{"id":28669,"date":"2023-01-04T14:30:55","date_gmt":"2023-01-04T06:30:55","guid":{"rendered":"https:\/\/www.fst.um.edu.mo\/personal\/?page_id=28669"},"modified":"2023-01-04T14:40:51","modified_gmt":"2023-01-04T06:40:51","slug":"mathexperiment","status":"publish","type":"page","link":"https:\/\/www.fst.um.edu.mo\/personal\/liluo\/mathexperiment\/","title":{"rendered":"Mathematics Experiments"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Coordinating Unit:<\/td>\nDepartment of Mathematics, Faculty of Science and Technology<\/td>\n<\/tr>\n
Supporting Unit(s):<\/td>\nNil<\/td>\n<\/tr>\n
Course Code:<\/td>\n<\/td>\nYear of Study:<\/td>\n3<\/td>\n<\/tr>\n
Course Title:<\/td>\nMathematics Experiments<\/td>\n<\/tr>\n
Compulsory\/Elective:<\/td>\nElective<\/td>\n<\/tr>\n
Course Prerequisites:<\/td>\nNumerical Analysis, Partial Differential Equations<\/td>\n<\/tr>\n
Prerequisite Knowledge:<\/td>\nCalculus, some basic knowledge of linear algebra, numerical analysis, and differential equations<\/td>\n<\/tr>\n
Duration:<\/td>\nOne semester<\/td>\nCredit Units:<\/td>\n3<\/td>\n<\/tr>\n
Class\/Laboratory Schedule:<\/td>\nThree hours of lecture and one hour of tutorial per week.<\/td>\n<\/tr>\n
Laboratory\/Software Usage:<\/td>\nMatlab<\/td>\n<\/tr>\n
Course Description:<\/td>\n\n

This course presents programming techniques with Matlab for numerical analysis and solutions to differential equations. It covers<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Programming with Matlab<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Application of Matlab to root finding, data interpolation, and numerical integration\/differentiation<\/p>\n

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

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Finite difference methods for partial differential equations (elliptic, parabolic, hyperbolic equations)<\/p>\n

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

Course Objectives:<\/td>\n\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Develop basic programming skills with Matlab<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Be able to use Matlab for basic numerical analysis problems<\/p>\n

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

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

Learning Outcomes (LOs):<\/td>\n\n

Understand the fundamentals of<\/p>\n

1.\u00a0\u00a0\u00a0\u00a0\u00a0 basic usage of Matlab<\/p>\n

2.\u00a0\u00a0\u00a0\u00a0\u00a0 numerical analysis by using Matlab;<\/p>\n

3.\u00a0\u00a0\u00a0\u00a0\u00a0 numerical methods for ordinary differential equations;<\/p>\n

4.\u00a0\u00a0\u00a0\u00a0\u00a0 finite difference methods for elliptic partial differential equations;<\/p>\n

5.\u00a0\u00a0\u00a0\u00a0\u00a0 finite difference methods for parabolic \u00a0partial differential equations;<\/p>\n

6.\u00a0\u00a0\u00a0\u00a0\u00a0 finite difference methods for hyperbolic partial differential equations;<\/p>\n<\/td>\n<\/tr>\n

\n

Texts & References:<\/p>\n

\u00a0<\/em><\/p>\n

(* recommended textbook(s))<\/em><\/p>\n<\/td>\n

\n

* \u201cNumerical Solution of Differential Equations: Introduction to Finite Difference and Finite Element Methods\u201d by Zhilin Li, Zhonghua Qiao, and Tao Tang.<\/p>\n

References:<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u201cNumerical Solution of Ordinary Differential Equations\u201d by Kendall Atkinson, Weimin Han, David Stewart.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u201cProgramming for Computations \u2013 MATLAB\/Octave\u201d by Svein Linge, Hans Petter Langtangen, Springer, 2016.<\/p>\n

\u00b7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u201cNumerical Methods Using MATLAB, 4th edition\u201d by George Lindfield, John Penny, 2019.<\/p>\n<\/td>\n<\/tr>\n

Student Assessment:<\/td>\n\n

Assignments: 35%<\/p>\n

Midterm: 20%<\/p>\n

Final examination: 45%<\/p>\n<\/td>\n<\/tr>\n

<\/td>\n\u221a \u00a0\u00a0 Assignments, quizzes, tests, midterm and final examination.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
Course Content:<\/p>\n

(topic outline)<\/td>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Week no.<\/td>\nTopics<\/td>\nAssignment no.<\/td>\nLO no.<\/td>\n<\/tr>\n
1<\/td>\nProgramming with Matlab: basic plotting, matrix\/array operation<\/td>\n<\/td>\n1<\/td>\n<\/tr>\n
2<\/td>\nProgramming with Matlab: M-file\/scripts, control flow and operators<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n
3<\/td>\nNumerical analysis: root finding, interpolation<\/td>\n2<\/td>\n2<\/td>\n<\/tr>\n
4<\/td>\nNumerical analysis: Integration, differentiation<\/td>\n\u00a03<\/td>\n2<\/td>\n<\/tr>\n
5<\/td>\n\u00a0Explicit and implicit methods for ordinary differential equations.<\/td>\n<\/td>\n3<\/td>\n<\/tr>\n
6<\/td>\n\u00a0High order methods for ordinary differential equations.<\/td>\n4<\/td>\n3<\/td>\n<\/tr>\n
7<\/td>\nFinite difference methods for one-dimensional boundary value problems.<\/td>\n<\/td>\n4<\/td>\n<\/tr>\n
<\/td>\nMidterm<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
8<\/td>\nLocal truncation error, consistency, stability, and convergence for finite difference methods.<\/p>\n

The ghost-point method.<\/td>\n

5<\/td>\n4<\/td>\n<\/tr>\n
9<\/td>\nFinite difference methods for two-dimensional elliptic partial differential equations.<\/td>\n<\/td>\n4<\/td>\n<\/tr>\n
10<\/td>\nIterative methods for solving sparse linear systems.<\/td>\n6<\/td>\n4<\/td>\n<\/tr>\n
11<\/td>\nFinite difference methods for parabolic\u00a0partial differential equations.<\/td>\n7<\/td>\n5<\/td>\n<\/tr>\n
13<\/td>\nFinite difference methods for first-order hyperbolic partial differential equations.<\/td>\n<\/td>\n6<\/td>\n<\/tr>\n
14<\/td>\nFinite difference methods for second-order hyperbolic partial differential equations.<\/td>\n8<\/td>\n6<\/td>\n<\/tr>\n
TBA<\/td>\nFinal Examination <\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Coordinating Unit: Department of Mathematics, Faculty of Science and Technology Supporting Unit(s): Nil Course Code: Year of Study: 3 Course Title: Mathematics Experiments Compulsory\/Elective: Elective Course Prerequisites: Numerical Analysis, Partial Differential Equations Prerequisite Knowledge: Calculus, some basic knowledge of linear algebra, numerical analysis, and differential equations Duration: One semester Credit Units: 3 Class\/Laboratory Schedule: Three … <\/p>\n

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