Numerical Methods by Farihah Noushene M.B.A

NUMERICAL METHODS has been written in accordance with the latest syllabus (Regulation 2017) of Anna University, Tamilnadu for B.E/B.Tech students. This book contains five chapters.

Chapter 1. SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS - Solution of algebraic and transcendental equations - Fixed point iteration method - Newton Raphson method- Solution of linear system of equations - Gauss elimination method - Pivoting - Gauss Jordan method - Iterative methods of Gauss Jacobi and Gauss Seidel - Matrix inversion by Gauss Jordan method - Eigen values of a matrix by power method

Chapter 2. INTERPOLATION AND APPROXIMATION - Interpolation with unequal intervals - Lagrange's interpolation - Newton's divided difference interpolation - Cubic Splines - Interpolation with equal intervals - Newton's forward and backward difference formulae

Chapter 3. NUMERICAL DIFFERENTIATION AND INTEGRATION -Approximation of derivatives using interpolation polynomials- Numerical integration by trapezoidal and Simphson's one by third rule and three by eight rules, Romberg method - Two and three point Gaussian quadrature formulas - Double integrals using trapezoidal and Simphson's rules

Chapter 4. INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS - Single Step methods - Taylor's series method - Euler's method - Modified Euler's method - Fourth order Runge-Kutta method for solving first order equations - Multi step methods - Milne's and Adams-Bashforth predictor corrector methods for solving first order equations

Chapter 5. BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS- Finite difference methods for solving two-point linear boundary value problems - Finite difference techniques for the solution of two dimensional Laplace's and Poisson's equations on rectangular domain - One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods-One dimensional wave equation by explicit method

Each unit contains a number of worked examples exclusively from Anna University semester question papers to illustrate the concept and formulae discussed. This book covers the past 20 years of Anna University examination questions and GATE questions with detailed explanations. The examples identified with year and semester. The book can serve as a 1-stop guide to numerical methods for all the branches on Engineering including Computer Science, Electronics, Electrical, Mechanical and Civil Engineering.

Suggestions for improvement of the text and intimation of misprints will be thankfully acknowledged.


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