SYLLABUS- NUMERICAL ANALYSIS & PROGRAMMING IN C, Unit-I
Solution of equations: bisection, Secant, Regula Falsi, Newton Raphson's method,
Roots of polynomials. Interpolation, Lagrange and Hermite interpolation, Divided
differences, Difference schemes, Interpolation formula using differences, Numerical
differentiation.
Unit-II
Numerical Quadrature: Newton Cotes Formulas, Gauss Quadrature Formulas,
Chebyshev's Formulas, Linear equations: Direct method 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.
Unit-III
Numerical solution of Ordinary differential equations: Euler method, single step
methods, Runge-Kutta method, Multi-step methods, Milne-Simpson method, Methods
based on Numerical integration, Methods based on numerical differentiation, boundary
value problems, Eigenvalue problems. Approximation: Different types of approximation,
Least square polynomial approximation, Polynomial approximation using Orthogonal
Polynomials, Approximation with Trigonometrical functions, Exponential functions,
Chebyshev Polynomials, Rational Functions.
Unit-IV
Programming in C: Programmer's model of computer, Algorithms, Data type,
Arithmetic and input/out instruction, Decisions, Control structures, Decision
statements, Logical and conditional operators, Loop case control structures, Functions,
Recursion, Preprocessors, Arrays, Puppetting of strings Structures, Pointers, File
formatting.

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