Holdings: Numerical methods for engineers and scientists

Numerical methods for engineers and scientists:

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Bibliographic Details
Main Author:	Hoffman, Joe D. (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Dekker 2001
Edition:	2. ed., rev. and expanded
Subjects:	Numerical analysis Numerische Mathematik
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 823 S. graph. Darst.
ISBN:	0824704436

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MARC


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Record in the Search Index

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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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spellingShingle	Hoffman, Joe D. Numerical methods for engineers and scientists Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd
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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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