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Continuum mechanics using Mathematica: fundamentals, applications and scientific computing

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Bibliographic Details
Main Authors:	Romano, Antonio (Author), Lancellotta, Renato (Author), Marasco, Addolorata 1972- (Author)
Format:	Book
Language:	English
Published:	Boston ; Basel ; Berlin Birkhäuser 2006
Series:	Modeling and simulation in science, engineering and technology
Subjects:	Mathematica (Computer file) Datenverarbeitung Continuum mechanics > Data processing Mathematica > Programm Kontinuumsmechanik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014741852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XII, 388 S. graph. Darst. 1 CD-ROM (12 cm)
ISBN:	9780817632403 0817632409

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Record in the Search Index

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adam_text	ANTONIO ROMANO RENATO LANCELLOTTA ADDOLORATA MARASCO CONTINUUM MECHANICS USING MATHEMATICA FUNDAMENTALS, APPLICATIONS AND SCIENTIFIC COMPUTING BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE IX 1 ELEMENTS OF LINEAR ALGEBRA 1 1.1 MOTIVATION TO STUDY LINEAR ALGEBRA 1 1.2 VECTOR SPACES AND BASES 2 1.3 EUCLIDEAN VECTOR SPACE 5 1.4 BASE CHANGES 9 1.5 VECTOR PRODUCT 11 1.6 MIXED PRODUCT 13 1.7 ELEMENTS OF TENSOR ALGEBRA 14 1.8 EIGENVALUES AND EIGENVECTORS OF A EUCLIDEAN SECOND-ORDER TENSOR 20 1.9 ORTHOGONAL TENSORS 24 1.10 CAUCHY S POLAR DECOMPOSITION THEOREM 28 1.11 HIGHER ORDER TENSORS 29 1.12 EUCLIDEAN POINT SPACE 30 1.13 EXERCISES 32 1.14 THE PROGRAM VECTORSYS 36 1.15 THE PROGRAM EIGENSYSTEMAG 41 2 VECTOR ANALYSIS 45 2.1 CURVILINEAR COORDINATES 45 2.2 EXAMPLES OF CURVILINEAR COORDINATES 48 2.3 DIFFERENTIATION OF VECTOR FIELDS 50 2.4 THE STOKES AND GAUSS THEOREMS 55 2.5 SINGULAR SURFACES 56 2.6 USEFUL FORMULAE 60 2.7 SOME CURVILINEAR COORDINATES 62 2.7.1 GENERALIZED POLAR COORDINATES 63 2.7.2 CYLINDRICAL COORDINATES 64 2.7.3 SPHERICAL COORDINATES 65 2.7.4 ELLIPTIC COORDINATES 66 VI CONTENTS 2.7.5 PARABOLIC COORDINATES 67 2.7.6 BIPOLAR COORDINATES 68 2.7.7 PROLATE AND OBLATE SPHEROIDAL COORDINATES 68 2.7.8 PARABOLOIDAL COORDINATES 69 2.8 EXERCISES 69 2.9 THE PROGRAM OPERATOR 70 3 FINITE AND INFINITESIMAL DEFORMATIONS 77 3.1 DEFORMATION GRADIENT 77 3.2 STRETCH RATIO AND ANGULAR DISTORTION 80 3.3 INVARIANTS OF C AND B 83 3.4 DISPLACEMENT AND DISPLACEMENT GRADIENT 84 3.5 INFINITESIMAL DEFORMATION THEORY 86 3.6 TRANSFORMATION RULES FOR DEFORMATION TENSORS 88 3.7 SOME RELEVANT FORMULAE 89 3.8 COMPATIBILITY CONDITIONS 92 3.9 CURVILINEAR COORDINATES 95 3.10 EXERCISES 96 3.11 THE PROGRAM DEFORMATION 101 4 KINEMATICS 109 4.1 VELOCITY AND ACCELERATION 109 4.2 VELOCITY GRADIENT 112 4.3 RIGID, IRROTATIONAL, AND ISOCHORIC MOTIONS 113 4.4 TRANSFORMATION RULES FOR A CHANGE OF FRAME 115 4.5 SINGULAR MOVING SURFACES 116 4.6 TIME DERIVATIVE OF A MOVING VOLUME 119 4.7 WORKED EXERCISES 123 4.8 THE PROGRAM VELOCITY 126 5 BALANCE EQUATIONS 131 5.1 GENERAL FORMULATION OF A BALANCE EQUATION 131 5.2 MASS CONSERVATION . . . 136 5.3 MOMENTUM BALANCE EQUATION 137 5.4 BALANCE OF ANGULAR MOMENTUM 140 5.5 ENERGY BALANCE 141 5.6 ENTROPY INEQUALITY 143 5.7 LAGRANGIAN FORMULATION OF BALANCE EQUATIONS 146 5.8 THE PRINCIPLE OF VIRTUAL DISPLACEMENTS 150 5.9 EXERCISES 151 CONTENTS VII CONSTITUTIVE EQUATIONS 155 6.1 CONSTITUTIVE AXIOMS 155 6.2 THERMOVISCOELASTIC BEHAVIOR 160 6.3 LINEAR THERMOELASTICITY 165 6.4 EXERCISES 169 SYMMETRY GROUPS: SOLIDS AND FLUIDS 171 7.1 SYMMETRY 171 7.2 ISOTROPIC SOLIDS 174 7.3 PERFECT AND VISCOUS FLUIDS 177 7.4 ANISOTROPIC SOLIDS 181 7.5 EXERCISES 183 7.6 THE PROGRAM LINELASTICITYTENSOR 185 WAVE PROPAGATION 189 8.1 INTRODUCTION 189 8.2 CAUCHY S PROBLEM FOR SECOND-ORDER PDES 190 8.3 CHARACTERISTICS AND CLASSIFICATION OF PDES 194 8.4 EXAMPLES 196 8.5 CAUCHY S PROBLEM FOR A QUASI-LINEAR FIRST-ORDER SYSTEM . 199 8.6 CLASSIFICATION OF FIRST-ORDER SYSTEMS 201 8.7 EXAMPLES 202 8.8 SECOND-ORDER SYSTEMS 206 8.9 ORDINARY WAVES 207 8.10 LINEARIZED THEORY AND WAVES 211 8.11 SHOCKWAVES 215 8.12 EXERCISES 218 8.13 THE PROGRAM PDEEQCLASS 221 8.14 THE PROGRAM PDESYSCLASS 227 8.15 THE PROGRAM WAVESI 233 8.16 THE PROGRAM WAVESII 239 FLUID MECHANICS 245 9.1 PERFECT FLUID 245 9.2 STEVINO S LAW AND ARCHIMEDES PRINCIPLE 246 9.3 FUNDAMENTAL THEOREMS OF FLUID DYNAMICS 250 9.4 BOUNDARY VALUE PROBLEMS FOR A PERFECT FLUID 254 9.5 2D STEADY FLOW OF A PERFECT FLUID 256 9.6 D ALEMBERT S PARADOX AND THE KUTTA-JOUKOWSKY THEOREM 264 9.7 LIFT AND AIRFOILS 267 9.8 NEWTONIAN FLUIDS 272 9.9 APPLICATIONS OF THE NAVIER-STOKES EQUATION 273 9.10 DIMENSIONAL ANALYSIS AND THE NAVIER-STOKES EQUATION . . . 274 9.11 BOUNDARY LAYER 276 CONTENTS 9.12 MOTION OF A VISCOUS LIQUID AROUND AN OBSTACLE 281 9.13 ORDINARY WAVES IN PERFECT FLUIDS 287 9.14 SHOCK WAVES IN FLUIDS 290 9.15 SHOCK WAVES IN A PERFECT GAS 293 9.16 EXERCISES 296 9.17 THE PROGRAM POTENTIAL 298 9.18 THE PROGRAM WING 306 9.19 THE PROGRAM JOUKOWSKY 309 9.20 THE PROGRAM JOUKOWSKYMAP 312 10 LINEAR ELASTICITY 317 10.1 BASIC EQUATIONS OF LINEAR ELASTICITY 317 10.2 UNIQUENESS THEOREMS 321 10.3 EXISTENCE AND UNIQUENESS OF EQUILIBRIUM SOLUTIONS 323 10.4 EXAMPLES OF DEFORMATIONS 327 10.5 THE BOUSSINESQ-PAPKOVICH-NEUBER SOLUTION 329 10.6 SAINT-VENANT S CONJECTURE 330 10.7 THE FUNDAMENTAL SAINT-VENANT SOLUTIONS 335 10.8 ORDINARY WAVES IN ELASTIC SYSTEMS 339 10.9 PLANE WAVES 345 10.10 REFLECTION OF PLANE WAVES IN A HALF-SPACE 350 10.11 RAYLEIGH WAVES 356 10.12 REFLECTION AND REFRACTION OF SH WAVES 359 10.13 HARMONIC WAVES IN A LAYER 362 10.14 EXERCISES 365 11 OTHER APPROACHES TO THERMODYNAMICS 367 11.1 BASIC THERMODYNAMICS 367 11.2 EXTENDED THERMODYNAMICS 370 11.3 SERRIN S APPROACH 372 11.4 AN APPLICATION TO VISCOUS FLUIDS 375 REFERENCES 379 INDEX 383
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spellingShingle	Romano, Antonio Lancellotta, Renato Marasco, Addolorata 1972- Continuum mechanics using Mathematica fundamentals, applications and scientific computing Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd
subject_GND	(DE-588)4268208-3 (DE-588)4032296-8
title	Continuum mechanics using Mathematica fundamentals, applications and scientific computing
title_auth	Continuum mechanics using Mathematica fundamentals, applications and scientific computing
title_exact_search	Continuum mechanics using Mathematica fundamentals, applications and scientific computing
title_full	Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco
title_fullStr	Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco
title_full_unstemmed	Continuum mechanics using Mathematica fundamentals, applications and scientific computing Antonio Romano ; Renato Lancellotta ; Addolorata Marasco
title_short	Continuum mechanics using Mathematica
title_sort	continuum mechanics using mathematica fundamentals applications and scientific computing
title_sub	fundamentals, applications and scientific computing
topic	Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm (DE-588)4268208-3 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd
topic_facet	Mathematica (Computer file) Datenverarbeitung Continuum mechanics Data processing Mathematica Programm Kontinuumsmechanik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014741852&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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