Guide To Scientific Computing, Second Edition

by Turner; Peter R.

• ISBN13: 9780849312427
• ISBN10: 0849312426
• Edition: 2nd
• Format: Nonspecific Binding
• Copyright: 2000-12-07
• Publisher: CRC Press

Summary

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

Preface
Number Representations and Errors	1	(19)
Introduction	1	(1)
Floating-point number	2	(6)
Sources of errors	8	(4)
Measures of error and precision	12	(3)
Floating-point arithmetic	15	(5)
Iterative Solution of Equations	20	(32)
Introduction	20	(2)
The bisection method	22	(5)
Function iteration	27	(8)
Newton's method	35	(6)
The secant method	41	(4)
2 equations in 2 unknowns: Newton's method	45	(4)
MATLAB functions for equation solving	49	(3)
Approximate Evaluation of Functions	52	(22)
Introduction	52	(1)
Series expansions	53	(7)
CORDIC algorithms	60	(13)
MATLAB functions	73	(1)
Interpolation	74	(45)
Introduction	74	(3)
Lagrange interpolation	77	(7)
Difference representations	84	(16)
Splines	100	(15)
MATLAB interpolation functions	115	(4)
Numerical Calculus	119	(52)
Introduction	119	(3)
Numerical integration: interpolatory quadrature rules	122	(10)
Composite formulas	132	(8)
Practical numerical integration	140	(9)
Improper integrals	149	(4)
Numerical differentiation	153	(6)
Maxima and minima	159	(9)
MATLAB functions for numerical calculus	168	(3)
Differential Equations	171	(39)
Introduction and Euler's method	171	(7)
Runge-Kutta methods	178	(8)
Multistep methods	186	(7)
Systems of differential equations	193	(5)
Boundary-value problems: (1) shooting methods	198	(6)
Boundary-value problems: (2) finite difference methods	204	(4)
MATLAB functions for ordinary differential equations	208	(2)
Linear Equations	210	(88)
Introduction	210	(2)
Gauss elimination	212	(13)
LU factorization: iterative refinement	225	(7)
Iterative methods	232	(7)
Linear least squares approximation	239	(9)
Eigenvalues	248	(9)
MATLAB's linear algebra functions	257	(4)
Appendices
A MATLAB Basics	261	(21)
B Answers to Selected Exercises	282	(16)
References and Further Reading	298	(1)
Index	299