Matlab Programming for Numerical Computation By Prof. Niket Kaisare | IIT Madras
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 programming
Get introduced to numerical methods for engineering problems
Will be able to use MATLAB to solve computational problems
SOFTWARE USED
We 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/).
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 methods
Lecture 2-1 Defining errors and precision in numerical methods
Lecture 2-2 Truncation and round-off errors
Lecture 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 variable
Lecture 3-2 Numerical differentiation: Higher derivatives
Lecture 3-3 Differentiation in multiple variables
Lecture 3-4 Newton-Cotes integration formulae
Lecture 3-5 Multi-step application of Trapezoidal rule
Lecture 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 MATLAB
Lecture 4-2 Gauss Elimination
Lecture 4-3 LU decomposition and partial pivoting
Lecture 4-4 Iterative methods: Gauss Siedel
Lecture 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 variable
Lecture 5-2 MATLAB function fzero in single variable
Lecture 5-3 Fixed-point iteration in single variable
Lecture 5-4 Newton-Raphson in single variable
Lecture 5-5 MATLAB function fsolve in single and multiple variables
Lecture 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 Introduction
Lecture 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 methods
Lecture 7-2 Second-Order Runge-Kutta Methods
Lecture 7-3 MATLAB ode45 algorithm in single variable
Lecture 7-4 Higher order Runge-Kutta methods
Lecture 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 variables
Lecture 8-2 Stiff ODEs and MATLAB ode15s algorithm
Lecture 8-3 Practical example for ODE-IVP
Lecture 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.
BOOKS AND REFERENCES
Textbook:
Fausett L.V. (2007) Applied Numerical Analysis Using MATLAB, 2nd Ed., Pearson Education
Reference Book:
Chapra S.C. and Canale R.P. (2006) Numerical Methods for Engineers, 5th Ed., McGraw Hill
Related NPTEL Video Courses:
Computational Techniques:
Numerical Methods and Programming:
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