Errors in Computer Arithmetic, Normalization.
Bisection, Falsiposition and Newton-Raphson methods for solution of nonlinear equations. Errors in the solutions, Convergence of Solutions.
Gauss, Gauss-Siedel and Iterative methods for system of linear equations. Ill conditioned system, Pivotal Condensation, Matrix Inversion, Eigen-values, Eigen-vector, Diagonalization of Real Symmetric Matrix by Jacobi’s Method.
Introduction to Finite Differences.
Polynomial Interpolation using Newton’s and Lagrange’s formulae.
Numerical Differentiation. Numerical Integration : Trapezoidal Rule, Simpson’s Rule, Weddle’s Rule, Gauss Quadrature Formula. Error in numerical Integration.
Numerical Solution of differential Equations: Picards Method, Taylor’s Series Method, Euler’s Method, Modified Euler’s Method, Runge-Kutta Method, Predictor-Corrector Method.
Suggested Readings:
1. V. Rajaraman, Computer Oriented Numerical Methods, PHI.
2. F.Acton, Numerical Methods that Work, Harper and Row.
3. S. D. Conte and C.D.Boor, Elementary Numerical Analysis, McGraw Hill.
4. S. S. Shastri, “Introductory Methods of Numerical Analysis”, PHI.
C. F. Gerald and P.O. Wheatley, Applied Numerical Analysis, Addision Wesley
- Summary book: Download Link
- Combinatorial Algorithms: Download Link
- Working in Matlab: Link
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