Book description
A text book designed exclusively for undergraduate students, Numerical Analysis presents the theoretical and numerical derivations amply supported by rich pedagogy for practice. With exhaustive theory to reinforce practical computations, the book delves into the concepts of errors in numerical computation, algebraic and transcendental equations, solution of linear system of equation, curve fitting, initialvalue problem for ordinary differential equations, boundaryvalue problems of second order partial differential equations and solution of difference equations with constant coefficient.
Table of contents
 Cover
 Title Page
 Contents
 Preface
 About the Authors
 Acknowledgements
 CHAPTER 1 ERRORS IN NUMERICAL COMPUTATIONS

CHAPTER 2 SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS
 2.0. Introduction
 2.1. Bisection Method or Bolzano Method
 2.2. Method of False Position or RegulaFalsi (in Latin)
 2.3. The Secant Method or the Chord Method
 2.4. The Method of Iteration or Fixed Point Iteration: x = f (x) Method
 2.5. NewtonRaphson Method or Newton’s Method of Finding a Root of f(x) = 0
 2.6. Generalised NewtonRaphson Method or Modified Newton’s Method
 2.7. Ramanujan’s Method
 2.8. Muller’s Method
 2.9. Chebyshev’s Method
 2.10. Convergence of Iteration Methods
 2.11. NewtonRaphson Method for NonLinear Equations in Two Variables
 2.12 Solution of Polynomial Equations
 Short Answer Questions
 CHAPTER 3 SOLUTION OF SYSTEM OF LINEAR ALGEBRAIC EQUATIONS

CHAPTER 4 POLYNOMIAL INTERPOLATION
 4.0. Introduction
 4.1. Finite Difference Operators
 4.2. Interpolation with Equally Spaced Arguments or Interpolation with Equal Intervals

4.3. Central Difference Interpolation Formulae
 4.3.1 Gauss’s Forward Formula for Interpolation
 Worked Examples
 4.3.2 Gauss’s Backward Formula for Interpolation
 Worked Examples
 Exercises 4.3
 4.3.3 Stirling’s Formula for Interpolation
 Worked Examples
 4.3.4 Bessel’s Formula for Interpolation
 Worked Examples
 4.3.5 LaplaceEverett Formula for Interpolation
 Worked Examples
 Exercises 4.4
 4.4. Interpolation with Unequal Intervals
 4.5. Errors in Interpolation Formulae
 4.6. Interpolation with a Cubic Spline
 Short Answer Questions
 CHAPTER 5 INVERSE INTERPOLATION
 CHAPTER 6 NUMERICAL DIFFERENTIATION

CHAPTER 7 NUMERICAL INTEGRATION
 7.0. Introduction
 7.1. A General Quadrature Formula or NewtonCotes Quadrature Formula
 7.2. Trapezoidal Rule
 7.3. Simpson’s Rule or Simpson’s Rule
 7.4. Simpson’s Rule
 7.5. Boole’s Rule
 7.6. Weddle’s Rule
 7.7. Error in Numerical Integration Formulae
 7.8. Romberg’s Method for Integration
 7.9. Two and Three Point Gaussian Quadrature Formulae
 7.10. EulerMaclaurin Formula for Numerical Integration
 7.11. Double Integration
 Short Answer Questions
 CHAPTER 8 CURVE FITTING

CHAPTER 9 INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
 9.0. Introduction
 9.1. Taylor’s Series Method
 9.2. Euler’s Method and Modified Euler’s Method
 9.3. RungeKutta Method (RK Method)
 9.4. RungeKutta Method for the Solution of Simultaneous Equations and Second Order Equations
 9.5. Milne’s Predictor–Corrector Method
 9.6. Adam’s Predictor and Corrector Method
 9.7. Picard’s Method
 Short Answer Questions
 CHAPTER 10 BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATION

CHAPTER 11 DIFFERENCE EQUATIONS
 11.0 Introduction
 11.1 Linear Difference Equation
 11.2 Solution of a Difference Equation
 11.3 Formation of a Difference Equation
 11.4. Linear Homogeneous Difference Equation with Constant Coefficients
 11.5. Some Basic Results of Difference Operator to Solve Difference Equations
 11.6. NonHomogeneous Linear Difference Equations with Constant Coefficients
 11.7. First Order Linear Difference Equation with Variable Coefficients
 Short Answer Questions
 Bibliography
Product information
 Title: Numerical Analysis, 1/e
 Author(s):
 Release date: April 2014
 Publisher(s): Pearson Education India
 ISBN: 9789332540804
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