Book description
Numerical Methods is a mathematical tool used by engineers and mathematicians to do scientific calculations. It is used to find solutions to applied problems where ordinary analytical methods fail. This book is intended to serve for the needs of courses in Numerical Methods at the Bachelors' and Masters' levels at various universities.
Table of contents
 Cover
 Title page
 Contents
 Dedication
 Preface
 Chapter 1. Preliminaries

Chapter 2. NonLinear Equations
 2.1 Classification of Methods
 2.2 Approximate Values of the Roots
 2.3 Bisection Method (Bolzano Method)
 2.4 Regula–Falsi Method
 2.5 Convergence of Regula–Falsi Method
 2.6 Newton–Raphson Method
 2.7 Square Root of a Number Using Newton–Raphson Method
 2.8 Order of Convergence of Newton–Raphson Method
 2.9 Fixed Point Iteration
 2.10 Convergence of Iteration Method
 2.11 Square Root of a Number Using Iteration Method
 2.12 Sufficient Condition for the Convergence of Newton–Raphson Method
 2.13 Newton’s Method for Finding Multiple Roots
 2.14 Newton–Raphson Method for Simultaneous Equations
 2.15 Graeffe’s Root Squaring Method
 2.16 Muller’s Method
 2.17 Bairstow Iterative Method
 Exercises
 Chapter 3. Linear Systems of Equations
 Chapter 4. Eigenvalues and Eigenvectors

Chapter 5. Finite Differences and Interpolation
 5.1 Finite Differences
 5.2 Factorial Notation
 5.3 Some More Examples of Finite Differences
 5.4 Error Propagation
 5.5 Numerical Unstability
 5.6 Interpolation
 5.7 Use of Interpolation Formulae
 5.8 Interpolation with UnequalSpaced Points
 5.9 Newton’s Fundamental (Divided Difference) Formula
 5.10 Error Formulae
 5.11 Lagrange’s Interpolation Formula
 5.12 Error in Lagrange’s Interpolation Formula
 5.13 Hermite Interpolation Formula
 5.14 Throwback Technique
 5.15 Inverse Interpolation
 5.16 Chebyshev Polynomials
 5.17 Approximation of a Function with a Chebyshev Series
 5.18 Interpolation by Spline Functions
 5.19 Existence of Cubic Spline
 Exercises
 Chapter 6. Curve Fitting

Chapter 7. Numerical Differentiation
 7.1 Centered Formula of Order O(h2)
 7.2 Centered Formula of Order O(h4)
 7.3 Error Analysis
 7.4 Richardson’s Extrapolation
 7.5 Central Difference Formula of Order O(h4) for f″(x)
 7.6 General Method for Deriving Differentiation Formulae
 7.7 Differentiation of a Function Tabulated in Unequal Intervals
 7.8 Differentiation of Lagrange’s Polynomial
 7.9 Differentiation of Newton Polynomial
 Exercises
 Chapter 8. Numerical Quadrature
 Chapter 9. Difference Equations

Chapter 10. Ordinary Differential Equations
 10.1 Initial Value Problems and Boundary Value Problems
 10.2 Classification of Methods of Solution
 10.3 SingleStep Methods
 10.4 Multistep Methods
 10.5 Stability of Methods
 10.6 Second Order Differential Equation
 10.7 Solution of Boundary Value Problems by Finite Difference Method
 10.8 Use of the Formula to Solve Boundary Value Problems
 10.9 Eigenvalue Problems
 Exercises

Chapter 11. Partial Differential Equations
 11.1 Formation of Difference Equation
 11.2 Geometric Representation of Partial Difference Quotients
 11.3 Standard Five Point Formula and Diagonal Five Point Formula
 11.4 Point Jacobi’s Method
 11.5 Gauss–Seidel Method
 11.6 Solution of Elliptic Equation by Relaxation Method
 11.7 Poisson’s Equation
 11.8 Eigenvalue Problems
 11.9 Parabolic Equations
 11.10 Iterative Method to Solve Parabolic Equations
 11.11 Hyperbolic Equations
 Exercises
 Chapter 12. Elements of C Language
 Appendix
 Bibliography
 Copyright
Product information
 Title: Numerical Methods
 Author(s):
 Release date: March 2010
 Publisher(s): Pearson India
 ISBN: 9788131732212
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