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Methods of Numerical Integration

E-BookPDFDRM AdobeE-Book
626 Seiten
Englisch
Elsevier Science & Techn.erschienen am10.05.20142. Auflage
Methods of Numerical Integrationmehr
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TaschenbuchKartoniert, Paperback
EUR32,50
E-BookPDFDRM AdobeE-Book
EUR70,95

Produkt

KlappentextMethods of Numerical Integration
Details
Weitere ISBN/GTIN9781483264288
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format HinweisDRM Adobe
Erscheinungsjahr2014
Erscheinungsdatum10.05.2014
Auflage2. Auflage
Seiten626 Seiten
SpracheEnglisch
Artikel-Nr.3171975
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
1;Front Cover;1
2;Methods of Numerical Integration;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface to First Edition;12
7;Preface to Second Edition;14
8;CHAPTER 1. INTRODUCTION;16
8.1;1.1 Why Numerical Integration?;16
8.2;1.2 Formal Differentiation and Integration on Computers;18
8.3;1.3 Numerical Integration and Its Appeal in Mathematics;19
8.4;1.4 Limitations of Numerical Integration;20
8.5;1.5 The Riemann Integral;22
8.6;1.6 Improper Integrals;25
8.7;1.7 The Riemann Integral in Higher Dimensions;32
8.8;1.8 More General Integrals;35
8.9;1.9 The Smoothness of Functions and Approximate Integration;35
8.10;1.10 Weight Functions;36
8.11;1.11 Some Useful Formulas;37
8.12;1.12 Orthogonal Polynomials;43
8.13;1.13 Short Guide to the Orthogonal Polynomials;48
8.14;1.14 Some Sets of Polynomials Orthogonal over Figures in the Complex Plane;57
8.15;1.15 Extrapolation and Speed-Up;58
8.16;1.16 Numerical Integration and the Numerical Solution of Integral Equations;63
9;CHAPTER 2. APPROXIMATE INTEGRATION OVER A FINITE INTERVAL;66
9.1;2.1 Primitive Rules;66
9.2;2.2 Simpson's Rule;72
9.3;2.3 Nonequally Spaced Abscissas;75
9.4;2.4 Compound Rules;85
9.5;2.5 Integration Formulas of Interpolatory Type;89
9.6;2.6 Integration Formulas of Open Type;107
9.7;2.7 Integration Rules of Gauss Type;110
9.8;2.8 Integration Rules Using Derivative Data;147
9.9;2.9 Integration of Periodic Functions;149
9.10;2.10 Integration of Rapidly Oscillatory Functions;161
9.11;2.11 Contour Integrals;183
9.12;2.12 Improper Integrals (Finite Interval);187
9.13;2.13 Indefinite Integration;205
10;CHAPTER 3. APPROXIMATE INTEGRATION OVER INFINITE INTERVALS;214
10.1;4.1 Types of Errors;286
10.2;4.2 Roundoff Error for a Fixed Integration Rule;287
10.3;4.3 Truncation Error;300
10.4;4.4 Special Devices;310
10.5;4.5 Error Estimates through Differences;312
10.6;4.6 Error Estimates through the Theory of Analytic Functions;315
10.7;4.7 Application of Functional Analysis to Numerical Integration;332
10.8;4.8 Errors for Integrands with Low Continuity;347
10.9;4.9 Practical Error Estimation;351
10.10;3.1 Change of Variable;214
10.11;3.2 Proceeding to the Limit;217
10.12;3.3 Truncation of the Infinite Interval;220
10.13;3.4 Primitive Rules for the Infinite Interval;222
10.14;3.5 Formulas of Interpolatory Type;234
10.15;3.6 Gaussian Formulas for the Infinite Interval;237
10.16;3.7 Convergence of Formulas of Gauss Type for Singly and Doubly Infinite Intervals;242
10.17;3.8 Oscillatory Integrands;245
10.18;3.9 The Fourier Transform;251
10.19;3.10 The Laplace Transform and Its Numerical Inversion;279
11;CHAPTER 4. ERROR ANALYSIS;286
11.1;4.1 Types of Errors;286
11.2;4.2 Roundoff Error for a Fixed Integration Rule;287
11.3;4.3 Truncation Error;300
11.4;4.4 Special Devices;310
11.5;4.5 Error Estimates through Differences;312
11.6;4.6 Error Estimates through the Theory of Analytic Functions;315
11.7;4.7 Application of Functional Analysis to Numerical Integration;332
11.8;4.8 Errors for Integrands with Low Continuity;347
11.9;4.9 Practical Error Estimation;351
12;CHAPTER 5. APPROXIMATE INTEGRATION IN TWO OR MORE DIMENSIONS;359
12.1;5.1 Introduction;359
12.2;5.2 Some Elementary Multiple Integrals over Standard Regions;361
12.3;5.3 Change of Order of Integration;363
12.4;5.4 Change of Variables;363
12.5;5.5 Decomposition into Elementary Regions;365
12.6;5.6 Cartesian Products and Product Rules;369
12.7;5.7 Rules Exact for Monomials;378
12.8;5.8 Compound Rules;394
12.9;5.9 Multiple Integration by Sampling;399
12.10;5.10 The Present State of the Art;430
13;CHAPTER 6. AUTOMATIC INTEGRATION;433
13.1;6.1 The Goals of Automatic Integration;433
13.2;6.2 Some Automatic Integrators;440
13.3;6.3 Romberg Integration;449
13.4;6.4 Automatic Integration Using Tschebyscheff Polynomials;461
13.5;6.5 Automatic Integration in Several Variables;465
13.6;6.6 Concluding Remarks;476
14;APPENDIX 1: ON THE PRACTICAL EVALUATION OF INTEGRALS;478
15;APPENDIX 2: FORTRAN PROGRAMS;495
16;APPENDIX 3: BIBLIOGRAPHY OF ALGOL, FORTRAN, AND PL/I PROCEDURES;524
17;APPENDIX 4: BIBLIOGRAPHY OF TABLES;533
18;APPENDIX 5: BIBLIOGRAPHY OF BOOKS AND ARTICLES;539
19;Index;620mehr