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. It is a core course for UG.
PRE-REQUISITES
Not Required
INDUSTRIES THAT WILL RECOGNIZE THIS COURSE
TCS, Intel, General Electric, General Motors, ABB, Nuclear Industries, etc.
3587 students have enrolled already!!
COURSE INSTRUCTORS
Dr.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.
Dr.Sanjeev Kumaris 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 PLAN 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 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)
SUGGESTED READING List of reference materials/books/ 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.
MORE DETAILS ABOUT THE COURSE
CERTIFICATION EXAM The exam is optional for a fee. Exams Date : September 24,2017 Time: Shift 1: 9am-12 noon; Shift 2: 2pm-5pm Any one shift can be chosen to write the exam for a course. 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. CERTIFICATE
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 Indian Institute of Technology Roorkee. It will be e-verifiable at nptel.ac.in/noc.
