutorial Notes
 Tutorial notes (By Feb 3)
 Tutorial notes (Feb 10)
 Tutorial notes (Feb 24)
 Tutorial notes (Mar 3)
 Tutorial notes (Mar 10)
 Tutorial notes (Mar 17)
 Tutorial notes (Mar 24)
 Tutorial notes (Apr 14)
Assignments
 Homework 1 (Due on Feb 5 before 11:59PM) [Updated: hint for Q6b added]]
 Homework 2 (Due on Feb 22 before 11:59PM)
 Homework 3 (Due on Mar 15 before 11:59PM)
 Homework 4 (Due on Apr 9 2021 before 11:59PM)
 Homework 5 (Due on May 5 2021 before 11:59PM)
Quizzes and Exams
 Practice midterm
 Practice midterm solution (Prepared by TA, for reference only)
 Midterm Examination (Due on March 13 before 10AM. Please submit your solution via the Blackboard system,)
 Practice final (please also revise all homework questions)
 Practice final suggested solution (Prepared by TA, for reference only)
 Final Examination (Due on May 8 before 8:30pm. Please submit your solution via the Blackboard system,)
Solutions
 Homework 1 solution (prepared by TA, for reference only)
 Homework 2 solution (prepared by TA, for reference only)
 Midterm Suggested solution (Prepared by TA, for reference only)
 Homework 3 solution (prepared by TA, for reference only)
 Homework 4 solution (prepared by TA, for reference only)
 Homework 5 solution (prepared by TA, for reference only)
Assessment Scheme
Homework  15%  
Midterm exam (March 12, Friday conducted online)  35%  
Final exam (May 7, 8:30pm)  50% 
Useful Links
 Lecture 1 recording
 Lecture 2 recording
 Lecture 3 recording
 Lecture 4 recording
 Lecture 5 recording
 Lecture 6 recording
 Lecture 7 recording
 Lecture 8 recording
 Lecture 9 recording
 Lecture 10 recording
 Tutorial on Feb 10
 Lecture 11 recording
 Lecture 12 recording
 Tutorial on Feb 24
 Lecture 13 recording
 Tutorial on Mar 3
 Lecture 14 recording
 Lecture 15 recording
 Lecture 16 recording
 Lecture 17 recording
 Tutorial on Mar 10
 Tutorial on Mar 17
 Lecture 18 recording
 Lecture 19 recording
 Lecture 20 recording
 Lecture 21 recording
 Lecture 22 recording
 Lecture 23 recording
 Lecture 24 recording
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