Krishna’s BSc. Obj. Numerical Analysis & Programming in C

SYLLABUS- B.SC. OBJ. NUMERICAL ANALYSIS & PROGRAMMING IN C,

Numerical Analysis

Unit 1
Shift operator, Forward and backward difference operators and their relationships, Fundamental theorem of difference calculus, Interpolation, Newton-Gregory’s forward and backward interpolation formulae.
Unit 2
Divided differences, Newton’s divided difference formula, Lagrange’s interpolation formula, Central differences, Formulae based on central differences : Gauss, Striling’s, Bessel’s and Everett’s interpolation formulae, Numerical differentiation.
Unit 3
Numerical integration, General quadrature formula, Trapezoidal and Simpson’s rules, Weddle’s rule, Cote’s formula, Numerical solution of first order differential equations : Euler’s method, Picard’s method, Runge-Kutta method and Milne’s method, Numerical solution of linear, homogeneous and simultaneous difference equations, Generating function method.
Unit 4
Solution of transcendental and polynomial equations by iteration, bisection, Regula-Falsi and Newton-Raphson methods, Algebraic eigen value problems : Power method, Jacobi’s method, Given’s method, Householder’s method and Q-R method, Approximation : Different types of approximations, Least square polynomial approximation, Polynomial approximation using orthogonal polynomials, Legendre approximation, Approximation with trigonometric functions, exponential functions, rational functions, Chebyshev polynomials. Programming in C
Unit 5
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.