Instructor

   Dr. Luo Li

   Email: liluo@um.edu.mo

   Teaching Assistant

   Mr. Ma Tianhao

   Email: yc17444@um.edu.mo

   Course Slides

Coordinating Unit Department of Mathematics, Faculty of Science and Technology
Course Code MATH3014
Course Title Topics in Applied Mathematics

(Numerical Methods for Differential Equations)
Lecture Time Monday   Thursday    14:30-15:45
Lab Time Wednesday    10:30-11:20
Class Room E11-1040
Compulsory/Elective Elective
Credit Units 3
Duration One semester
Course Prerequisites MATH1001, MATH2007
Prerequisite Knowledge Calculus, some basic knowledge of linear algebra, numerical analysis, and differential equations
Class Schedule 2.5 hours of lecture and 45 mins of tutorial per week.
Laboratory/Software Usage Matlab
Course Description This course presents mathematical and computational fundamentals of the numerical solution for scientific problems. It covers

·         Explicit and implicit methods for ordinary differential equations

·         Finite difference methods for partial differential equations

·         Finite element methods for elliptic equations

·         Consistency, convergence, stability of numerical methods

·         Solution of linear systems

·         Programming with Matlab
Course Objectives ·         Understand the fundamental principles of numerical methods for differential equations

·         Familiar with numerical schemes for solving scientific problems

·         Develop basic programming skills
Learning Outcomes ·         Understand numerical methods and how they are used to obtain approximate solution to differential equations

·         Analyze the accuracy of numerical methods.

·         Implement numerical methods on computers.

·         Write well-documented software.
Textbook

 

 “Numerical Solution of Differential Equations: Introduction to Finite Difference and Finite Element Methods” by Zhilin Li, Zhonghua Qiao, and Tao Tang.
References “Numerical Solution of Ordinary Differential Equations” by Kendall Atkinson, Weimin Han, David Stewart.

“Finite Difference Methods for Ordinary and Partial Differential Equations” by Randy LeVeque.

“Introduction to Matlab for Engineering Students” by David Houcque.
Student Assessment Assignments: 20%

Midterm examination: 20%

Final examination: 60%
Pedagogical Methods 1.       Lecture

In the lectures, the instructor will motivate the basic methods and present the derivation, formulation, and analysis of numerical methods with sample codes. Students are encouraged to preview the materials before the lecture.

2.       Tutorial

In tutorial classes, the teaching assistant will work on sample problems that aim to enhance the understanding of the lecture materials and ability to solve practical problems. Students are encouraged to complete the remaining excises afterwards.

3.       Exercise

In the assignments, students will be asked to solve some problems and present one’s results in a written report.
Course Content
Week No. Topics Assignment No.
1-3 Explicit and implicit methods for ordinary differential equations

local/global truncation error, stability, convergence

 1
4-5 Finite difference methods for one-dimensional boundary value problems 2
6-7 Finite difference methods for two-dimensional elliptic partial differential equations 3
8 Midterm Project
9-10 Finite difference methods for parabolic  partial differential equations 4
11-12 Finite difference methods for hyperbolic partial differential equations 5
12-13 Finite element methods for one-dimensional boundary value problems
TBA Final examination