Numerical methods for engineers and scientists:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
2001
|
| Ausgabe: | 2. ed., rev. and expanded |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 823 S. graph. Darst. |
| ISBN: | 0824704436 |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical methods for engineers and scientists |c Joe D. Hoffman |
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| 264 | 1 | |a New York [u.a.] |b Dekker |c 2001 | |
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Datensatz im Suchindex
| _version_ | 1804128764121055232 |
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| adam_text | NUMERICAL METHODS FOR ENGINEERS AND SCIENTISTS SECOND EDITION REVISED
AND EXPANDED M A R C E L M D E * * E R JOE D. HOFFMAN DEPARTMENT OF
MECHANICAL ENGINEERING PURDUE UNIVERSITY WEST LAFAYETTE, INDIANA MARCEL
DEKKER, INC. NEW YORK * BASEL CONTENTS PREFACE V CHAPTER 0. INTRODUCTION
1 0.1. OBJECTIVES AND APPROACH 1 0.2. ORGANIZATION OF THE BOOK 2 0.3.
EXAMPLES 2 0.4. PROGRAMS 3 0.5. PROBLEMS 3 0.6. SIGNIFICANT DIGITS,
PRECISION, ACCURACY, ERRORS, AND NUMBER REPRESENTATION 4 0.7. SOFTWARE
PACKAGES AND LIBRARIES 6 0.8. THE TAYLOR SERIES AND THE TAYLOR
POLYNOMIAL 7 PARTI. BASIC TOOLS OF NUMERICAL ANALYSIS 11 1.1. SYSTEMS OF
LINEAR ALGEBRAIC EQUATIONS 11 1.2. EIGENPROBLEMS 13 1.3. ROOTS OF
NONLINEAR EQUATIONS 14 1.4. POLYNOMIAL APPROXIMATION AND INTERPOLATION
14 1.5. NUMERICAL DIFFERENTIATION AND DIFFERENCE FORMULAS 15 1.6.
NUMERICAL INTEGRATION 16 1.7. SUMMARY 16 CHAPTER 1. SYSTEMS OF LINEAR
ALGEBRAIC EQUATIONS 17 1.1. INTRODUCTION 18 1.2. PROPERTIES OF MATRICES
AND DETERMINANTS 21 1.3. DIRECT ELIMINATION METHODS 30 1.4. LU
FACTORIZATION 45 1.5. TRIDIAGONAL SYSTEMS OF EQUATIONS 49 1.6. PITFALLS
OF ELIMINATION METHODS 52 1.7. ITERATIVE METHODS 59 1.8. PROGRAMS 67
1.9. SUMMARY 76 EXERCISE PROBLEMS 77 CHAPTER 2. EIGENPROBLEMS 81 2.1.
INTRODUCTION 81 2.2. MATHEMATICAL CHARACTERISTICS OF EIGENPROBLEMS 85
2.3. THE POWER METHOD 89 VII VIII CONTENTS 2.4. 2.5. 2.6. 2.7. 2.8. 2.9.
CHAPT 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7. 3.8. 3.9. CHAPT 4.1. 4.2. 4.3.
4.4. 4.5. 4.6. 4.7. 4.8. 4.9. 4.10. 4.11. 4.12. CHAPT 5.1. 5.2. 5.3.
5.4. 5.5. 5.6. 5.7. 5.8. CHAPT 6.1. 6.2. 6.3. THE DIRECT METHOD THE QR
METHOD EIGENVECTORS OTHER METHODS PROGRAMS SUMMARY EXERCISE PROBLEMS **
3. NONLINEAR EQUATIONS INTRODUCTION GENERAL FEATURES OF ROOT FINDING
CLOSED DOMAIN (BRACKETING) METHODS OPEN DOMAIN METHODS POLYNOMIALS
PITFALLS OF ROOT FINDING METHODS AND OTHER METHODS OF ROOT FINDING
SYSTEMS OF NONLINEAR EQUATIONS PROGRAMS SUMMARY EXERCISE PROBLEMS ER 4.
POLYNOMIAL APPROXIMATION AND INTERPOLATION INTRODUCTION PROPERTIES OF
POLYNOMIALS DIRECT FIT POLYNOMIALS LAGRANGE POLYNOMIALS DIVIDED
DIFFERENCE TABLES AND DIVIDED DIFFERENCE POLYNOMIALS DIFFERENCE TABLES
AND DIFFERENCE POLYNOMIALS INVERSE INTERPOLATION MULTIVARIATE
APPROXIMATION CUBIC SPLINES LEAST SQUARES APPROXIMATION PROGRAMS SUMMARY
EXERCISE PROBLEMS ER 5. NUMERICAL DIFFERENTIATION AND DIFFERENCE
FORMULAS INTRODUCTION UNEQUALLY SPACED DATA EQUALLY SPACED DATA TAYLOR
SERIES APPROACH DIFFERENCE FORMULAS ERROR ESTIMATION AND EXTRAPOLATION
PROGRAMS SUMMARY EXERCISE PROBLEMS ER 6. NUMERICAL INTEGRATION
INTRODUCTION DIRECT FIT POLYNOMIALS NEWTON-COTES FORMULAS 101 104 110
111 112 118 119 127 127 130 135 140 155 167 169 173 179 181 187 188 190
197 198 204 208 217 218 221 225 235 242 243 251 251 254 257 264 270 270
273 279 279 285 285 288 290 CONTENTS IX 6.4. EXTRAPOLATION AND ROMBERG
INTEGRATION 297 6.5. ADAPTIVE INTEGRATION 299 6.6. GAUSSIAN QUADRATURE
302 6.7. MULTIPLE INTEGRALS 306 6.8. PROGRAMS 311 6.9. SUMMARY 315
EXERCISE PROBLEMS 316 PART II. ORDINARY DIFFERENTIAL EQUATIONS 323 II.
1. INTRODUCTION 323 11.2. GENERAL FEATURES OF ORDINARY DIFFERENTIAL
EQUATIONS 323 11.3. CLASSIFICATION OF ORDINARY DIFFERENTIAL EQUATIONS
325 11.4. CLASSIFICATION OF PHYSICAL PROBLEMS 326 11.5. INITIAL-VALUE
ORDINARY DIFFERENTIAL EQUATIONS 327 *.6. BOUNDARY-VALUE ORDINARY
DIFFERENTIAL EQUATIONS 330 II.7. SUMMARY 332 CHAPTER 7. ONE-DIMENSIONAL
INITIAL-VALUE ORDINARY DIFFERENTIAL EQUATIONS 335 7.1. INTRODUCTION 336
7.2. GENERAL FEATURES OF INITIAL-VALUE ODES 340 7.3. THE TAYLOR SERIES
METHOD 343 7.4. THE FINITE DIFFERENCE METHOD 346 7.5. THE FIRST-ORDER
EULER METHODS 352 7.6. CONSISTENCY, ORDER, STABILITY, AND CONVERGENCE
359 7.7. SINGLE-POINT METHODS 364 7.8. EXTRAPOLATION METHODS 378 7.9.
MULTIPOINT METHODS 381 7.10. SUMMARY OF METHODS AND RESULTS 391 7.11.
NONLINEAR IMPLICIT FINITE DIFFERENCE EQUATIONS 393 7.12. HIGHER-ORDER
ORDINARY DIFFERENTIAL EQUATIONS 397 7.13. SYSTEMS OF FIRST-ORDER
ORDINARY DIFFERENTIAL EQUATIONS 398 7.14. STIFF ORDINARY DIFFERENTIAL
EQUATIONS 401 7.15. PROGRAMS 408 7.16. SUMMARY 414 EXERCISE PROBLEMS 416
CHAPTER 8. ONE-DIMENSIONAL BOUNDARY-VALUE ORDINARY DIFFERENTIAL
EQUATIONS 435 8.1. INTRODUCTION 436 8.2. GENERAL FEATURES OF
BOUNDARY-VALUE ODES 439 8.3. THE SHOOTING (INITIAL-VALUE) METHOD 441
8.4. THE EQUILIBRIUM (BOUNDARY-VALUE) METHOD 450 8.5. DERIVATIVE (AND
OTHER) BOUNDARY CONDITIONS 458 8.6. HIGHER-ORDER EQUILIBRIUM METHODS 466
8.7. THE EQUILIBRIUM METHOD FOR NONLINEAR BOUNDARY-VALUE PROBLEMS 471
8.8. THE EQUILIBRIUM METHOD ON NONUNIFORM GRIDS 477 8.9. EIGENPROBLEMS
480 8.10. PROGRAMS 483 8.11. SUMMARY 488 EXERCISE PROBLEMS 490 X PART
III. PARTIAL DIFFERENTIAL EQUATIONS 501 III. 1. INTRODUCTION 501 111.2.
GENERAL FEATURES OF PARTIAL DIFFERENTIAL EQUATIONS 502 111.3.
CLASSIFICATION OF PARTIAL DIFFERENTIAL EQUATIONS 504 111.4.
CLASSIFICATION OF PHYSICAL PROBLEMS 511 111.5. ELLIPTIC PARTIAL
DIFFERENTIAL EQUATIONS 516 111.6. PARABOLIC PARTIAL DIFFERENTIAL
EQUATIONS 519 111.7. HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS 520
111.8. THE CONVECTION-DIFFUSION EQUATION 523 111.9. INITIAL VALUES AND
BOUNDARY CONDITIONS 524 ***. WELL-POSED PROBLEMS 525 III.LL. SUMMARY 526
CHAPTER 9. ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS 527 9.1. INTRODUCTION
527 9.2. GENERAL FEATURES OF ELLIPTIC PDES 531 9.3. THE FINITE
DIFFERENCE METHOD 532 9.4. FINITE DIFFERENCE SOLUTION OF THE LAPLACE
EQUATION 536 9.5. CONSISTENCY, ORDER, AND CONVERGENCE 543 9.6. ITERATIVE
METHODS OF SOLUTION 546 9.7. DERIVATIVE BOUNDARY CONDITIONS 550 9.8.
FINITE DIFFERENCE SOLUTION OF THE POISSON EQUATION 552 9.9. HIGHER-ORDER
METHODS 557 9.10. NONRECTANGULAR DOMAINS 562 9.11. NONLINEAR EQUATIONS
AND THREE-DIMENSIONAL PROBLEMS 570 9.12. THE CONTROL VOLUME METHOD 571
9.13. PROGRAMS 575 9.14. SUMMARY 580 EXERCISE PROBLEMS 582 CHAPTER 10.
PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS 587 10.1. INTRODUCTION 587
10.2. GENERAL FEATURES OF PARABOLIC PDES 591 10.3. THE FINITE DIFFERENCE
METHOD 593 10.4. THE FORWARD-TIME CENTERED-SPACE (FTCS) METHOD 599 10.5.
CONSISTENCY, ORDER, STABILITY, AND CONVERGENCE 605 10.6. THE RICHARDSON
AND DUFORT-FRANKEL METHODS 611 10.7. IMPLICIT METHODS 613 10.8.
DERIVATIVE BOUNDARY CONDITIONS 623 10.9. NONLINEAR EQUATIONS AND
MULTIDIMENSIONAL PROBLEMS 625 10.10. THE CONVECTION-DIFFUSION EQUATION
629 10.11. ASYMPTOTIC STEADY STATE SOLUTION TO PROPAGATION PROBLEMS 637
10.12. PROGRAMS 639 10.13. SUMMARY 645 EXERCISE PROBLEMS 646 CHAPTER 11.
HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS 651 11.1. INTRODUCTION 651
11.2. GENERAL FEATURES OF HYPERBOLIC PDES 655 CONTENTS XI 11.3. THE
FINITE DIFFERENCE METHOD 657 11.4. THE FORWARD-TIME CENTERED-SPACE
(FTCS) METHOD AND THE LAX METHOD 659 11.5. LAX-WENDROFF TYPE METHODS 655
11.6. UPWIND METHODS 673 11.7. THE BACKWARD-TIME CENTERED-SPACE (BTCS)
METHOD 677 11.8. NONLINEAR EQUATIONS AND MULTIDIMENSIONAL PROBLEMS 682
11.9. THE WAVE EQUATION 683 11.10. PROGRAMS 691 11.11. SUMMARY 701
EXERCISE PROBLEMS 702 CHAPTER 12. THE FINITE ELEMENT METHOD 711 12.1.
INTRODUCTION 711 12.2. THE RAYLEIGH-RITZ, COLLOCATION, AND GALERKIN
METHODS 713 12.3. THE FINITE ELEMENT METHOD FOR BOUNDARY VALUE PROBLEMS
724 12.4. THE FINITE ELEMENT METHOD FOR THE LAPLACE (POISSON) EQUATION
739 12.5. THE FINITE ELEMENT METHOD FOR THE DIFFUSION EQUATION 752 12.6.
PROGRAMS 759 12.7. SUMMARY 769 EXERCISE PROBLEMS 770 REFERENCES 775
ANSWERS TO SELECTED PROBLEMS 779 INDEX 795
|
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| edition | 2. ed., rev. and expanded |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:25Z |
| institution | BVB |
| isbn | 0824704436 |
| language | English |
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| physical | XI, 823 S. graph. Darst. |
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| spelling | Hoffman, Joe D. Verfasser aut Numerical methods for engineers and scientists Joe D. Hoffman 2. ed., rev. and expanded New York [u.a.] Dekker 2001 XI, 823 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009524838&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoffman, Joe D. Numerical methods for engineers and scientists Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical methods for engineers and scientists |
| title_auth | Numerical methods for engineers and scientists |
| title_exact_search | Numerical methods for engineers and scientists |
| title_full | Numerical methods for engineers and scientists Joe D. Hoffman |
| title_fullStr | Numerical methods for engineers and scientists Joe D. Hoffman |
| title_full_unstemmed | Numerical methods for engineers and scientists Joe D. Hoffman |
| title_short | Numerical methods for engineers and scientists |
| title_sort | numerical methods for engineers and scientists |
| topic | Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerical analysis Numerische Mathematik |
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