Matlab Programming for Numerical Computation

COURSE LAYOUT

The course will be covered in eight modules. Various aspects of MATLAB programming for numerical computation will be covered in these modules, with each module dedicated to on equivalent numerical topic. Each module will be covered in one week, with 2–2.5 hours lectures per week. There will be self-study problems at the end of several of these lectures. Assignments will also be posted periodically.

Module 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 Lecture 1-1 Basics of MATLAB programming Lecture 1-2 Array operations in MATLAB Lecture 1-3 Loops and execution control Lecture 1-4 Working with files: Scripts and Functions Lecture 1-5 Plotting and program output

Module 2: Approximations and Errors

Taylor’s / Maclaurin series expansion of some functions will be used to introduce approximations and errors in computational methodsLecture 2-1 Defining errors and precision in numerical methodsLecture 2-2 Truncation and round-off errorsLecture 2-3 Error propagation, Global and local truncation errors

Module 3: 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.Lecture 3-1 Numerical Differentiation in single variableLecture 3-2 Numerical differentiation: Higher derivativesLecture 3-3 Differentiation in multiple variablesLecture 3-4 Newton-Cotes integration formulaeLecture 3-5 Multi-step application of Trapezoidal ruleLecture 3-6 MATLAB functions for integration

Module 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.Lecture 4-1 Linear algebra in MATLABLecture 4-2 Gauss EliminationLecture 4-3 LU decomposition and partial pivotingLecture 4-4 Iterative methods: Gauss SiedelLecture 4-5 Special Matrices: Tri-diagonal matrix algorithm

Module 5: Nonlinear Equations

After introduction to bisection rule, this module primarily covers Newton-Raphson method and MATLAB routines fzero and fsolve.Lecture 5-1 Nonlinear equations in single variableLecture 5-2 MATLAB function fzero in single variableLecture 5-3 Fixed-point iteration in single variableLecture 5-4 Newton-Raphson in single variableLecture 5-5 MATLAB function fsolve in single and multiple variablesLecture 5-6 Newton-Raphson in multiple variables

Module 6: Regression and Interpolation

The focus will be practical ways of using linear and nonlinear regression and interpolation functions in MATLAB.Lecture 6-1 IntroductionLecture 6-2 Linear least squares regression(including lsqcurvefit function)Lecture 6-3 Functional and nonlinear regression (including lsqnonlin function)Lecture 6-4 Interpolation in MATLAB using spline and pchip

Module 7: Ordinary Differential Equations (ODE) – Part 1

Explicit ODE solving techniques in single variable will be covered in this module.Lecture 7-1 Introduction to ODEs; Implicit and explicit Euler’s methodsLecture 7-2 Second-Order Runge-Kutta MethodsLecture 7-3 MATLAB ode45 algorithm in single variableLecture 7-4 Higher order Runge-Kutta methodsLecture 7-5 Error analysis of Runge-Kutta method

Module 8: Ordinary Differential Equations (ODE) – Practical aspects

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.Lecture 8-1 MATLAB ode45 algorithm in multiple variablesLecture 8-2 Stiff ODEs and MATLAB ode15s algorithmLecture 8-3 Practical example for ODE-IVPLecture 8-4 Solving transient PDE using Method of Lines
Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.