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

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.

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

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/).

**Dr. Niket Kaisare** is an Associate Professor of Chemical Engineering in IIT-Madras. He works in the area of modeling, design and control for energy applications. He has over 7 years of research/teaching experience in academia, and three-year experience in Industrial R&D. He uses computational software, including MATLAB, FORTRAN, Aspen and FLUENT extensively in his research and teaching.

**Faculty web-page:**
http://www.che.iitm.ac.in/~nkaisare/

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**REFERENCE MATERIALS****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:**

http://nptel.ac.in/courses/103106074/**Numerical Methods and Programming:**

http://nptel.ac.in/courses/122106033/

- The exam is optional for a fee.
- Date and Time of Exams:
**31 March 2019(Sunday)** - Time of Exam: Morning session 9am to 2 noon; Afternoon session: 2pm to 5pm
- Registration url: Announcements will be made when the registration form is open for registrations.
- The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.

- Final score will be calculated as: 25% assignment score + 75% final exam score
- 25% assignment score is calculated as 25% of average of best 6 out of 8 assignments
- E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup. It will have the logos of NPTEL and IIT MADRAS. It will be e-verifiable at nptel.ac.in/noc.