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 hours of lecture and one hour of tutorial per week.
Laboratory/Software Usage: Matlab
Course Description:

This course presents programming techniques with Matlab for numerical analysis and solutions to differential equations. It covers

·        Programming with Matlab

·        Application of Matlab to root finding, data interpolation, and numerical integration/differentiation

·        Explicit and implicit methods for ordinary differential equations

·        Finite difference methods for partial differential equations (elliptic, parabolic, hyperbolic equations)

·        Solution of linear systems
Course Objectives:

·        Develop basic programming skills with Matlab

·        Be able to use Matlab for basic numerical analysis problems

·        Understand the fundamental principles of numerical methods for differential    equations

·        Familiar with numerical schemes for solving scientific problems
Learning Outcomes (LOs):

Understand the fundamentals of

1.      basic usage of Matlab

2.      numerical analysis by using Matlab;

3.      numerical methods for ordinary differential equations;

4.      finite difference methods for elliptic partial differential equations;

5.      finite difference methods for parabolic  partial differential equations;

6.      finite difference methods for hyperbolic partial differential equations;

Texts & References:

 

(* recommended textbook(s))

* “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.

·        “Programming for Computations – MATLAB/Octave” by Svein Linge, Hans Petter Langtangen, Springer, 2016.

·        “Numerical Methods Using MATLAB, 4th edition” by George Lindfield, John Penny, 2019.
Student Assessment:

Assignments: 35%

Midterm: 20%

Final examination: 45%
√    Assignments, quizzes, tests, midterm and final examination.
Course Content:

(topic outline)

  

Week no. Topics Assignment no. LO no.
1 Programming with Matlab: basic plotting, matrix/array operation 1
2 Programming with Matlab: M-file/scripts, control flow and operators 1 1
3 Numerical analysis: root finding, interpolation 2 2
4 Numerical analysis: Integration, differentiation  3 2
5  Explicit and implicit methods for ordinary differential equations. 3
6  High order methods for ordinary differential equations. 4 3
7 Finite difference methods for one-dimensional boundary value problems. 4
Midterm
8 Local truncation error, consistency, stability, and convergence for finite difference methods.

The ghost-point method.

 5 4
9 Finite difference methods for two-dimensional elliptic partial differential equations. 4
10 Iterative methods for solving sparse linear systems. 6 4
11 Finite difference methods for parabolic partial differential equations. 7 5
13 Finite difference methods for first-order hyperbolic partial differential equations. 6
14 Finite difference methods for second-order hyperbolic partial differential equations. 8 6
TBA Final Examination