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Syllabus for the Exam
 
SECTION A
Solution of Equations: Bisection, Secant, Regula Falsi, Newton’s Method, Roots of Polynomials. Interpolation: Lagrange and Hermite Interpolation, Divided Differences, Difference Schemes, Interpolation Formulas using Difference. Numerical Differentiation. Numerical Quadrature: Newton-Cote’s Formulas, Gauss Quadrature Formulas, Chebychev’s Formulas. 
SECTION B
Linear Equations: Direct Methods for Solving Systems of Linear Equations (Gauss Elimination, LU Decomposition, Cholesky Decomposition), Iterative Methods (Jacobi, Gauss-Seidel, Relaxation Methods). The Algebraic Eigenvalue problem: Jacobi’s Method, Givens’ Method, Householder’s Method, Power Method, QR Method, Lanczos’ Method. Ordinary Differential Equations: Euler Method, Single-step Methods, Runge-Kutta’s Method, Multi-step Methods.