Calculus of Finite Differences & Numerical Analysis

SYLLABUS - CALCULUS OF FINITE DIFFERENCE & NUMERICAL ANALYSIS. PROGRAMMING IN C
Programmer’s Model of a Computer, Algorithms, Flow Charts, Data Types, Arithmetic and Input/Output Instructions, Decisions Control Structures, Decision Statements, Logical and Conditional Operators, Loop, Case Control tructures, Functions, Recursions, Preprocessors, Arrays, Puppetting of Strings, Structures, Pointers, File Formating.
NUMERICAL ANALYSIS
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 Differences.
Numerical Differentiation
Numerical Quadrature: Newton-Cote‘s Formulas, Gauss Quadrature Formulas, Chebychev’s Formulas.
Linear Equations: Direct Methods for Solving Systems of Linear Equations (Guass Elimination, LU Decomposition, Cholesky Decomposition), Iterative Methods (Jacobi, Gauss-Seidel, Relaxation Methods).
The Algebraic Eigen Value Problem: Jacobi’s Method, Given’s 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, Milne-Simpson Method, Methods Based on Numerical
Integration, Methods Based on Numerical Differentiation, Boundary Value Problems, Eigen Value Problems.
Approximation: Different Types of Approximation, Least Square Polynomial Approximation, Polynomial Approximation using Orthogonal Polynomials, Approximation with Trigonometric Functions, Exponential Functions, Chebychew Polynomials, Rational Functions.