Mathematics for engineers: 4 Numerics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
München
Oldenbourg
2010
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 345 S. Ill., graph. Darst. 24 cm 1 CD-ROM (12 cm) |
| ISBN: | 9783486590425 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804140849965039616 |
|---|---|
| adam_text | CONTENTS 1. OUTLINE 1.1. INTRODUCTION 1 1.2. CONCEPT OF THE TEXT 2 1.3.
ORGANIZATION OF THE TEXT * 1.4. PRESENTATION OF THE MATERIAL 4 2.
SIMULATION METHODS 2.1 INTRODUCTION 5 2.2 SIMULATION 7 2.2.1 STRUCTURE
OF MODELS 7 2.2.2 REQUIREMENTS ON A MODELING PROCESS 14 2.2.3 MODELLING
PROCESS 15 2.2.4 OBJECT-ORIENTED APPROACH USING CLASSES 16 2.2.5 TESTS
AND EXERCISES 20 2.2.5.1 TEST PROBLEMS 20 2.2.5.2 EXERCISES 21 2.3 CAR
ON A BUMPY ROAD 21 2.3.1 MODELLING STEPS 21 2.3.1.1 HARDWARE 21 2.3.1.2
FORMULATION 22 2.3.2 CLASS DEFINITIONS 22 2.3.2.1 CLASS FOR SETUP 24
2.3.2.2 CLASS BODY 24 2.3.2.3 CLASSES FOR AXLES 25 2.3.2.4 CLASS CAR 26
2.3.2.5 CLASS SIMULATION 27 2.3.3 OBJECTS 29 2.3.3.1 BODY OBJECT 30
2.3.3.2 AXLE OBJECT 30 2.3.3.3 CAR OBJECT 32 2.3.3.4 SIMULATION OBJECT
32 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/996543120
DIGITALISIERT DURCH MATHEMATICS FOR ENGINEERS 3. NUMBERS AND ERRORS 3.1
INTRODUCTION 36 3.2 NUMBERS AND REPRESENTATION 37 3.2.1 NUMBERS ON THE
REAL LINE 37 3.2.2 REPRESENTATION OF NUMBERS 43 3.2.3 TESTS AND
EXERCISES 48 3.2.3.1 TEST PROBLEMS 48 3.2.3.2 EXERCISES 48 3.3 ERRORS ON
COMPUTERS 49 3.3.1 THEORY OF ROUNDING ERRORS 63 3.3.2 TESTS AND
EXERCISES 67 3.3.2.1 TEST PROBLEMS 67 3.3.2.2 EXERCISES 67 3.4
APPROXIMATIONS 69 3.4.1 IMPORTANT PROPERTIES OF POLYNOMIALS 69 3.4.2
POLYNOMIAL APPROXIMATION BY INTERPOLATION 72 3.4.3 POLYNOMIAL
APPROXIMATION BY LEAST SQUARES 77 3.4.4 LEAST SQUARES APPROXIMATION AND
ORTHOGONAL POLYNOMIALS 79 3.4.4.1 LEGENDRE POLYNOMIALS 80 3.4.4.2
CHEBYSHEV POLYNOMIALS OF THE FIRST KIND 81 3.4.4.3 CHEBYSHEV POLYNOMIALS
OF THE SECOND KIND 83 3.4.4.4 LAGUERRE POLYNOMIALS 84 3.4.4.5 HERMITE
POLYNOMIALS 86 3.4.5 LOCAL QUADRATIC APPROXIMATION 92 3.4.6 MACLAURIN
POLYNOMIAL 95 3.4.7 TAYLOR POLYNOMIAL 98 3.4.8 -REMAINDER 99 3.4.9
TESTS AND EXERCISES 102 3.4.9.1 TEST PROBLEMS 103 3.4.9.2 EXERCISES 103
3.5 POWER SERIES AND TAYLOR SERIES 104 3.5.1 DEFINITION AND PROPERTIES
OF SERIES 104 3.5.2 DIFFERENTIATING AND INTEGRATING POWER SERIES 108
3.5.3 PRACTICAL WAYS TO FIND POWER SERIES 111 3.5.4 GENERALIZED POWER
SERIES 114 3.5.4.1 FOURIER SUM 114 3.5.4. 6.2.5.2 EXERCISES 242 CONTENTS
4. ROOTS OF EQUATIONS 4.1 INTRODUCTION 123 4.2 SIMPLE ROOT FINDING
METHODS 125 4.2.1 THE BISECTION METHOD 129 4.2.2 METHOD OF FALSE
POSITION 133 4.2.3 SECANT METHOD 136 4.2.4 NEWTON S METHOD 141 4.2.5
FIXED-POINT METHOD 151 4.2.6 TESTS AND EXERCISES 166 4.2.6.1 TEST
PROBLEMS 166 4.2.6.2 EXERCISES 167 5. NUMERICAL INTEGRATION 5.1
INTRODUCTION 169 5.2 TRAPEZOIDAL AND SIMPSON METHOD 170 5.2.1
TRAPEZOIDAL METHOD 170 5.2.2 SIMPSON S METHOD 176 5.2.3 GENERALIZED
INTEGRATION RULES 182 5.2.4 ERROR ESTIMATIONS FOR TRAPEZOIDAL AND
SIMPLSON S RULE 186 5.2.4.1 ERROR FORMULAS FOR SIMPSON S RULE 190 5.2.5
TESTS AND EXERCISES 195 5.2.5.1 TEST PROBLEMS 195 5.2.5.2 EXERCISES 195
5.3 GAUSSIAN NUMERICAL INTEGRATION 197 5.3.1 TESTS AND EXERCISES 209
5.3.1.1 TEST PROBLEMS 209 5.3.1.2 EXERCISES 209 5.4 MONTE CARLO
INTEGRATION 210 5.4.1 TESTS AND EXERCISES 213 5.4.1.1 TEST PROBLEMS 213
5.4.1.2 EXERCISES 213 6. SOLUTIONS OF EQUATIONS 6.1 INTRODUCTION 215 6.2
SYSTEMS OF LINEAR EQUATIONS 216 6.2.1 GAUSS ELIMINATION METHOD 220 6.2.2
OPERATIONS COUNT 225 6.2.3 LU FACTORIZATION 227 6.2.4 ITERATIVE
SOLUTIONS 236 6.2.5 TESTS AND EXERCISES 242 6.2.5.1 TEST PROBLEMS 242
MATHEMATICS FOR ENGINEERS 6.3 EIGENVALUE PROBLEM 244 6.3.1 TESTS AND
EXERCISES 254 6.3.1.1 TEST PROBLEMS 254 6.3.1.2 EXERCISES 254 7.
ORDINARY DIFFERENTIAL EQUATIONS 7.1 INTRODUCTION 255 7.2 MATHEMATICAL
PRELIMINARIES 256 7.2.1 TESTS AND EXERCISES 261 7.2.1.1 TEST PROBLEMS
261 7.2.1.2 EXERCISES 261 7.3 NUMERICAL INTEGRATION BY TAYLOR SERIES 262
7.3.1 IMPLICIT AND PREDICTOR-CORRECTOR METHODS 271 7.3.2 TESTS AND
EXERCISES 275 7.3.2.1 TEST PROBLEMS 275 7.3.2.2 EXERCISES 275 7.4
RUNGE-KUTTA METHODS 277 7.4.1 TESTS AND EXERCISES 285 7.4.1.1 TEST
PROBLEMS 286 7.4.1.2 EXERCISES 286 7.5 STIFF DIFFERENTIAL EQUATIONS 287
7.5.1 TESTS AND EXERCISES 289 7.5.1.1 TEST PROBLEMS 289 7.5.1.2
EXERCISES 289 7.6 TWO-POINT BOUNDARY VALUE PROBLEMS 289 7.6.1 THE
SHOOTING METHOD 296 7.6.2 THE OPTIMIZATION APPROACH 301 7.6.3 THE FINITE
DIFFERENCE APPROACH 309 7.6.4 THE COLLOCATION METHOD 316 7.6.5 TESTS AND
EXERCISES 319 7.6.5.1 TEST PROBLEMS 319 7.6.5.2 EXERCISES 319 7.7 FINITE
ELEMENTS AND BOUNDARY VALUE METHODS 321 7.7.1 FINITE ELEMENTS FOR
ORDINARY DIFFERENTIAL EQUATIONS 322 7.7.2 TESTS AND EXERCISES 334
7.7.2.1 TEST PROBLEMS 334 7.7.2.2 EXERCISES 334 APPENDIX A. FUNCTIONS
USED SYSTE
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:31Z |
| institution | BVB |
| isbn | 9783486590425 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018731810 |
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| physical | XII, 345 S. Ill., graph. Darst. 24 cm 1 CD-ROM (12 cm) |
| publishDate | 2010 |
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| publishDateSort | 2010 |
| publisher | Oldenbourg |
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| spelling | Baumann, Gerd 1956- Verfasser (DE-588)142960241 aut Mathematics for engineers 4 Numerics by Gerd Baumann München Oldenbourg 2010 XII, 345 S. Ill., graph. Darst. 24 cm 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematik (DE-588)4037944-9 s DE-604 (DE-604)BV035874038 4 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018731810&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baumann, Gerd 1956- Mathematics for engineers Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4123623-3 |
| title | Mathematics for engineers |
| title_auth | Mathematics for engineers |
| title_exact_search | Mathematics for engineers |
| title_full | Mathematics for engineers 4 Numerics by Gerd Baumann |
| title_fullStr | Mathematics for engineers 4 Numerics by Gerd Baumann |
| title_full_unstemmed | Mathematics for engineers 4 Numerics by Gerd Baumann |
| title_short | Mathematics for engineers |
| title_sort | mathematics for engineers numerics |
| topic | Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Lehrbuch |
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