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Numerical Methods Second Edition  
Published by Vijay Nicole Imprints Private Limited
Publication Date:  Available in all formats
ISBN: 9789394681101

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Table of contents

Biographical note

This revised second edition of Numerical Methods has been written in accordance with the latest syllabus of Anna University, for B.E./B.Tech. students. A solved-problems approach is adopted to learning concepts and hence each chapter has numerous solved examples and exercises.

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This revised second edition of Numerical Methods has been written in accordance with the latest syllabus of Anna University, for B.E./B.Tech. students. A solved-problems approach is adopted to learning concepts and hence each chapter has numerous solved examples and exercises.

Table of contents
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • Chapter 1 Solution of Equations and Eigen Value Problems
    • List of Formulae
    • Introduction
    • Fundamental Theorem of Algebra
    • Intermediate Value Theorem
      • Method of False Position (or) Regula Falsi Methods
      • Newton’s Method of Successive Approximation (or) Newton-Raphson Method
      • Fixed Point Iteration x–g(x) Method
    • Solution of Simultaneous Linear Algebraic Equations
      • Introduction
      • Gauss-Elimination Method
      • Gauss-Jordan Elimination Method
      • Iterative Method (or) Indirect Method
    • Gauss-Jacobi Method
    • Gauss-Seidel Method
    • Inverse of a Matrix by Gauss-Jordan Method
    • Power Method
    • Jacobi Method for Finding Eigen Values
    • Rotation Matrix
      • Extension to Higher Order Symmetric Matrices
      • Two Marks Questions and Answers
  • Chapter 2 Interpolation and Approximation
    • List of Formulae
    • Introduction
    • Interpolation with Unequal Intervals
      • Lagrange’s Interpolation Formula
    • Inverse Interpolation
      • Cubic Spline Interpolation (or) Interpolating with a Cubic Spline
      • Deduction
    • Forward Difference Operator
      • Newton’s Forward Interpolation Formula
    • Backward Differences
      • Newton’s Backward Interpolation Formula
    • Error in Polynomial Interpolation
      • Error in Newton’s Forward Interpolation Formula
      • Error in Newton’s Backward Interpolation Formula
    • Divided Differences
      • Properties of Divided Differences
      • Relation Between Divided Difference and Forward Differences
    • Newton’s Interpolation Formula for Unequal Intervals (or) Newton’s Divided Difference Formula
      • Two Marks Questions and Answers
  • Chapter 3 Numerical Differentiation and Integration
    • List of Formulae
    • Numerical Differentiation
      • Newton’s Forward Difference Formula to Find the Derivative
      • Newton’s Backward Difference Formula to Compute the Derivatives
      • Remarks on Numerical Differentiation
      • Maxima and Minima of a Tabulated Function
    • Numerical Integration
      • Newton-Cote’s Formula (or) A General Quadrature Formula for Equidistant Ordinates
      • Trapezoidal Rule
      • Simpson’s One-Third Rule
      • Simpson’s Three-Eight Rule
      • Comparison of Trapezoidal, Simpson’s and Romberg’s Method
    • Double Integral
      • Trapezoidal Rule
      • Simpson’s Rule for Double Integration
    • Romberg’s Method
    • Gaussian Quadrature
      • Two Points Gaussian Quadrature
      • Three Points Gaussian Quadrature
      • Two Marks Questions and Answers
  • Chapter 4 Initial Value Problems for Ordinary Differential Equations
    • List of Formulae
    • Introduction
    • Numerical Solution of a Differential Equation
      • Solution by Taylor Series
      • Taylor Series Method for Simultaneous First Order Differential Equations
    • Taylor Series Method for Second Order Differential Equation
    • Euler’s Method
      • Improved Euler Method
      • Modified Euler Method
      • Runge-Kutta Method
      • Second Order Runge-Kutta Method
      • Third Order Runge-Kutta Method
      • Fourth Order Runge-Kutta Method
      • Runge-Kutta Method for Simultaneous First Order Differential Equations
      • Runge-Kutta Method for Second Order Differential Equations
      • Predictor-Corrector Methods
      • Milne’s Predictor-Corrector Formulae
      • Adam-Bashforth (or Adam’s) Predictor-Corrector Method
      • Two Marks Questions and Answers
  • Chapter 5 Boundary Value Problems in Ordinary and Partial Differential Equations
    • List of Formulae
    • Introduction
    • Difference Quotients
    • Graphical Representation of Partial Quotients
    • Classification of Partial Differential Equations of the Second Order
    • Elliptic Equations
      • Solution of Laplace’s Equation
    • Liebmann’s Iteration Process
    • Poisson’s Equation
    • Parabolic Equations
      • Bender-Schmidt Method
    • Crank-Nicholson Difference Method
    • Hyperbolic Equations
    • Solution of Partial Differential Equations by the Method of Relaxation
      • Two Marks Questions and Answers
  • Model Question Papers
  • Solved Question Paper
Biographical note

S Kalavathy is Professor, Department of Mathematics, RMD Engineering College, Chennai. She has over 23 years of experience in teaching Mathematics and has written several books including best sellers on Engineering Mathematics and Operational Research.

M Joice Punitha is Senior Lecturer, Department of Mathematics, RMD Engineering College, Chennai. She has over 8 years of experience in teaching Mathematics. Her areas of interest include Graph Theory and Discrete Mathematics.

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