MATH3310 - Computational and Applied Mathematics - 2024/25
Announcement
Submission of homework assignments
- Log onto https://blackboard.cuhk.edu.hk/ and click on our course 2024R1 Computational and Applied Mathematics (MATH3310). Click on "Course contents" and click on "Homework X (Due...)". Follow the instructions therein to upload your solution.
- Homework 1 has been posted. It will be due on September 24 before 11:59PM. Please submit the homework via the Blackboard system.
- There will be no tutorial in the first week.
General Information
Lecturer
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Prof. Ronald Lok Ming LUI
- Office: LSB 207
- Tel: 3943-7975
- Email:
Teaching Assistant
-
Xu Zhehao
- Office: LSB 222B
- Tel: 3943-7963
- Email:
-
Chen Qiguang
- Office: LSB 222B
- Tel: 3943-7963
- Email:
Time and Venue
- Lecture: Tu 4:30PM - 6:15PM (Mong Man Wai Bldg 710); Th 1:30PM - 2:15PM (Lee Shau Kee Building LT4)
- Tutorial: Th 12:30PM - 1:15PM (Lee Shau Kee Building LT4)
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
- Lecture 1: Revision of 1030/1038
- Lecture 2: Replacement Theorem and Direct Sum
- Lecture 3: Dimension of direct sum, direct product and quotient space
- Lecture 4: More about quotient space
- Lecture 5: Existence of basis using Zorn’s lemma and linear transformation (1)
- Lecture 6: Linear Transformation (2)
- Lecture 7: Matrix representation of linear transformation
- Lecture 8: Invertibility and Isomorphism
- Lecture 9: Isomorphism, Space of linear transformation, change of coordinates
- Lecture 10: Dual space (1)
- Lecture 11: Dual map, Diagonalizibility, Eigenvalues and Eigenvectors
- Lecture 12: Eigenspaces, algebraic multiplicities, geometric multiplicities and diagonalizability
- Lecture 13: Conditions for diagonalizability , T-invariant subspaces (1)
- Lecture 14: T-invariance subspaces (2), Cayley-Hamilton Theorem, Inner product space
Class Notes
- Course outline
- Class note 1
- Class note 2
- Class note 3
- Class note 4
- Class note 5
- Class note 6
- Class note 7
- Class note 8
- Class note 9
- Class note 10
- Class note 11
- Class note 12
- Class note 13
- Class note 14
- Class note 15
Tutorial Notes
- Tutorial 1(Sep 12)
- Tutorial 2(Sep 19)
- Solution to exercise in Tutorial1&2
- Tutorial 3（October 3）
- Tutorial 4 (October 10) (revised)
- Tutorial 5 (October 24) (not completed)
Assignments
- Assignment 1 (Due on Sept. 24 before 23:59)
- Assignment 2 (Due on Oct. 14 before 23:59)
- Assignment 3 (Due on Nov 5 before 23:59)
Quizzes and Exams
Solutions
Assessment Scheme
| Homework | 15% | |
| Midterm (October 17, 12:30pm-2:15pm in class) | 35% | |
| Final (TBA) | 50% |
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: October 30, 2024 15:50:30