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Guide To Scientific Computing, Second Edition - Peter R. Turner

Guide To Scientific Computing, Second Edition

Paperback Published: 1st November 2000
ISBN: 9780849312427
Number Of Pages: 312

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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.

Preface
Number Representations and Errorsp. 1
Introductionp. 1
Floating-point numberp. 2
Sources of errorsp. 8
Measures of error and precisionp. 12
Floating-point arithmeticp. 15
Iterative Solution of Equationsp. 20
Introductionp. 20
The bisection methodp. 22
Function iterationp. 27
Newton's methodp. 35
The secant methodp. 41
2 equations in 2 unknowns: Newton's methodp. 45
MATLAB functions for equation solvingp. 49
Approximate Evaluation of Functionsp. 52
Introductionp. 52
Series expansionsp. 53
CORDIC algorithmsp. 60
MATLAB functionsp. 73
Interpolationp. 74
Introductionp. 74
Lagrange interpolationp. 77
Difference representationsp. 84
Splinesp. 100
MATLAB interpolation functionsp. 115
Numerical Calculusp. 119
Introductionp. 119
Numerical integration: interpolatory quadrature rulesp. 122
Composite formulasp. 132
Practical numerical integrationp. 140
Improper integralsp. 149
Numerical differentiationp. 153
Maxima and minimap. 159
MATLAB functions for numerical calculusp. 168
Differential Equationsp. 171
Introduction and Euler's methodp. 171
Runge-Kutta methodsp. 178
Multistep methodsp. 186
Systems of differential equationsp. 193
Boundary-value problems: (1) shooting methodsp. 198
Boundary-value problems: (2) finite difference methodsp. 204
MATLAB functions for ordinary differential equationsp. 208
Linear Equationsp. 210
Introductionp. 210
Gauss eliminationp. 212
LU factorization: iterative refinementp. 225
Iterative methodsp. 232
Linear least squares approximationp. 239
Eigenvaluesp. 248
MATLAB's linear algebra functionsp. 257
Appendices
MATLAB Basicsp. 261
Answers to Selected Exercisesp. 282
References and Further Readingp. 298
Indexp. 299
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780849312427
ISBN-10: 0849312426
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 312
Published: 1st November 2000
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 24.77 x 17.78  x 1.91
Weight (kg): 0.54
Edition Number: 2
Edition Type: New edition