Numerical mathematics and computing:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Monterey, Calif.
Brooks/Cole
1985
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 562 S. graph. Darst. |
| ISBN: | 0534043569 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical mathematics and computing |c Ward Cheney ; David Kincaid |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Monterey, Calif. |b Brooks/Cole |c 1985 | |
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| 650 | 4 | |a Fortran (Langage de programmation) | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a FORTRAN (Computer program language) | |
| 650 | 4 | |a Numerical analysis |x Data processing | |
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Record in the Search Index
| _version_ | 1804118047910264832 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 Programming Suggestions 2
1.2 Review of Taylor Series 17
£m NUMBER REPRESENTATION AND ERRORS 34
2.1 Representation of Numbers in Different Bases 34
2.2 Floating-Point Number System 45
2.3 Loss of Significance 59
3 LOCATING ROOTS OF EQUATIONS 74
3.1 Bisection Method 76
3.2 Newton s Method 83
*3.3 Secant Method 97
4 INTERPOLATION AND NUMERICAL DIFFERENTIATION 105
4.1 Polynomial Interpolation 106
*4.2 Errors in Polynomial Interpolation 128
4.3 Estimating Derivatives and Richardson Extrapolation 136
S) NUMERICAL INTEGRATION 150
5.1 Definite Integral 150
5.2 Trapezoid Rule 159
Throughout this text, some sections are indicated with asterisks. These sections may be
skipped at the instructor s discretion.
5.3 Romberg Algorithm 171
*5.4 An Adaptive Simpson s Scheme 183
*5.5 Gaussian Quadrature Formulas 192
O SYSTEMS OF LINEAR EQUATIONS 201
6.1 Naive Gaussian Elimination 202
6.2 Gaussian Elimination with Scaled Partial Pivoting 214
6.3 Tridiagonal and Other Band Systems 231
*6.4 LU Factorization 240
I APPROXIMATION BY SPLINE FUNCTIONS 258
7.1 First-Degree and Second-Degree Splines 258
7.2 Natural Cubic Splines 268
*7.3 B Splines 287
*7.4 Interpolation and Approximation by B Splines 294
O ORDINARY DIFFERENTIAL EQUATIONS 303
8.1 Taylor Series Methods 305
8.2 Runge-Kutta Methods 311
*8.3 Stability and Adaptive Runge-Kutta Methods 322
Sj MONTE CARLO METHODS AND SIMULATION 333
9.1 Random Numbers 333
9.2 Estimation of Areas and Volumes by Monte Carlo Techniques 344
9.3 Simulation 351
111 SMOOTHING OF DATA
U AND THE METHOD OF LEAST SQUARES 362
10.1 The Method of Least Squares 362
*10.2 Orthogonal Systems and Chebyshev Polynomials 369
10.3 Other Examples of the Least Squares Principle 383
1 I SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS 390
11.1 Methods for First-Order Systems 390
11.2 Higher-Order Equations and Systems 398
*11.3 Adams-Moulton Methods 404
•4 O BOUNDARY VALUE PROBLEMS
I £L FOR ORDINARY DIFFERENTIAL EQUATIONS 410
12.1 Shooting Method 411
12.2 A Discretization Method 417
I W PARTIAL DIFFERENTIAL EQUATIONS 427
13.1 Parabolic Problems 429
13.2 Hyperbolic Problems 437
13.3 Elliptic Problems 443
1 4 THE MINIMIZATION OF MULTIVARIATE FUNCTIONS 456
14.1 One-Variable Case 457
14.2 Multivariate Case 470
1 O LINEAR PROGRAMMING 483
15.1 Standard Forms and Duality 483
15.2 Simplex Method 494
15.3 Approximate Solution of Inconsistent Linear Systems 499
APPENDIX A:
REVIEW OF FORTRAN 77 PROGRAMMING 505
APPENDIX B:
LINEAR ALGEBRA CONCEPTS AND NOTATION 529
Answers for Selected Problems 540
References 554
Index 557
|
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| author | Cheney, Elliott W. 1929- Kincaid, David 1942- |
| author_GND | (DE-588)122199545 (DE-588)121384152 |
| author_facet | Cheney, Elliott W. 1929- Kincaid, David 1942- |
| author_role | aut aut |
| author_sort | Cheney, Elliott W. 1929- |
| author_variant | e w c ew ewc d k dk |
| building | Verbundindex |
| bvnumber | BV003703003 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 900 |
| ctrlnum | (OCoLC)11497963 (DE-599)BVBBV003703003 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV003703003 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:06Z |
| institution | BVB |
| isbn | 0534043569 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002357139 |
| oclc_num | 11497963 |
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| owner | DE-384 DE-739 |
| owner_facet | DE-384 DE-739 |
| physical | XIII, 562 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Brooks/Cole |
| record_format | marc |
| spelling | Cheney, Elliott W. 1929- Verfasser (DE-588)122199545 aut Numerical mathematics and computing Ward Cheney ; David Kincaid 2. ed. Monterey, Calif. Brooks/Cole 1985 XIII, 562 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse numérique - Informatique Fortran (Langage de programmation) Datenverarbeitung FORTRAN (Computer program language) Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s Algorithmus (DE-588)4001183-5 s Datenverarbeitung (DE-588)4011152-0 s 1\p DE-604 Kincaid, David 1942- Verfasser (DE-588)121384152 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002357139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cheney, Elliott W. 1929- Kincaid, David 1942- Numerical mathematics and computing Analyse numérique - Informatique Fortran (Langage de programmation) Datenverarbeitung FORTRAN (Computer program language) Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd Algorithmus (DE-588)4001183-5 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4001183-5 (DE-588)4011152-0 |
| title | Numerical mathematics and computing |
| title_auth | Numerical mathematics and computing |
| title_exact_search | Numerical mathematics and computing |
| title_full | Numerical mathematics and computing Ward Cheney ; David Kincaid |
| title_fullStr | Numerical mathematics and computing Ward Cheney ; David Kincaid |
| title_full_unstemmed | Numerical mathematics and computing Ward Cheney ; David Kincaid |
| title_short | Numerical mathematics and computing |
| title_sort | numerical mathematics and computing |
| topic | Analyse numérique - Informatique Fortran (Langage de programmation) Datenverarbeitung FORTRAN (Computer program language) Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd Algorithmus (DE-588)4001183-5 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| topic_facet | Analyse numérique - Informatique Fortran (Langage de programmation) Datenverarbeitung FORTRAN (Computer program language) Numerical analysis Data processing Numerische Mathematik Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002357139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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