## 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, initial-value problem for ordinary differential equations, boundary-value problems of second order partial differential equations and solution of difference equations with constant coefficient.

1. Cover
2. Title Page
3. Contents
4. Preface
6. Acknowledgements
7. CHAPTER 1 ERRORS IN NUMERICAL COMPUTATIONS
1. 1.0. Introduction
2. 1.1. Accuracy of Numbers
3. 1.2. Errors and their Analysis
4. 1.3. A General Formula for Error
5. 1.4. Error in Series Approximation
8. CHAPTER 2 SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS
1. 2.0. Introduction
2. 2.1. Bisection Method or Bolzano Method
3. 2.2. Method of False Position or ­Regula-Falsi (in Latin)
4. 2.3. The Secant Method or the Chord Method
5. 2.4. The Method of Iteration or Fixed Point Iteration: x = f (x) Method
6. 2.5. Newton-Raphson Method or Newton’s Method of Finding a Root of f(x) = 0
7. 2.6. Generalised Newton-Raphson Method or Modified Newton’s Method
8. 2.7. Ramanujan’s Method
9. 2.8. Muller’s Method
10. 2.9. Chebyshev’s Method
11. 2.10. Convergence of Iteration Methods
12. 2.11. Newton-Raphson Method for Non-Linear Equations in Two Variables
13. 2.12 Solution of Polynomial Equations
9. CHAPTER 3 SOLUTION OF SYSTEM OF LINEAR ALGEBRAIC EQUATIONS
1. 3.0. Introduction
2. 3.1. Direct Methods
3. 3.2. Iterative Methods
4. 3.3. Eigen Value Problem
5. 3.4. Method of Factorisation or Method of Triangularisation
10. CHAPTER 4 POLYNOMIAL INTERPOLATION
1. 4.0. Introduction
2. 4.1. Finite Difference Operators
3. 4.2. Interpolation with Equally Spaced Arguments or Interpolation with Equal Intervals
4. 4.3. Central Difference Interpolation Formulae
5. 4.4. Interpolation with Unequal Intervals
6. 4.5. Errors in Interpolation Formulae
7. 4.6. Interpolation with a Cubic Spline
11. CHAPTER 5 INVERSE INTERPOLATION
1. 5.0. Introduction
2. 5.1. Lagrange’s Inverse Interpolation Formula
3. 5.2. Successive Approximation Method or Iteration Method
4. 5.3. Reversion of Series Method
12. CHAPTER 6 NUMERICAL DIFFERENTIATION
1. 6.0. Introduction
2. 6.1. Numerical Differentiation
3. 6.2. Maxima and Minima of Tabulated Function
13. CHAPTER 7 NUMERICAL INTEGRATION
1. 7.0. Introduction
3. 7.2. Trapezoidal Rule
4. 7.3. Simpson’s Rule or Simpson’s Rule
5. 7.4. Simpson’s Rule
6. 7.5. Boole’s Rule
7. 7.6. Weddle’s Rule
8. 7.7. Error in Numerical Integration Formulae
9. 7.8. Romberg’s Method for Integration
10. 7.9. Two and Three Point Gaussian Quadrature Formulae
11. 7.10. Euler-Maclaurin Formula for Numerical Integration
12. 7.11. Double Integration
14. CHAPTER 8 CURVE FITTING
1. 8.0. Introduction
2. 8.1. Method of Least Squares
3. 8.2. Method of Group Averages
4. 8.3. Method of the Sum of Exponentials
5. 8.4. Method of Moments
15. CHAPTER 9 INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
1. 9.0. Introduction
2. 9.1. Taylor’s Series Method
3. 9.2. Euler’s Method and Modified Euler’s Method
4. 9.3. Runge-Kutta Method (R-K Method)
5. 9.4. Runge-Kutta Method for the Solution of Simultaneous Equations and Second Order Equations
6. 9.5. Milne’s Predictor–Corrector Method
7. 9.6. Adam’s Predictor and Corrector Method
8. 9.7. Picard’s Method
16. CHAPTER 10 BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATION
1. 10.0. Introduction
2. 10.1 Finite Difference Methods for Solution of Second Order Ordinary Differential Equations
3. 10.2. Numerical Solution of Partial Differential Equations
4. 10.3. One Dimensional Heat Equation
5. 10.4. One-Dimensional Wave Equation
17. CHAPTER 11 DIFFERENCE EQUATIONS
1. 11.0 Introduction
2. 11.1 Linear Difference Equation
3. 11.2 Solution of a Difference Equation
4. 11.3 Formation of a Difference Equation
5. 11.4. Linear Homogeneous Difference Equation with Constant Coefficients
6. 11.5. Some Basic Results of Difference Operator to Solve Difference Equations
7. 11.6. Non-Homogeneous Linear Difference Equations with Constant Coefficients
8. 11.7. First Order Linear Difference Equation with Variable Coefficients