Holdings: Mathematical physics

Mathematical physics: applied mathematics for scientists and engineers

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Bibliographic Details
Main Author:	Kusse, Bruce R. 1938- (Author)
Format:	Book
Language:	English
Published:	Weinheim Wiley-VCH 2006
Edition:	2. ed.
Series:	Physics textbook
Subjects:	Physique mathématique Mathematische Physik Mathematical physics Lehrbuch
Online Access:	Table of contents only Inhaltsverzeichnis
Item Description:	Includes bibliographical references (p. 671) and index
Physical Description:	XI, 678 S. graph. Darst. 24 cm
ISBN:	3527406727

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MARC


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adam_text	BRUCE R. KUSSE AND ERIK A. WESTWIG MATHEMATICAL PHYSICS APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 2ND EDITION WILEY- VCH WILEY-VCH VERLAG GMBH & CO. KGAA CONTENTS 1 A REVIEW OF VECTOR AND MATRIX ALGEBRA USING SUBSCRIPT/SUMMATION CONVENTIONS 1 1.1 NOTATION, 1 1.2 VECTOR OPERATIONS, 5 2 DIFFERENTIAL AND INTEGRAL OPERATIONS ON VECTOR AND SCALAR FIELDS 18 2.1 PLOTTING SCALAR AND VECTOR FIELDS, 18 2.2 INTEGRAL OPERATORS, 20 2.3 DIFFERENTIAL OPERATIONS, 23 2.4 INTEGRAL DEFINITIONS OF THE DIFFERENTIAL OPERATORS, 34 2.5 THE THEOREMS, 35 3 CURVILINEAR COORDINATE SYSTEMS 44 3.1 THE POSITION VECTOR, 44 3.2 THE CYLINDRICAL SYSTEM, 45 3.3 THE SPHERICAL SYSTEM, 48 3.4 GENERAL CURVILINEAR SYSTEMS, 49 3.5 THE GRADIENT, DIVERGENCE, AND CURL IN CYLINDRICAL AND SPHERICAL SYSTEMS, 58 VII VLII CONTENTS 4 INTRODUCTION TO TENSORS 67 4.1 THE CONDUCTIVITY TENSOR AND OHM S LAW, 67 4.2 GENERAL TENSOR NOTATION AND TERMINOLOGY, 71 4.3 TRANSFORMATIONS BETWEEN COORDINATE SYSTEMS, 71 4.4 TENSOR DIAGONALIZATION, 78 4.5 TENSOR TRANSFORMATIONS IN CURVILINEAR COORDINATE SYSTEMS, 84 4.6 PSEUDO-OBJECTS, 86 5 THE DIRAC S-FUNCTION 100 5.1 EXAMPLES OF SINGULAR FUNCTIONS IN PHYSICS, 100 5.2 TWO DEFINITIONS OF S(0, 103 5.3 5-FUNCTIONS WITH COMPLICATED ARGUMENTS, 108 5.4 INTEGRALS AND DERIVATIVES OF S(T), 111 5.5 SINGULAR DENSITY FUNCTIONS, 114 5.6 THE INFINITESIMAL ELECTRIC DIPOLE, 121 5.7 RIEMANN INTEGRATION AND THE DIRAC S-FUNCTION, 125 6 INTRODUCTION TO COMPLEX VARIABLES 135 6.1 A COMPLEX NUMBER REFRESHER, 135 6.2 FUNCTIONS OF A COMPLEX VARIABLE, 138 6.3 DERIVATIVES OF COMPLEX FUNCTIONS, 140 6.4 THE CAUCHY INTEGRAL THEOREM, 144 6.5 CONTOUR DEFORMATION, 146 6.6 THE CAUCHY INTEGRAL FORMULA, 147 6.7 TAYLOR AND LAURENT SERIES, 150 6.8 THE COMPLEX TAYLOR SERIES, 153 6.9 THE COMPLEX LAURENT SERIES, 159 6.10 THE RESIDUE THEOREM, 171 6.11 DEFINITE INTEGRALS AND CLOSURE, 175 6.12 CONFORMAL MAPPING, 189 CONTENTS IX 7 FOURIER SERIES 219 7.1 THE SINE-COSINE SERIES, 219 7.2 THE EXPONENTIAL FORM OF FOURIER SERIES, 227 7.3 CONVERGENCE OF FOURIER SERIES, 231 7.4 THE DISCRETE FOURIER SERIES, 234 8 FOURIER TRANSFORMS 250 8.1 FOURIER SERIES AS T O - OO, 250 8.2 ORTHOGONALITY, 253 8.3 EXISTENCE OF THE FOURIER TRANSFORM, 254 8.4 THE FOURIER TRANSFORM CIRCUIT, 256 8.5 PROPERTIES OF THE FOURIER TRANSFORM, 258 8.6 FOURIER TRANSFORMS*EXAMPLES, 267 8.7 THE SAMPLING THEOREM, 290 9 LAPLACE TRANSFORMS 303 9.1 LIMITS OF THE FOURIER TRANSFORM, 303 9.2 THE MODIFIED FOURIER TRANSFORM, 306 9.3 THE LAPLACE TRANSFORM, 313 9.4 LAPLACE TRANSFORM EXAMPLES, 314 9.5 PROPERTIES OF THE LAPLACE TRANSFORM, 318 9.6 THE LAPLACE TRANSFORM CIRCUIT, 327 9.7 DOUBLE-SIDED OR BILATERAL LAPLACE TRANSFORMS, 331 10 DIFFERENTIAL EQUATIONS 339 10.1 TERMINOLOGY, 339 10.2 SOLUTIONS FOR FIRST-ORDER EQUATIONS, 342 10.3 TECHNIQUES FOR SECOND-ORDER EQUATIONS, 347 10.4 THE METHOD OF FROBENIUS, 354 10.5 THE METHOD OF QUADRATURE, 358 10.6 FOURIER AND LAPLACE TRANSFORM SOLUTIONS, 366 10.7 GREEN S FUNCTION SOLUTIONS, 376 X CONTENTS 11 SOLUTIONS TO LAPLACE S EQUATION 424 11.1 CARTESIAN SOLUTIONS, 424 11.2 EXPANSIONS WITH EIGENFUNCTIONS, 433 11.3 CYLINDRICAL SOLUTIONS, 441 11.4 SPHERICAL SOLUTIONS, 458 12 INTEGRAL EQUATIONS 491 12.1 CLASSIFICATION OF LINEAR INTEGRAL EQUATIONS, 492 12.2 THE CONNECTION BETWEEN DIFFERENTIAL AND INTEGRAL EQUATIONS, 493 12.3 METHODS OF SOLUTION, 498 13 ADVANCED TOPICS IN COMPLEX ANALYSIS 509 13.1 MULTIVALUED FUNCTIONS, 509 13.2 THE METHOD OF STEEPEST DESCENT, 542 14 TENSORS IN NON-ORTHOGONAL COORDINATE SYSTEMS 562 14.1 A BRIEF REVIEW OF TENSOR TRANSFORMATIONS, 562 14.2 NON-ORTHONORMAL COORDINATE SYSTEMS, 564 15 INTRODUCTION TO GROUP THEORY 597 15.1 THE DEFINITION OF A GROUP, 597 15.2 FINITE GROUPS AND THEIR REPRESENTATIONS, 598 15.3 SUBGROUPS, COSETS, CLASS, AND CHARACTER, 607 15.4 IRREDUCIBLE MATRIX REPRESENTATIONS, 612 15.5 CONTINUOUS GROUPS, 630 APPENDIX A THE LEVI-CIVITA IDENTITY 639 APPENDIX B THE CURVILINEAR CURL 641 APPENDIX C THE DOUBLE INTEGRAL IDENTITY 645 APPENDIX D GREEN S FUNCTION SOLUTIONS 647 APPENDIX E PSEUDOVECTORS AND THE MIRROR TEST 653 CONTENTS XI APPENDIX F CHRISTOFFEL SYMBOLS AND COVARIANT DERIVATIVES 655 APPENDIX G CALCULUS OF VARIATIONS 661 ERRATA LIST 665 BIBLIOGRAPHY 671 INDEX 673
adam_txt	BRUCE R. KUSSE AND ERIK A. WESTWIG MATHEMATICAL PHYSICS APPLIED MATHEMATICS FOR SCIENTISTS AND ENGINEERS 2ND EDITION WILEY- VCH WILEY-VCH VERLAG GMBH & CO. KGAA CONTENTS 1 A REVIEW OF VECTOR AND MATRIX ALGEBRA USING SUBSCRIPT/SUMMATION CONVENTIONS 1 1.1 NOTATION, 1 1.2 VECTOR OPERATIONS, 5 2 DIFFERENTIAL AND INTEGRAL OPERATIONS ON VECTOR AND SCALAR FIELDS 18 2.1 PLOTTING SCALAR AND VECTOR FIELDS, 18 2.2 INTEGRAL OPERATORS, 20 2.3 DIFFERENTIAL OPERATIONS, 23 2.4 INTEGRAL DEFINITIONS OF THE DIFFERENTIAL OPERATORS, 34 2.5 THE THEOREMS, 35 3 CURVILINEAR COORDINATE SYSTEMS 44 3.1 THE POSITION VECTOR, 44 3.2 THE CYLINDRICAL SYSTEM, 45 3.3 THE SPHERICAL SYSTEM, 48 3.4 GENERAL CURVILINEAR SYSTEMS, 49 3.5 THE GRADIENT, DIVERGENCE, AND CURL IN CYLINDRICAL AND SPHERICAL SYSTEMS, 58 VII VLII CONTENTS 4 INTRODUCTION TO TENSORS 67 4.1 THE CONDUCTIVITY TENSOR AND OHM'S LAW, 67 4.2 GENERAL TENSOR NOTATION AND TERMINOLOGY, 71 4.3 TRANSFORMATIONS BETWEEN COORDINATE SYSTEMS, 71 4.4 TENSOR DIAGONALIZATION, 78 4.5 TENSOR TRANSFORMATIONS IN CURVILINEAR COORDINATE SYSTEMS, 84 4.6 PSEUDO-OBJECTS, 86 5 THE DIRAC S-FUNCTION 100 5.1 EXAMPLES OF SINGULAR FUNCTIONS IN PHYSICS, 100 5.2 TWO DEFINITIONS OF S(0, 103 5.3 5-FUNCTIONS WITH COMPLICATED ARGUMENTS, 108 5.4 INTEGRALS AND DERIVATIVES OF S(T), 111 5.5 SINGULAR DENSITY FUNCTIONS, 114 5.6 THE INFINITESIMAL ELECTRIC DIPOLE, 121 5.7 RIEMANN INTEGRATION AND THE DIRAC S-FUNCTION, 125 6 INTRODUCTION TO COMPLEX VARIABLES 135 6.1 A COMPLEX NUMBER REFRESHER, 135 6.2 FUNCTIONS OF A COMPLEX VARIABLE, 138 6.3 DERIVATIVES OF COMPLEX FUNCTIONS, 140 6.4 THE CAUCHY INTEGRAL THEOREM, 144 6.5 CONTOUR DEFORMATION, 146 6.6 THE CAUCHY INTEGRAL FORMULA, 147 6.7 TAYLOR AND LAURENT SERIES, 150 6.8 THE COMPLEX TAYLOR SERIES, 153 6.9 THE COMPLEX LAURENT SERIES, 159 6.10 THE RESIDUE THEOREM, 171 6.11 DEFINITE INTEGRALS AND CLOSURE, 175 6.12 CONFORMAL MAPPING, 189 CONTENTS IX 7 FOURIER SERIES 219 7.1 THE SINE-COSINE SERIES, 219 7.2 THE EXPONENTIAL FORM OF FOURIER SERIES, 227 7.3 CONVERGENCE OF FOURIER SERIES, 231 7.4 THE DISCRETE FOURIER SERIES, 234 8 FOURIER TRANSFORMS 250 8.1 FOURIER SERIES AS T O - OO, 250 8.2 ORTHOGONALITY, 253 8.3 EXISTENCE OF THE FOURIER TRANSFORM, 254 8.4 THE FOURIER TRANSFORM CIRCUIT, 256 8.5 PROPERTIES OF THE FOURIER TRANSFORM, 258 8.6 FOURIER TRANSFORMS*EXAMPLES, 267 8.7 THE SAMPLING THEOREM, 290 9 LAPLACE TRANSFORMS 303 9.1 LIMITS OF THE FOURIER TRANSFORM, 303 9.2 THE MODIFIED FOURIER TRANSFORM, 306 9.3 THE LAPLACE TRANSFORM, 313 9.4 LAPLACE TRANSFORM EXAMPLES, 314 9.5 PROPERTIES OF THE LAPLACE TRANSFORM, 318 9.6 THE LAPLACE TRANSFORM CIRCUIT, 327 9.7 DOUBLE-SIDED OR BILATERAL LAPLACE TRANSFORMS, 331 10 DIFFERENTIAL EQUATIONS 339 10.1 TERMINOLOGY, 339 10.2 SOLUTIONS FOR FIRST-ORDER EQUATIONS, 342 10.3 TECHNIQUES FOR SECOND-ORDER EQUATIONS, 347 10.4 THE METHOD OF FROBENIUS, 354 10.5 THE METHOD OF QUADRATURE, 358 10.6 FOURIER AND LAPLACE TRANSFORM SOLUTIONS, 366 10.7 GREEN'S FUNCTION SOLUTIONS, 376 X CONTENTS 11 SOLUTIONS TO LAPLACE'S EQUATION 424 11.1 CARTESIAN SOLUTIONS, 424 11.2 EXPANSIONS WITH EIGENFUNCTIONS, 433 11.3 CYLINDRICAL SOLUTIONS, 441 11.4 SPHERICAL SOLUTIONS, 458 12 INTEGRAL EQUATIONS 491 12.1 CLASSIFICATION OF LINEAR INTEGRAL EQUATIONS, 492 12.2 THE CONNECTION BETWEEN DIFFERENTIAL AND INTEGRAL EQUATIONS, 493 12.3 METHODS OF SOLUTION, 498 13 ADVANCED TOPICS IN COMPLEX ANALYSIS 509 13.1 MULTIVALUED FUNCTIONS, 509 13.2 THE METHOD OF STEEPEST DESCENT, 542 14 TENSORS IN NON-ORTHOGONAL COORDINATE SYSTEMS 562 14.1 A BRIEF REVIEW OF TENSOR TRANSFORMATIONS, 562 14.2 NON-ORTHONORMAL COORDINATE SYSTEMS, 564 15 INTRODUCTION TO GROUP THEORY 597 15.1 THE DEFINITION OF A GROUP, 597 15.2 FINITE GROUPS AND THEIR REPRESENTATIONS, 598 15.3 SUBGROUPS, COSETS, CLASS, AND CHARACTER, 607 15.4 IRREDUCIBLE MATRIX REPRESENTATIONS, 612 15.5 CONTINUOUS GROUPS, 630 APPENDIX A THE LEVI-CIVITA IDENTITY 639 APPENDIX B THE CURVILINEAR CURL 641 APPENDIX C THE DOUBLE INTEGRAL IDENTITY 645 APPENDIX D GREEN'S FUNCTION SOLUTIONS 647 APPENDIX E PSEUDOVECTORS AND THE MIRROR TEST 653 CONTENTS XI APPENDIX F CHRISTOFFEL SYMBOLS AND COVARIANT DERIVATIVES 655 APPENDIX G CALCULUS OF VARIATIONS 661 ERRATA LIST 665 BIBLIOGRAPHY 671 INDEX 673
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spelling	Kusse, Bruce R. 1938- Verfasser (DE-588)130871788 aut Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse ; Erik A. Westwig 2. ed. Weinheim Wiley-VCH 2006 XI, 678 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Physics textbook Includes bibliographical references (p. 671) and index Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Westwig, Erik A. Sonstige oth http://www.loc.gov/catdir/toc/fy0610/2006277389.html Table of contents only HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014975493&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kusse, Bruce R. 1938- Mathematical physics applied mathematics for scientists and engineers Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd
subject_GND	(DE-588)4037952-8 (DE-588)4123623-3
title	Mathematical physics applied mathematics for scientists and engineers
title_auth	Mathematical physics applied mathematics for scientists and engineers
title_exact_search	Mathematical physics applied mathematics for scientists and engineers
title_exact_search_txtP	Mathematical physics applied mathematics for scientists and engineers
title_full	Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse ; Erik A. Westwig
title_fullStr	Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse ; Erik A. Westwig
title_full_unstemmed	Mathematical physics applied mathematics for scientists and engineers Bruce R. Kusse ; Erik A. Westwig
title_short	Mathematical physics
title_sort	mathematical physics applied mathematics for scientists and engineers
title_sub	applied mathematics for scientists and engineers
topic	Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd
topic_facet	Physique mathématique Mathematische Physik Mathematical physics Lehrbuch
url	http://www.loc.gov/catdir/toc/fy0610/2006277389.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014975493&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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