# Numerical methods

By Prof. Ameeya Kumar Nayak, Prof. Sanjeev Kumar   |   IIT Roorkee
Learners enrolled: 4524

This course is a basic course offered to UG student of Engineering/Science background. It contains solution of system of linear equations, roots of non-linear equations, interpolation, numerical differentiation and integration. It plays an important role for solving various engineering sciences problems.  Therefore, it has tremendous applications in diverse fields in engineering sciences.

INTENDED AUDIENCE: UG students of technical universities/colleges.
PREREQUISITES:          NIL
INDUSTRY SUPPORT:   TCS, Intel, General Electric, General Motors, ABB, Nuclear Industries, etc.
Summary
 Course Status : Completed Course Type : Core Duration : 8 weeks Category : Mathematics Credit Points : 2 Level : Undergraduate Start Date : 26 Aug 2019 End Date : 18 Oct 2019 Exam Date : 16 Nov 2019 IST

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

### Course layout

Week 1: Introduction to significant digits and errors, Solution of system of linear Equations (direct methods, Iterative methods, Ill-conditioned systems)
Week 2: Roots of Nonlinear Equations (Bisection method, Regula-Falsi method, Newton-Raphson method, Fixed point iteration method, convergence criteria
Week 3: Eigenvalues and Eigenvectors, Gerschgorin circle theorem , Jacobi method, Power methods
Week 4: Interpolation (Finite difference operators, difference tables, Newton's Forward/Backward difference)
Week 5: Interpolation ( Central difference  formula's i.e.  Bessel and Stirling’s interpolation formulae, Divided differences, Lagrange interpolation and Newton’s divided   difference interpolation)
Week 6: Numerical Differentiation (Using Forward/ Backward/central difference formula) Week:7 Integration (Trapezoidal and Simpson's rules for integration)
Week 8: Solution of first order and second order ordinary differential equations (Euler method, Euler modified method, Runge-Kutta methods, Milne PC method)

### Books and references

1. Gerald, C. F. and Wheatly, P. O.," Applied Numerical Analysis", 6th Edition, Wesley.
2. Jain, M. K., Iyengar, S. R. K. and Jain, R. K., "Numerical Methods for Scientific and Engineering Computation", New Age Pvt. Pub, New Delhi.
3. Conte, S. D. and De Boor, C., "Elementary Numerical Analysis", Mc Graw Hill Publisher.
4. Krishnamurthy, E. V. & Sen, S. K., "Applied Numerical Analysis", East West Publication.

### Instructor bio

Prof. Ameeya Kumar Nayak  is  Associate  Professor  in  Department  of  Mathematics  at  IIT Roorkee and actively involved in teaching and research in the direction of numerical modeling of fluid flow problems for last ten years. His research interests are in the fundamental understanding of species transport in macro and micro-scale confinements with applications in biomedical devices and micro electro mechanical systems. He has authored and co-authored more than 28 peer-reviewed journal papers, which includes publications in Springer, ASME, American Chemical Society and Elsevier journals. He is also active in writing book chapter with reputed international publication house.

Prof.Sanjeev Kumar is working as an associate professor with  Department of Mathematics, IIT Roorkee. Earlier, he worked as a postdoctoral fellow with Department of Mathematics and Computer Science, University of Udine, Italy and assistant professor with IIT Roorkee. He is actively involved in teaching and research in the area of computational algorithms, inverse problems and image processing. He has published more than 55 papers in various international journals conferences of repute. He has completed a couple of sponsored research projects and written several chapters in reputed books published with Springer and CRC press.

### 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 centers.
• The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
• Date and Time of Exams: 16th 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 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 Roorkee. 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.