Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab) = 3:0:1 (3 lectures and 1 two-hour lab weekly)
Prerequisites: Class XII Mathematics
Overview: Numerical Analysis takes up the problems of practical computation that arise in various areas of mathematics, physics and engineering. The focus is on analyzing the numerical methods and algorithms for obtaining approximate solutions, error estimates and rate of convergence, and implementation of computer programs.
- Solving Equations: Iterative methods, Bisection method, Secant method, Newton-Raphson method, Rates of convergence, Roots of polynomials.
- Interpolation: Lagrange and Hermite interpolation, Interpolating polynomials using difference operators.
- Numerical Differentiation: Methods based on interpolation, methods based on finite difference operators.
- Numerical Integration: Newton-Cotes formula, Gauss quadrature, Chebyshev’s formula.
- Systems of Linear Equations: Direct methods (Gauss elimination, Gauss-Jordan method, LU decomposition, Cholesky decomposition), Iterative methods (Jacobi, Seidel, and Relaxation methods)
- Labs: Computational work using C, Python or Matlab.
- E. Suli and D. Mayers, Introduction to Numerical Analysis, Cambridge University Press, 2003.
- R.L. Burden and J.D. Faires, Numerical Analysis, Cengage Learning, 9th Edition, 2010.
- M.K. Jain, S.R.K. Iyengar, and R.K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International Ltd., 1999.
- J.H. Mathews and K. Fink, Numerical Methods using Matlab, PHI Learning, 4th Edition, 2003.