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Introduction to Numerical Methods and MATLAB Implementations and Applications

ISBN-10: 0201308606
ISBN-13: 9780201308600
Edition: 2001
List price: $117.80 Buy it from $71.74
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Description: Designed to give undergraduate engineering students a practical and rigorous introduction to the fundamentals of numerical computation. This book is a thoroughly modern exposition of classic numerical methods using MATLAB. The fundamental theory of  More...

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Book details

List price: $117.80
Copyright year: 2001
Publisher: Prentice Hall PTR
Publication date: 8/24/2000
Binding: Hardcover
Pages: 786
Size: 7.25" wide x 9.25" long x 1.25" tall
Weight: 2.882
Language: English

Designed to give undergraduate engineering students a practical and rigorous introduction to the fundamentals of numerical computation. This book is a thoroughly modern exposition of classic numerical methods using MATLAB. The fundamental theory of each method is briefly developed. Rather than providing a detailed numerical analysis, the behavior of the methods is exposed by carefully designed numerical experiments. The methods are then exercised on several nontrivial example problems from engineering practice. The material in each chapter is organized as a progression from the simple to the complex. This leads the student to an understanding of the sophisticated numerical methods that are part of MATLAB. An integral part of the book is the Numerical Methods with MATLAB (NMM) Toolbox, which provides 150 programs and over forty data sets. The NMM Toolbox is a library of numerical techniques implemented in structured and clearly written code.

(NOTE: Chapters 2-12 conclude with Summary.)
Introduction
Terminology
MATLAB Overview
Organization of the Book
Rating Systems for Exercises
MATLAB Basics
Interactive Computing with MATLAB
Running MATLAB
Matrices and Vectors
Additional Types of Variables
Managing the Interactive Environment
Plotting in MATLAB
MATLAB Programming
Script m-Files
Function m-Files
Input and Output
Flow Control
Vectorization
Deus ex Machina
Organizing and Debugging MATLAB Programs
Organizing and Documenting m-Files
Organizing a Numerical Solution
Debugging
Numerical Techniques
Unavoidable Errors in Computing
Digital Representation of Numbers
Finite Precision Arithmetic
Truncation Error of Algorithms
Finding the Roots of f(x)=0
Preliminaries
Fixed-Point Iteration
Bisection
Newton's Method
The Secant Method
Hybrid Methods
Roots of Polynomials
A Review of Linear Algebra
Vectors
Matrices
Mathematical Properties of Vectors and Matrices
Special Matrices
Solving Systems of Equations
Basic Concepts
Gaussian Elimination
Limitations on Numerical Solutions to Ax = b
Factorization Methods
Nonlinear Systems of Equations
Least-Squares Fitting of a Curve to Data
Fitting a Line to Data
Least-Squares Fit to a Linear Combination of Functions
Multivariate Linear Least-Squares Fitting
Interpolation
Basic Ideas
Interpolating Polynomials of Arbitrary Degree
Piecewise Polynomial Interpolation
MATLAB's Built in Interpolation Functions
Numerical Integration
Basic Ideas and Nomenclature
Newton-Cotes Rules
Gaussian Quadrature
Adaptive Quadrature
Improper Integrals and Other Complications
Numerical Integration of Ordinary Differential Equations
Basic Ideas and Nomenclature
Euler's Method
Higher Order One-Step Methods
Adaptive Stepsize Algorithms
Coupled ODEs
Additional Topics
Bibliography
Eigenvalues and Eigensystems
Eigenvectors Map onto Themselves
Mathematical Preliminaries
The Power Method
Built-in Functions for Eigenvalue Computation
Singular Value Decomposition
Sparse Matrices
Storage and Flop Savings
MATLAB Sparse Matrix Format
MATLAB Toolbox Functions
Listings for NMM Toolbox m-Files
Subject Index

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