Matlab Programming for Numerical Computation

Course Outline

The course will be covered in twelve modules. Various aspects of MATLAB programming for numerical computation will be covered in these modules, with each module dedicated to an equivalent numerical topic. There will be self-study problems and graded assignment problems given each week, which are to be solved using MATLAB. The course plan is:

1. Introduction to MATLAB Programming: This module will introduce the students to MATLAB programming through a few examples. Students who have used MATLAB are still recommended to do this module, as it introduces MATLAB in context of how we use it in this course
2. Building your Code with MATLAB: This module covers MATLAB Script and Function files, loops, execution control, best-practices for MATLAB functions and tips on how to debug a MATLAB code.
3. Approximations and Errors: Taylor’s / Maclaurin series expansion of some functions will be used to introduce approximations and errors in computational methods
4. Linear Equations: The focus of this module is to do a quick introduction of most popular numerical methods in linear algebra, and use of MATLAB to solve practical problems.
   
5. Nonlinear Equations: After introduction to bisection rule, this module primarily covers Newton-Raphson method and MATLAB routines fzero and fsolve.
6. Numerical Differentiation and Integration: Methods of numerical differentiation and integration, trade-off between truncation and round-off errors, error propagation and MATLAB functions for integration will be discussed.

7. Ordinary Differential Equations (ODE): Explicit ODE solving techniques in single variable will be covered in this module.

8. ODE-IVP in Multiple Variables: This module will cover ODE solving in multiple variables, stiff systems, and practical problems. The importance of ODEs in engineering is reflected by the fact that two modules are dedicated to ODEs.

9. Regression and Interpolation: The focus will be practical ways of using linear and nonlinear regression and interpolation functions in MATLAB.

10. ODE-BVP and DAE: ODE-Boundary Value Problems; Differential Algebraic Equations

11. Partial Differential Equations (PDEs): Practical ways of solving Hyperbolic and Parabolic PDEs

12. Bringing it all together: Optimization andSolving interesting computational problems by bringing together multiple concepts

Update: Based on feedback from previous students, Final Exam will be based on the material covered in the first nine weeks of the course. Assignments will continue to be given in the last three weeks. This allows learners to "digest" the material and perform well in the exam.

This course was first introduced as an eight-week course in 2016. With feedback from students, this course was expanded to twelve-week (three credits) course in 2023. Some new aspects have been introduced and additional video lectures have been added to better explain some important concepts.

Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.