{"id":18886,"date":"2021-12-22T16:05:11","date_gmt":"2021-12-22T08:05:11","guid":{"rendered":"https:\/\/www.fst.um.edu.mo\/personal\/?page_id=18886"},"modified":"2022-08-09T15:35:25","modified_gmt":"2022-08-09T07:35:25","slug":"math3014","status":"publish","type":"page","link":"https:\/\/www.fst.um.edu.mo\/personal\/liluo\/math3014\/","title":{"rendered":"MATH3014"},"content":{"rendered":"

\u00a0 \u00a0Instructor<\/strong><\/span><\/p>\n

\u00a0 \u00a0Dr. Luo Li<\/span><\/p>\n

\u00a0 \u00a0Email: liluo@um.edu.mo<\/span><\/p>\n

\u00a0 \u00a0Teaching Assistant<\/strong><\/span><\/p>\n

\u00a0 \u00a0Mr. Ma Tianhao <\/span><\/p>\n

\u00a0 \u00a0Email: yc17444@um.edu.mo<\/span><\/p>\n

\u00a0 \u00a0Course Slides<\/a><\/strong><\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Coordinating Unit<\/span><\/td>\nDepartment of Mathematics, Faculty of Science and Technology<\/span><\/td>\n<\/tr>\n
Course Code<\/span><\/td>\nMATH3014<\/span><\/td>\n<\/tr>\n
Course Title<\/span><\/td>\nTopics in Applied Mathematics<\/span><\/p>\n

(Numerical Methods for Differential Equations)<\/span><\/td>\n<\/tr>\n

Lecture Time<\/span><\/td>\nMonday\u00a0\u00a0 Thursday\u00a0\u00a0\u00a0 14:30-15:45<\/span><\/td>\n<\/tr>\n
Lab Time<\/span><\/td>\nWednesday\u00a0\u00a0\u00a0 10:30-11:20<\/span><\/td>\n<\/tr>\n
Class Room<\/span><\/td>\nE11-1040<\/span><\/td>\n<\/tr>\n
Compulsory\/Elective<\/span><\/td>\nElective<\/span><\/td>\n<\/tr>\n
Credit Units<\/span><\/td>\n3<\/span><\/td>\n<\/tr>\n
Duration<\/span><\/td>\nOne semester<\/span><\/td>\n<\/tr>\n
Course Prerequisites<\/span><\/td>\nMATH1001, MATH2007<\/span><\/td>\n<\/tr>\n
Prerequisite Knowledge<\/span><\/td>\nCalculus, some basic knowledge of linear algebra, numerical analysis, and differential equations<\/span><\/td>\n<\/tr>\n
Class Schedule<\/span><\/td>\n2.5 hours of lecture and 45 mins of tutorial per week.<\/span><\/td>\n<\/tr>\n
Laboratory\/Software Usage<\/span><\/td>\nMatlab<\/span><\/td>\n<\/tr>\n
Course Description<\/span><\/td>\nThis course presents mathematical and computational fundamentals of the numerical solution for scientific problems. It covers<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Explicit and implicit methods for ordinary differential equations<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Finite difference methods for partial differential equations<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Finite element methods for elliptic equations<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Consistency, convergence, stability of numerical methods<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Solution of linear systems<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Programming with Matlab<\/span><\/td>\n<\/tr>\n

Course Objectives<\/span><\/td>\n\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Understand the fundamental principles of numerical methods for differential equations<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Familiar with numerical schemes for solving scientific problems<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Develop basic programming skills<\/span><\/td>\n<\/tr>\n

Learning Outcomes<\/span><\/td>\n\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Understand numerical methods and how they are used to obtain approximate solution to differential equations<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Analyze the accuracy of numerical methods.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Implement numerical methods on computers.<\/span><\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Write well-documented software.<\/span><\/td>\n<\/tr>\n

Textbook<\/span><\/p>\n

 <\/td>\n

\u201cNumerical Solution of Differential Equations: Introduction to Finite Difference and Finite Element Methods<\/em><\/a>\u201d by Zhilin Li, Zhonghua Qiao, and Tao Tang.<\/span><\/td>\n<\/tr>\n
References<\/span><\/td>\n\u201cNumerical Solution of Ordinary Differential Equations<\/a><\/em>\u201d by Kendall Atkinson, Weimin Han, David Stewart.<\/span><\/p>\n

“Finite Difference Methods for Ordinary and Partial Differential Equations<\/em><\/a>” by Randy LeVeque.<\/span><\/p>\n

\u201cIntroduction to Matlab for Engineering Students<\/em><\/a>\u201d by David Houcque.<\/span><\/td>\n<\/tr>\n

Student Assessment<\/span><\/td>\nAssignments: 20%<\/span><\/p>\n

Midterm examination: 20%<\/span><\/p>\n

Final examination: 60%<\/span><\/td>\n<\/tr>\n

Pedagogical Methods<\/span><\/td>\n1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Lecture<\/span><\/p>\n

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.<\/span><\/p>\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Tutorial<\/span><\/p>\n

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.<\/span><\/p>\n

3.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Exercise<\/span><\/p>\n

In the assignments, students will be asked to solve some problems and present one\u2019s results in a written report.<\/span><\/td>\n<\/tr>\n

Course Content<\/span><\/td>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Week No.<\/span><\/td>\nTopics<\/span><\/td>\nAssignment No.<\/span><\/td>\n<\/tr>\n
1-3<\/span><\/td>\nExplicit and implicit methods for ordinary differential equations<\/span><\/p>\n

local\/global truncation error, stability, convergence<\/span><\/td>\n

1<\/span><\/td>\n<\/tr>\n
4-5<\/span><\/td>\nFinite difference methods for one-dimensional boundary value problems<\/span><\/td>\n2<\/span><\/td>\n<\/tr>\n
6-7<\/span><\/td>\nFinite difference methods for two-dimensional elliptic partial differential equations<\/span><\/td>\n3<\/span><\/td>\n<\/tr>\n
8<\/span><\/td>\nMidterm Project<\/span><\/td>\n<\/td>\n<\/tr>\n
9-10<\/span><\/td>\nFinite difference methods for parabolic \u00a0partial differential equations<\/span><\/td>\n4<\/span><\/td>\n<\/tr>\n
11-12<\/span><\/td>\nFinite difference methods for hyperbolic partial differential equations<\/span><\/td>\n5<\/span><\/td>\n<\/tr>\n
12-13<\/span><\/td>\nFinite element methods for one-dimensional boundary value problems<\/span><\/td>\n<\/td>\n<\/tr>\n
TBA<\/span><\/td>\nFinal examination<\/span><\/td>\n<\/td>\n<\/tr>\n
<\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

\u00a0 \u00a0Instructor \u00a0 \u00a0Dr. Luo Li \u00a0 \u00a0Email: liluo@um.edu.mo \u00a0 \u00a0Teaching Assistant \u00a0 \u00a0Mr. Ma Tianhao \u00a0 \u00a0Email: yc17444@um.edu.mo \u00a0 \u00a0Course 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\u00a0\u00a0 Thursday\u00a0\u00a0\u00a0 14:30-15:45 Lab Time Wednesday\u00a0\u00a0\u00a0 10:30-11:20 … <\/p>\n

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