MATLAB is a popular language for numerical computation. This course introduces students to MATLAB programming, and demonstrate it’s use for scientific computations. The basis of computational techniques are expounded through various coding examples and problems, and practical ways to use MATLAB will be discussed. The objective of this course is to introduce undergraduate students to computational methods using MATLAB. At the end of this course, a student would: Learn basics of MATLAB programmingGet introduced to numerical methods for engineering problemsWill be able to use MATLAB to solve computational problems
SOFTWARE USEDWe will use MATLAB in this course. Course lectures, practice problems and assignments will be given using MATLAB. MATLAB Online is a fully-featured browser-based version of MATLAB. With support from MathWorks, access to MATLAB Online is provided to all the enrolled students for the duration of this course. INTENDED AUDIENCE :This course is targeted towards scientists and engineers interested in using MATLAB programming for numerical computations. Examples taken in this course will be of generic interest to a wide range of students.This is a hands-on (like a laboratory) elective course. Intended audience include undergraduates, people with BE / ME / MS / MSc degrees; The course may be useful for PhD students also PRE-REQUISITES :The students for this course are expected to know basics of linear algebra and calculus. These are covered in Introductory Math course(s) for Engineers (typically done in first year).This is intended to be practical (laboratory) course. Some prior background in programming will be useful, though not required. Likewise, students who have either completed or are currently doing “Numerical Methods” / “Computational Techniques” will find it easier to follow this course. Theoretical aspects of methods covered in this lab can be found in NPTEL course on “Computational Techniques” (http://nptel.ac.in/courses/103106074/).
INDUSTRY SUPPORT : Nill
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
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.