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Swayam Central

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/).

INDUSTRY SUPPORT : Nill

Learners enrolled: 2192

SUMMARY

Course Status : Upcoming
Course Type : Elective
Duration : 8 weeks
Start Date : 27 Jan 2020
End Date : 20 Mar 2020
Exam Date : 29 Mar 2020
Enrollment Ends : 03 Feb 2020
Category :
  • Multidisciplinary
  • Level : Undergraduate/Postgraduate
    This is an AICTE approved FDP course

    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

    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:

    INSTRUCTOR BIO

    Prof. Niket Kaisare

    IIT Madras
    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/

    COURSE CERTIFICATE

    • The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
    • The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
    Date and Time of Exams: 29th March 2020, Morning session 9am to 12 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. If there are any changes, it will be mentioned then.
    • Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

    CRITERIA TO GET A CERTIFICATE:
    • Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments
     given in the course. 
    • Exam score = 75% of the proctored certification exam score out of 100
    • Final score = Average assignment score + Exam score

    YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. 
    • If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
    • 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.
    • Only the e-certificate will be made available. Hard copies will not be dispatched.

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