Instructor
Dr. Luo Li
Email: liluo@um.edu.mo
Teaching Assistant
Mr. Ma Tianhao
Email: yc17444@um.edu.mo
| Coordinating Unit | Department of Mathematics, Faculty of Science and Technology | ||||||||||||||||||||||||||||||
| Course Code | MATH3014 | ||||||||||||||||||||||||||||||
| Course Title | Topics in Applied Mathematics
(Numerical Methods for Differential Equations) |
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| 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 |
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| Course Objectives | · Understand the fundamental principles of numerical methods for differential equations
· Familiar with numerical schemes for solving scientific problems · Develop basic programming skills |
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| 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. |
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| Textbook
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“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. |
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| Student Assessment | Assignments: 20%
Midterm examination: 20% Final examination: 60% |
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| 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. |
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| Course Content |
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