2nd Edition

Guide To Scientific Computing



ISBN 9780849312427
Published December 7, 2000 by CRC Press
312 Pages

USD $74.95

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Book Description

Guide to Scientific Computing provides an introduction to the many problems of scientific computing, as well as the wide variety of methods used for their solution. It is ideal for anyone who needs an understanding of numerical mathematics or scientific computing - whether in mathematics, the sciences, engineering, or economics.
This book provides an appreciation of the need for numerical methods for solving different types of problems, and discusses basic approaches. For each of the problems mathematical justification and examples provide both practical evidence and motivations for the reader to follow. Practical justification of the methods is presented through computer examples and exercises. The major effort of programming is removed from the reader, as are the harder parts of analysis, so that the focus is clearly on the basics. Since some algebraic manipulation is unavoidable, it is carefully explained when necessary, especially in the early stages.
Guide to Scientific Computing includes an introduction to MATLAB, but the code used is not intended to exemplify sophisticated or robust pieces of software; it is purely illustrative of the methods under discussion. The book has an appendix devoted to the basics of the MATLAB package, its language and programming. The book provides an introduction to this subject which is not, in its combined demands of computing, motivation, manipulation, and analysis, paced such that only the most able can understand.

Table of Contents

Number Representations and Errors
Introduction
Floating-Point Number
Sources of Errors
Measures of Error and Precision
Floating-Point Arithmetic
Iterative Solution of Equations
Introduction
The Bisection Method
Function Iteration
Newton's Method
The Secant Method
2 Equations in 2 Unknowns: Newton's Method
MATLAB Functions for Equation Solving
Approximate Evaluation of Functions
Introduction
Series Expansions
CORDIC Algorithms
MATLAB Functions
Interpolation
Introduction
Lagrange Interpolation
Difference Representations
Splines
MATLAB Interpolation Functions
Numerical Calculus
Introduction
Numerical Integration: Interpolatory Quadrature Rules
Composite Formulas
Practical Numerical Integration
Improper Integrals
Numerical Differentiation
Maxima and Minima
MATLAB Functions for Numerical Calculus
Differential Equations
Introduction and Euler's Method
Runge-Kutta Methods
Multistep Methods
Systems of Differential Equations
Boundary-Value Problems (1) Shooting Methods
Boundary-Value Problems (2) Finite Difference Methods
MATLAB Functions for Ordinary Differential Equations
Linear Equations
Introduction
Gauss Elimination
LU Factorization: Iterative Refinement
Iterative Methods
Linear Least Squares Approximation
Eigenvalues
MATLAB's Linear Algebra Functions
Appendices
MATLAB Basics
Answers to Selected Exercises
References and Further Reading
Index

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