An Introduction to Numerical Methods. A MATLAB Approach, Second Edition

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This book introduces readers to the theory and applications of the most commonly used techniques for solving numerical problems on a personal computer.

Out of stock

Language ENGLISH
Publish year 2005
Pages 624 pages
ISBN 9781439868997

Description

Updated to reflect the latest version of MATLAB, the second edition of this title introduces the theory and applications of the most commonly used techniques for solving numerical problems on a computer. It covers a wide range of useful algorithms, each presented with full details so that readers can visualize and interpret each step.

Features

– A new chapter on numerical optimization
– New sections on finite elements
– More exercises and applied problems in each chapter
– MATLAB incorporated as an integral part of the text

Review

Kharab and Guenther offer an attractive, clear, error-free, and well-written introduction to numerical methods ? Highly recommended. (J.H. Ellison on the first edition in CHOICE0

Table of Contents

INTRODUCTION

About the software MATLAB
An Introduction to MATLAB
Taylor Series

NUMBER SYSTEM AND ERRORS

Floating-Point Arithmetic
Round-Off Errors
Truncation Error
Interval Arithmetic

ROOTS OF EQUATIONS

The Bisection Method
The Method of False Position
Fixed-Point Iteration
The Secant method
Newton’s Method
Convergence of the Newton and Secant Methods
Multiple Roots and the Modified Newton Method
Newton’s Method for Nonlinear Systems

SYSTEM OF LINEAR EQUATIONS

Matrices and Matrix Operations
Na’ve Gaussian Elimination
Gaussian Elimination with Scaled Partial Pivoting
LU Decomposition
Iterative Methods

INTERPOLATION

Polynomial Interpolation Theory
Newton’s Divided Difference Interpolating Polynomial
The Error of the Interpolating Polynomial
Lagrange Interpolating Polynomial

INTERPOLATION WITH SPLINE FUNCTIONS

Piecewise Linear Interpolation
Quadratic Spline
Natural Cubic Splines

THE METHOD OF LEAST SQUARES

Linear Least Squares
Least Squares Polynomial
Nonlinear Least Squares
Trigonometric Least Squares Polynomial

NUMERICAL OPTIMIZATION

Analysis of Single-Variable Functions
Line Search Methods
Minimization Using Derivatives

NUMERICAL DIFFERENTIATION

Numerical Differentiation
Richardson’s Formula

NUMERICAL INTEGRATION

Trapezoidal Rule
Simpson’s Rule
Romberg Algorithm
Gaussian Quadrature

NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS

Euler’s Method
Error Analysis
Higher Order Taylor Series Methods
Runge-Kutta Methods
Multistep Methods
Adams-Bashforth Method
Predictor-Corrector Methods
Adams-Moulton Method
Numerical Stability
Higher Order Equations and Systems of Differential Equations
Implicit Methods and Stiff Systems
Phase Plane Analysis: Chaotic Differential Equations

BOUNDARY-VALUE PROBLEMS

Finite-Difference Methods
Shooting Methods

EIGENVALUES AND EIGENVECTORS

Basic Theory
The Power Method
The Quadratic Method
Eigenvalues for Boundary-Value Problems
Bifurcations in Differential Equations

PARTIAL DIFFERENTIAL EQUATIONS

Parabolic Equations
Hyperbolic Equations
Elliptic Equations
Introduction to Finite Element Method

Bibliography and References
Appendices
Calculus Review
MATLAB Built-in Functions
Text MATLAB Functions
Answers to Selected Exercises
Index

Each chapter also contains a section of Applied Problems.

Additional information

Weight1300 g
Co author

Publisher

Language

ENGLISH

Pages

624

Year of publication

2005

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