Swayam Central

# Numerical Methods for Engineers

By Prof. Niket Kaisare   |   IIT Madras

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

Learners enrolled: 1078

### SUMMARY

 Course Status : Completed Course Type : Core Duration : 12 weeks Start Date : 29 Jul 2019 End Date : 18 Oct 2019 Exam Date : 16 Nov 2019 Category : Multidisciplinary Level : Undergraduate

### 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
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

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

### INSTRUCTOR BIO

Dr. 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 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.

### 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: 16 November 2019, 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 are being discontinued from July 2019 semester and will not be dispatched