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

WeekNo.

Topics

1.

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

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

8.

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

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/).

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