Verfügbarkeit: Approximation techniques for engineers

Approximation techniques for engineers:

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Bibliographische Detailangaben
1. Verfasser:	Komzsik, Louis (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton, FL [u.a.] CRC/Taylor & Francis 2007
Schriftenreihe:	Electrical, mechanical, and aerospace engineering
Schlagworte:	Ingeniería - Métodos de aproximación Ingénierie - Méthodes des approximations Teoría de la aproximación Théorie de l'approximation Ingenieurwissenschaften Approximation theory Engineering > Approximation methods Approximationstheorie Näherungsverfahren
Online-Zugang:	Table of contents only Publisher description Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XVII, 296 S. Ill., graph. Darst.
ISBN:	9780849392771 0849392772

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Datensatz im Suchindex

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adam_text	APPROXIMATION TECHNIQUES FOR ENGINEERS LOUIS KOMZSIK UGS CORP. CYPRESS, CALIFORNIA @ TAY LOR &. FRANCIS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE VII ACKNOWLEDGMENTS IX ABOUT THE AUTHOR XI I DATA APPROXIMATIONS 1 1 CLASSICAL INTERPOLATION METHODS 3 1.1 NEWTON INTERPOLATION 4 1.1.1 EQUIDISTANT NEWTON INTERPOLATION 5 1.1.2 COMPUTATIONAL EXAMPLE 7 1.2 LAGRANGE INTERPOLATION 10 1.2.1 EQUIDISTANT LAGRANGE INTERPOLATION 10 1.2.2 COMPUTATIONAL EXAMPLE 11 1.2.3 PARAMETRIC LAGRANGE INTERPOLATION 13 1.3 HERMITE INTERPOLATION 15 1.3.1 COMPUTATIONAL EXAMPLE 17 1.4 INTERPOLATION OF FUNCTIONS OF TWO VARIABLES WITH POLYNOMIALS . 19 REFERENCES 20 2 APPROXIMATION WITH SPLINES 23 2.1 NATURAL CUBIC SPLINES 24 2.1.1 EQUIDISTANT NATURAL SPLINE APPROXIMATION 26 2.1.2 COMPUTATIONAL EXAMPLE 27 2.2 BEZIER SPLINES 28 2.2.1 RATIONAL BEZIER SPLINES 32 2.2.2 COMPUTATIONAL EXAMPLE 35 2.3 APPROXIMATION WITH B-SPLINES 38 2.3.1 COMPUTATIONAL EXAMPLE 39 2.3.2 NONUNIFORM B-SPLINES 41 2.3.3 NONUNIFORM RATIONAL B-SPLINES 43 2.4 SURFACE SPLINE APPROXIMATION 43 2.4.1 COONS SURFACES 44 2.4.2 COMPUTATIONAL EXAMPLE 48 2.4.3 BEZIER SURFACES 51 2.4.4 TRIANGULAER SURFACE PATCHES 54 XIII XIV CONTENTS 2.4.5 COMPUTATIONAL EXAMPLE 57 REFERENCES 59 3 LEAST SQUARES APPROXIMATION 61 3.1 THE LEAST SQUARES PRINCIPLE 61 3.2 LINEAR LEAST SQUARES APPROXIMATION 62 3.3 POLYNOMIAL LEAST SQUARES APPROXIMATION 63 3.4 COMPUTATIONAL EXAMPLE 65 3.5 EXPONENTIAL AND LOGARITHMIC LEAST SQUARES APPROXIMATIONS . . 67 3.6 NONLINEAR LEAST SQUARES APPROXIMATION 68 3.6.1 COMPUTATIONAL EXAMPLE 70 3.7 TRIGONOMETRIE LEAST SQUARES APPROXIMATION 72 3.7.1 COMPUTATIONAL EXAMPLE 74 3.8 DIRECTIONAL LEAST SQUARES APPROXIMATION 75 3.9 WEIGHTED LEAST SQUARES APPROXIMATION 76 REFERENCES 77 4 APPROXIMATION OF FUNETIONS 79 4.1 LEAST SQUARES APPROXIMATION OF FUNETIONS 79 4.2 APPROXIMATION WITH LEGENDRE POLYNOMIALS 81 4.2.1 GRAM-SCHMIDT ORTHOGONALIZATION 81 4.2.2 COMPUTATIONAL EXAMPLE 84 4.3 CHEBYSHEV APPROXIMATION 85 4.3.1 COLLAPSING A POWER SERIES 88 4.3.2 COMPUTATIONAL EXAMPLE 89 4.4 FOURIER APPROXIMATION 90 4.4.1 COMPUTATIONAL EXAMPLE 93 4.4.2 COMPLEX FOURIER APPROXIMATION 94 4.5 PADE APPROXIMATION 96 4.5.1 COMPUTATIONAL EXAMPLE 97 REFERENCES 100 5 NUMERICAL DIFFERENTIATION 101 5.1 FINITE DIFFERENCE FORMULAE 101 5.1.1 THREE-POINT FINITE DIFFERENCE FORMULAE 102 5.1.2 COMPUTATIONAL EXAMPLE 105 5.2 HIGHER ORDER DERIVATIVES 106 5.3 RICHARDSON S EXTRAPOLATION 108 5.3.1 COMPUTATIONAL EXAMPLE 110 5.4 MULTIPOINT FINITE DIFFERENCE FORMULAE 111 REFERENCES 115 CONTENTS XV 6 NUMERICAL INTEGRATION 117 6.1 THE NEWTON-COTES CLASS 117 6.1.1 THE TRAPEZOID RULE 118 6.1.2 SIMPSON S RULE 119 6.1.3 COMPUTATIONAL EXAMPLE 122 6.1.4 OPEN NEWTON-COTES FORMULAE 123 6.2 ADVANCED NEWTON-COTES METHODS 125 6.2.1 COMPOSITE METHODS 125 6.2.2 ROMBERG S METHOD 127 6.2.3 COMPUTATIONAL EXAMPLE 129 6.3 GAUSSIAN QUADRATURE 130 6.3.1 COMPUTATIONAL EXAMPLE 133 6.4 INTEGRATION OF FUNCTIONS OF MULTIPLE VARIABLES 135 6.4.1 GAUSSIAN CUBATURE 136 6.5 CHEBYSHEV QUADRATURE 136 6.6 NUMERICAL INTEGRATION OF PERIODIC FUNCTIONS 137 REFERENCES 139 II APPROXIMATE SOLUTIONS 141 7 NONLINEAR EQUATIONS IN ONE VARIABLE 143 7.1 GENERAL EQUATIONS 143 7.1.1 THE METHOD OF BISECTION 143 7.1.2 THE SECANT METHOD 145 7.1.3 FIXED POINT ITERATION 147 7.1.4 COMPUTATIONAL EXAMPLE 148 7.2 NEWTON S METHOD 149 7.3 SOLUTION OF ALGEBRAIC EQUATIONS 153 7.3.1 STURM SEQUENCE 153 7.3.2 HORNER S SCHEME OF EVALUATING POLYNOMIALS 154 7.3.3 COMPUTATIONAL EXAMPLE 155 7.4 AITKEN S ACCELERATION 157 7.4.1 COMPUTATIONAL EXAMPLE 158 REFERENCES 159 8 SYSTEMS OF NONLINEAR EQUATIONS 161 8.1 THE GENERALIZED FIXED POINT METHOD 161 8.2 THE METHOD OF STEEPEST DESCENT 163 8.2.1 COMPUTATIONAL EXAMPLE 165 8.3 THE GENERALIZATION OF NEWTON S METHOD 167 8.3.1 COMPUTATIONAL EXAMPLE 167 8.4 QUASI-NEWTON METHOD 169 8.4.1 COMPUTATIONAL EXAMPLE 170 8.5 NONLINEAR STATIC ANALYSIS APPLICATION 171 REFERENCES 173 XVI CONTENTS 9 ITERATIVE SOLUTION OF LINEAR SYSTEMS 175 9.1 ITERATIVE SOLUTION OF LINEAR SYSTEMS 175 9.2 SPLITTING METHODS 177 9.2.1 JACOBI METHOD 177 9.2.2 GAUSS-SEIDEL METHOD 177 9.2.3 SUCCESSIVE OVERRELAXATION METHOD 178 9.2.4 COMPUTATIONAL FORMULATION OF SPLITTING METHODS . . . . 179 9.3 RITZ-GALERKIN METHOD 180 9.4 CONJUGATE GRADIENT METHOD 182 9.4.1 COMPUTATIONAL EXAMPLE 184 9.5 PRECONDITIONING TECHNIQUES 185 9.5.1 APPROXIMATE INVERSE 187 9.6 BICONJUGATE GRADIENT METHOD 188 9.7 LEAST SQUARES SYSTEMS 190 9.7.1 QR FACTORIZATION 191 9.7.2 COMPUTATIONAL EXAMPLE 192 9.8 THE MINIMUM RESIDUAL APPROACH 194 9.9 ALGEBRAIC MULTIGRID METHOD 196 9.10 LINEAR STATIC ANALYSIS APPLICATION 198 REFERENCES 199 10 APPROXIMATE SOLUTION OF EIGENVALUE PROBLEMS 201 10.1 CLASSICAL ITERATIONS 201 10.2 THE RAYLEIGH-RITZ PROCEDURE 203 10.3 THE LANCZOS METHOD 204 10.3.1 TRUNCATED LANCZOS PROCESS ACCURACY 206 10.4 THE SOLUTION OF THE TRIDIAGONAL EIGENVALUE PROBLEM 207 10.5 THE BIORTHOGONAL LANCZOS METHOD 209 10.5.1 COMPUTATIONAL EXAMPLE 210 10.6 THE ARNOLDI METHOD 215 10.7 THE BLOCK LANCZOS METHOD 216 10.7.1 PRECONDITIONED BLOCK LANCZOS METHOD 217 10.8 NORMAL MODES ANALYSIS APPLICATION 218 REFERENCES 219 11 INITIAL VALUE PROBLEMS 221 11.1 SOLUTION OF INITIAL VALUE PROBLEMS 221 11.2 SINGLE-STEP METHODS 223 11.2.1 EULER S METHOD 223 11.2.2 TAYLOR METHODS 225 11.2.3 COMPUTATIONAL EXAMPLE 226 11.2.4 RUNGE-KUTTA METHODS 227 11.2.5 COMPUTATIONAL EXAMPLE 229 11.3 MULTISTEP METHODS 230 11.3.1 EXPLICIT METHODS 230 XV11 11.3.2 IMPLICIT METHODS 233 11.3.3 PREDICTOR-CORRECTOR TECHNIQUE 233 11.3.4 GRAGG S METHOD OF EXTRAPOLATION 235 11.3.5 COMPUTATIONAL EXAMPLE 239 11.3.6 FEHLBERG S METHOD OF STEP SIZE ADJUSTMENT 240 11.3.7 STABILITY OF MULTISTEP TECHNIQUES 242 11.4 INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS .... 242 11.4.1 COMPUTATIONAL EXAMPLE 244 11.5 INITIAL VALUE PROBLEMS OF HIGHER ORDER ORDINARY DIFFERENTIAL EQUA- TIONS 246 11.5.1 COMPUTATIONAL EXAMPLE 247 11.6 TRANSIENT RESPONSE ANALYSIS APPLICATION 248 REFERENCES 249 12 BOUNDARY VALUE PROBLEMS 251 12.1 BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS . 251 12.1.1 NONLINEAR BOUNDARY VALUE PROBLEMS 252 12.1.2 LINEAR BOUNDARY VALUE PROBLEMS 252 12.2 THE FINITE DIFFERENCE METHOD FOR BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS 253 12.3 BOUNDARY VALUE PROBLEMS OF PARTIAL DIFFERENTIAL EQUATIONS . . . 256 12.4 THE FINITE DIFFERENCE METHOD FOR BOUNDARY VALUE PROBLEMS OF PARTIAL DIFFERENTIAL EQUATIONS 257 12.4.1 COMPUTATIONAL EXAMPLE 260 12.5 THE FINITE ELEMENT METHOD 264 12.5.1 FINITE ELEMENT SHAPE FUNCTIONS 267 12.5.2 FINITE ELEMENT MATRIX GENERATION AND ASSEMBLY .... 268 12.5.3 COMPUTATIONAL EXAMPLE 269 12.6 FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL CONTINUUM .... 276 12.6.1 TETRAHEDRAL FINITE ELEMENT 277 12.6.2 FINITE ELEMENT MATRIX IN PARAMETRIC COORDINATES . . . 279 12.6.3 LOCAL TO GLOBAL COORDINATE TRANSFORMATION 281 12.7 FLUID-STRUCTURE INTERACTION APPLICATION 283 REFERENCES 284 CLOSING REMARKS 285 LIST OF FIGURES 288 LIST OF TABLES 289 ANNOTATION 291 INDEX 293
adam_txt	APPROXIMATION TECHNIQUES FOR ENGINEERS LOUIS KOMZSIK UGS CORP. CYPRESS, CALIFORNIA @ TAY LOR &. FRANCIS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE VII ACKNOWLEDGMENTS IX ABOUT THE AUTHOR XI I DATA APPROXIMATIONS 1 1 CLASSICAL INTERPOLATION METHODS 3 1.1 NEWTON INTERPOLATION 4 1.1.1 EQUIDISTANT NEWTON INTERPOLATION 5 1.1.2 COMPUTATIONAL EXAMPLE 7 1.2 LAGRANGE INTERPOLATION 10 1.2.1 EQUIDISTANT LAGRANGE INTERPOLATION 10 1.2.2 COMPUTATIONAL EXAMPLE 11 1.2.3 PARAMETRIC LAGRANGE INTERPOLATION 13 1.3 HERMITE INTERPOLATION 15 1.3.1 COMPUTATIONAL EXAMPLE 17 1.4 INTERPOLATION OF FUNCTIONS OF TWO VARIABLES WITH POLYNOMIALS . 19 REFERENCES 20 2 APPROXIMATION WITH SPLINES 23 2.1 NATURAL CUBIC SPLINES 24 2.1.1 EQUIDISTANT NATURAL SPLINE APPROXIMATION 26 2.1.2 COMPUTATIONAL EXAMPLE 27 2.2 BEZIER SPLINES 28 2.2.1 RATIONAL BEZIER SPLINES 32 2.2.2 COMPUTATIONAL EXAMPLE 35 2.3 APPROXIMATION WITH B-SPLINES 38 2.3.1 COMPUTATIONAL EXAMPLE 39 2.3.2 NONUNIFORM B-SPLINES 41 2.3.3 NONUNIFORM RATIONAL B-SPLINES 43 2.4 SURFACE SPLINE APPROXIMATION 43 2.4.1 COONS SURFACES 44 2.4.2 COMPUTATIONAL EXAMPLE 48 2.4.3 BEZIER SURFACES 51 2.4.4 TRIANGULAER SURFACE PATCHES 54 XIII XIV CONTENTS 2.4.5 COMPUTATIONAL EXAMPLE 57 REFERENCES 59 3 LEAST SQUARES APPROXIMATION 61 3.1 THE LEAST SQUARES PRINCIPLE 61 3.2 LINEAR LEAST SQUARES APPROXIMATION 62 3.3 POLYNOMIAL LEAST SQUARES APPROXIMATION 63 3.4 COMPUTATIONAL EXAMPLE 65 3.5 EXPONENTIAL AND LOGARITHMIC LEAST SQUARES APPROXIMATIONS . . 67 3.6 NONLINEAR LEAST SQUARES APPROXIMATION 68 3.6.1 COMPUTATIONAL EXAMPLE 70 3.7 TRIGONOMETRIE LEAST SQUARES APPROXIMATION 72 3.7.1 COMPUTATIONAL EXAMPLE 74 3.8 DIRECTIONAL LEAST SQUARES APPROXIMATION 75 3.9 WEIGHTED LEAST SQUARES APPROXIMATION 76 REFERENCES 77 4 APPROXIMATION OF FUNETIONS 79 4.1 LEAST SQUARES APPROXIMATION OF FUNETIONS 79 4.2 APPROXIMATION WITH LEGENDRE POLYNOMIALS 81 4.2.1 GRAM-SCHMIDT ORTHOGONALIZATION 81 4.2.2 COMPUTATIONAL EXAMPLE 84 4.3 CHEBYSHEV APPROXIMATION 85 4.3.1 COLLAPSING A POWER SERIES 88 4.3.2 COMPUTATIONAL EXAMPLE 89 4.4 FOURIER APPROXIMATION 90 4.4.1 COMPUTATIONAL EXAMPLE 93 4.4.2 COMPLEX FOURIER APPROXIMATION 94 4.5 PADE APPROXIMATION 96 4.5.1 COMPUTATIONAL EXAMPLE 97 REFERENCES 100 5 NUMERICAL DIFFERENTIATION 101 5.1 FINITE DIFFERENCE FORMULAE 101 5.1.1 THREE-POINT FINITE DIFFERENCE FORMULAE 102 5.1.2 COMPUTATIONAL EXAMPLE 105 5.2 HIGHER ORDER DERIVATIVES 106 5.3 RICHARDSON'S EXTRAPOLATION 108 5.3.1 COMPUTATIONAL EXAMPLE 110 5.4 MULTIPOINT FINITE DIFFERENCE FORMULAE 111 REFERENCES 115 CONTENTS XV 6 NUMERICAL INTEGRATION 117 6.1 THE NEWTON-COTES CLASS 117 6.1.1 THE TRAPEZOID RULE 118 6.1.2 SIMPSON'S RULE 119 6.1.3 COMPUTATIONAL EXAMPLE 122 6.1.4 OPEN NEWTON-COTES FORMULAE 123 6.2 ADVANCED NEWTON-COTES METHODS 125 6.2.1 COMPOSITE METHODS 125 6.2.2 ROMBERG'S METHOD 127 6.2.3 COMPUTATIONAL EXAMPLE 129 6.3 GAUSSIAN QUADRATURE 130 6.3.1 COMPUTATIONAL EXAMPLE 133 6.4 INTEGRATION OF FUNCTIONS OF MULTIPLE VARIABLES 135 6.4.1 GAUSSIAN CUBATURE 136 6.5 CHEBYSHEV QUADRATURE 136 6.6 NUMERICAL INTEGRATION OF PERIODIC FUNCTIONS 137 REFERENCES 139 II APPROXIMATE SOLUTIONS 141 7 NONLINEAR EQUATIONS IN ONE VARIABLE 143 7.1 GENERAL EQUATIONS 143 7.1.1 THE METHOD OF BISECTION 143 7.1.2 THE SECANT METHOD 145 7.1.3 FIXED POINT ITERATION 147 7.1.4 COMPUTATIONAL EXAMPLE 148 7.2 NEWTON'S METHOD 149 7.3 SOLUTION OF ALGEBRAIC EQUATIONS 153 7.3.1 STURM SEQUENCE 153 7.3.2 HORNER'S SCHEME OF EVALUATING POLYNOMIALS 154 7.3.3 COMPUTATIONAL EXAMPLE 155 7.4 AITKEN'S ACCELERATION 157 7.4.1 COMPUTATIONAL EXAMPLE 158 REFERENCES 159 8 SYSTEMS OF NONLINEAR EQUATIONS 161 8.1 THE GENERALIZED FIXED POINT METHOD 161 8.2 THE METHOD OF STEEPEST DESCENT 163 8.2.1 COMPUTATIONAL EXAMPLE 165 8.3 THE GENERALIZATION OF NEWTON'S METHOD 167 8.3.1 COMPUTATIONAL EXAMPLE 167 8.4 QUASI-NEWTON METHOD 169 8.4.1 COMPUTATIONAL EXAMPLE 170 8.5 NONLINEAR STATIC ANALYSIS APPLICATION 171 REFERENCES 173 XVI CONTENTS 9 ITERATIVE SOLUTION OF LINEAR SYSTEMS 175 9.1 ITERATIVE SOLUTION OF LINEAR SYSTEMS 175 9.2 SPLITTING METHODS 177 9.2.1 JACOBI METHOD 177 9.2.2 GAUSS-SEIDEL METHOD 177 9.2.3 SUCCESSIVE OVERRELAXATION METHOD 178 9.2.4 COMPUTATIONAL FORMULATION OF SPLITTING METHODS . . . . 179 9.3 RITZ-GALERKIN METHOD 180 9.4 CONJUGATE GRADIENT METHOD 182 9.4.1 COMPUTATIONAL EXAMPLE 184 9.5 PRECONDITIONING TECHNIQUES 185 9.5.1 APPROXIMATE INVERSE 187 9.6 BICONJUGATE GRADIENT METHOD 188 9.7 LEAST SQUARES SYSTEMS 190 9.7.1 QR FACTORIZATION 191 9.7.2 COMPUTATIONAL EXAMPLE 192 9.8 THE MINIMUM RESIDUAL APPROACH 194 9.9 ALGEBRAIC MULTIGRID METHOD 196 9.10 LINEAR STATIC ANALYSIS APPLICATION 198 REFERENCES 199 10 APPROXIMATE SOLUTION OF EIGENVALUE PROBLEMS 201 10.1 CLASSICAL ITERATIONS 201 10.2 THE RAYLEIGH-RITZ PROCEDURE 203 10.3 THE LANCZOS METHOD 204 10.3.1 TRUNCATED LANCZOS PROCESS ACCURACY 206 10.4 THE SOLUTION OF THE TRIDIAGONAL EIGENVALUE PROBLEM 207 10.5 THE BIORTHOGONAL LANCZOS METHOD 209 10.5.1 COMPUTATIONAL EXAMPLE 210 10.6 THE ARNOLDI METHOD 215 10.7 THE BLOCK LANCZOS METHOD 216 10.7.1 PRECONDITIONED BLOCK LANCZOS METHOD 217 10.8 NORMAL MODES ANALYSIS APPLICATION 218 REFERENCES 219 11 INITIAL VALUE PROBLEMS 221 11.1 SOLUTION OF INITIAL VALUE PROBLEMS 221 11.2 SINGLE-STEP METHODS 223 11.2.1 EULER'S METHOD 223 11.2.2 TAYLOR METHODS 225 11.2.3 COMPUTATIONAL EXAMPLE 226 11.2.4 RUNGE-KUTTA METHODS 227 11.2.5 COMPUTATIONAL EXAMPLE 229 11.3 MULTISTEP METHODS 230 11.3.1 EXPLICIT METHODS 230 XV11 11.3.2 IMPLICIT METHODS 233 11.3.3 PREDICTOR-CORRECTOR TECHNIQUE 233 11.3.4 GRAGG'S METHOD OF EXTRAPOLATION 235 11.3.5 COMPUTATIONAL EXAMPLE 239 11.3.6 FEHLBERG'S METHOD OF STEP SIZE ADJUSTMENT 240 11.3.7 STABILITY OF MULTISTEP TECHNIQUES 242 11.4 INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS . 242 11.4.1 COMPUTATIONAL EXAMPLE 244 11.5 INITIAL VALUE PROBLEMS OF HIGHER ORDER ORDINARY DIFFERENTIAL EQUA- TIONS 246 11.5.1 COMPUTATIONAL EXAMPLE 247 11.6 TRANSIENT RESPONSE ANALYSIS APPLICATION 248 REFERENCES 249 12 BOUNDARY VALUE PROBLEMS 251 12.1 BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS . 251 12.1.1 NONLINEAR BOUNDARY VALUE PROBLEMS 252 12.1.2 LINEAR BOUNDARY VALUE PROBLEMS 252 12.2 THE FINITE DIFFERENCE METHOD FOR BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS 253 12.3 BOUNDARY VALUE PROBLEMS OF PARTIAL DIFFERENTIAL EQUATIONS . . . 256 12.4 THE FINITE DIFFERENCE METHOD FOR BOUNDARY VALUE PROBLEMS OF PARTIAL DIFFERENTIAL EQUATIONS 257 12.4.1 COMPUTATIONAL EXAMPLE 260 12.5 THE FINITE ELEMENT METHOD 264 12.5.1 FINITE ELEMENT SHAPE FUNCTIONS 267 12.5.2 FINITE ELEMENT MATRIX GENERATION AND ASSEMBLY . 268 12.5.3 COMPUTATIONAL EXAMPLE 269 12.6 FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL CONTINUUM . 276 12.6.1 TETRAHEDRAL FINITE ELEMENT 277 12.6.2 FINITE ELEMENT MATRIX IN PARAMETRIC COORDINATES . . . 279 12.6.3 LOCAL TO GLOBAL COORDINATE TRANSFORMATION 281 12.7 FLUID-STRUCTURE INTERACTION APPLICATION 283 REFERENCES 284 CLOSING REMARKS 285 LIST OF FIGURES 288 LIST OF TABLES 289 ANNOTATION 291 INDEX 293
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id	DE-604.BV022193736
illustrated	Illustrated
index_date	2024-07-02T16:22:12Z
indexdate	2024-07-09T20:52:06Z
institution	BVB
isbn	9780849392771 0849392772
language	English
lccn	2006040582
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-015405268
oclc_num	67728350
open_access_boolean
owner	DE-703 DE-91G DE-BY-TUM DE-29T
owner_facet	DE-703 DE-91G DE-BY-TUM DE-29T
physical	XVII, 296 S. Ill., graph. Darst.
publishDate	2007
publishDateSearch	2007
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publisher	CRC/Taylor & Francis
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series2	Electrical, mechanical, and aerospace engineering
spelling	Komzsik, Louis Verfasser (DE-588)1220387932 aut Approximation techniques for engineers Louis Komzsik Boca Raton, FL [u.a.] CRC/Taylor & Francis 2007 XVII, 296 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Electrical, mechanical, and aerospace engineering Includes bibliographical references and index Ingeniería - Métodos de aproximación Ingénierie - Méthodes des approximations Teoría de la aproximación Théorie de l'approximation Ingenieurwissenschaften Approximation theory Engineering Approximation methods Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Näherungsverfahren (DE-588)4206467-3 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 s Näherungsverfahren (DE-588)4206467-3 s DE-604 Approximationstheorie (DE-588)4120913-8 s 1\p DE-604 http://www.loc.gov/catdir/toc/fy0701/2006040582.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0654/2006040582-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015405268&sequence=000001&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	Komzsik, Louis Approximation techniques for engineers Ingeniería - Métodos de aproximación Ingénierie - Méthodes des approximations Teoría de la aproximación Théorie de l'approximation Ingenieurwissenschaften Approximation theory Engineering Approximation methods Approximationstheorie (DE-588)4120913-8 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Näherungsverfahren (DE-588)4206467-3 gnd
subject_GND	(DE-588)4120913-8 (DE-588)4137304-2 (DE-588)4206467-3
title	Approximation techniques for engineers
title_auth	Approximation techniques for engineers
title_exact_search	Approximation techniques for engineers
title_exact_search_txtP	Approximation techniques for engineers
title_full	Approximation techniques for engineers Louis Komzsik
title_fullStr	Approximation techniques for engineers Louis Komzsik
title_full_unstemmed	Approximation techniques for engineers Louis Komzsik
title_short	Approximation techniques for engineers
title_sort	approximation techniques for engineers
topic	Ingeniería - Métodos de aproximación Ingénierie - Méthodes des approximations Teoría de la aproximación Théorie de l'approximation Ingenieurwissenschaften Approximation theory Engineering Approximation methods Approximationstheorie (DE-588)4120913-8 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Näherungsverfahren (DE-588)4206467-3 gnd
topic_facet	Ingeniería - Métodos de aproximación Ingénierie - Méthodes des approximations Teoría de la aproximación Théorie de l'approximation Ingenieurwissenschaften Approximation theory Engineering Approximation methods Approximationstheorie Näherungsverfahren
url	http://www.loc.gov/catdir/toc/fy0701/2006040582.html http://www.loc.gov/catdir/enhancements/fy0654/2006040582-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015405268&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT komzsiklouis approximationtechniquesforengineers

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