Numerical Methods For Engineers

By Prof. Niket Kaisare | IIT Madras

Learners enrolled: 909 | Exam registration: 39

ABOUT THE COURSE:
The development of fast, efficient and inexpensive computers has significantly increased the range of engineering problems that can be solved reliably. Numerical Methods use computers to solve problems by step-wise, repeated and iterative solution methods, which would otherwise be tedious or unsolvable by hand-calculations. This course is designed to give an overview of numerical methods of interest to scientists and engineers. However, the focus being on the techniques themselves, rather than specific applications, the contents should be relevant to varied fields such as engineering, management, economics, etc.

INTENDED AUDIENCE: First/Second Year UG students in any branch of engineering (or science)

PREREQUISITES: 12th standard Math background

Summary

Course Status :	Completed
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Multidisciplinary Advanced Mechanics Computational Engineering Computational Chemical Engineering
Credit Points :	3
Level :	Undergraduate
Start Date :	24 Jul 2023
End Date :	13 Oct 2023
Enrollment Ends :	07 Aug 2023
Exam Registration Ends :	18 Aug 2023
Exam Date :	28 Oct 2023 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week-1: Introduction & Approximations: Motivation and Applications; Accuracy and precision; Truncation and round-off errors; Binary Number System; Error propagation
Week-2: Linear Systems and Equations: Matrix representation; Cramer’s rule; Gauss Elimination; Matrix Inversion; LU Decomposition;
Week-3: Linear Systems and Equations: Iterative Methods; Relaxation Methods; Eigen Values
Week-4: Algebraic Equations: Bracketing Methods: Introduction to Algebraic Equations; Bracketing methods: Bisection, Reguli-Falsi;
Week-5: Algebraic Equations: Open Methods: Secant; Fixed point iteration; Newton-Raphson; Multivariate Newton’s method
Week-6: Numerical Differentiation: Numerical differentiation; error analysis; higher order formulae
Week-7: Integration and Integral Equations: Trapezoidal rules; Simpson’s rules; Quadrature
Week-8: Regression: Linear regression; Least squares; Total Least Squares;
Week-9: Interpolation and Curve Fitting: Interpolation; Newton’s Difference Formulae; Cubic Splines
Week-10: ODEs: Initial Value Problems: Introduction to ODE-IVP; Euler’s methods; Runge-Kutta methods; Predictor-corrector methods;
Week-11: ODE-IVP (Part-2): Extension to multi-variable systems; Adaptive step size; Stiff ODEs
Week-12: ODEs: Boundary Value Problems: Shooting method; Finite differences; Over/Under Relaxation (SOR)

Books and references

Gupta S.K. (1995) Numerical Methods for Engineers, New Age International
Chapra S.C. and Canale R.P. (2006) Numerical Methods for Engineers, 5th Ed., McGraw Hill

Instructor bio

Prof. Niket Kaisare

IIT Madras

Prof. Niket Kaisare is a Professor of Chemical Engineering in IIT-Madras. He works in the area of modeling, design and control for energy applications. He has over ten 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 TAs:

Sayoni Maiti is a 2nd year PhD student and a PMRF scholar enrolled under the Interdisciplinary Programme of Mathematical Sciences at the Indian Institute of Science (IISc), Bengaluru. She is studying the interface of cancer and type 2 diabetes by understanding the effect of hyperglycemia (a condition prevalent in diabetes) on the growth, survival, and metabolism of cancer cells via both experimental and mathematical modeling techniques.
Student web-page: https://sayonimaiti.wordpress.com/

Rohit Kumar Singh is a 2nd year PhD student enrolled under PMRF scheme at department of Physics, IIT Madras. He's working in the area of Experimental High Energy Physics. His research involves analysing the Heavy Ion collision data from CMS experiment at CERN and understanding the properties of Quark-Gluon Plasma.
Student web-page: https://sites.google.com/smail.iitm.ac.in/rohit-s/home

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: 28 October 2023 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 8 assignments out of the total 12 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.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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