Availability: Mathematical methods for physicists | Technische Universität München

Mathematical methods for physicists: a comprehensive guide

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Bibliographic Details
Main Authors:	Arfken, George B. 1922- (Author), Weber, Hans-Jurgen (Author), Harris, Frank E. 1929- (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier / Academic Press 2013
Edition:	7. ed.
Subjects:	Mathematical analysis Mathematische Methode Vektorrechnung Physik Schrödinger-Gleichung Analysis Elektromagnetismus Mathematische Physik Maxwellsche Gleichungen Theorie Physiker Mathematik Quantenmechanik Aufgabensammlung Lehrbuch
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XIII, 1205 S. graph. Darst.
ISBN:	9780123846549

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adam_text	Titel: Mathematical methods for physicists Autor: Arfken, George B Jahr: 2013 Contents Preface xi 1 Mathematical Preliminaries 1 1.1 Infinite Series................................ 1 1.2 Series of Functions............................. 21 1.3 Binomial Theorem ............................. 33 1.4 Mathematical Induction .......................... 40 1.5 Operations on Series Expansions of Functions.............. 41 1.6 Some Important Series........................... 45 1.7 Vectors ................................... 46 1.8 Complex Numbers and Functions..................... 53 1.9 Derivatives and Extrema.......................... 62 1.10 Evaluation of Integrals........................... 65 1.11 Dirac Delta Function............................ 75 Additional Readings............................ 82 2 Determinants and Matrices 83 2.1 Determinants................................ 83 2.2 Matrices................................... 95 Additional Readings............................ 121 3 Vector Analysis 123 3.1 Review of Basic Properties......................... 124 3.2 Vectors in 3-D Space............................ 126 3.3 Coordinate Transformations........................ 133 Contents 3.4 Rotations in R3............................... 139 3.5 Differential Vector Operators....................... 143 3.6 Differential Vector Operators: Further Properties............ 153 3.7 Vector Integration ............................. 159 3.8 Integral Theorems ............................. 164 3.9 Potential Theory.............................. 170 3.10 Curvilinear Coordinates.......................... 182 Additional Readings............................ 203 4 Tensors and Differential Forms 205 4.1 Tensor Analysis............................... 205 4.2 Pseudotensors, Dual Tensors....................... 215 4.3 Tensors in General Coordinates...................... 218 4.4 Jacobians.................................. 227 4.5 Differential Forms............................. 232 4.6 Differentiating Forms ........................... 238 4.7 Integrating Forms ............................. 243 Additional Readings............................ 249 5 Vector Spaces 251 5.1 Vectors in Function Spaces ........................ 251 5.2 Gram-Schmidt Orthogonalization..................... 269 5.3 Operators.................................. 275 5.4 Self-Adjoint Operators........................... 283 5.5 Unitary Operators ............................. 287 5.6 Transformations of Operators....................... 292 5.7 Invariants.................................. 294 5.8 Summary-Vector Space Notation..................... 296 Additional Readings............................ 297 6 Eigenvalue Problems 299 6.1 Eigenvalue Equations ........................... 299 6.2 Matrix Eigenvalue Problems........................ 301 6.3 Hermitian Eigenvalue Problems...................... 310 6.4 Hermitian Matrix Diagonalization .................... 311 6.5 Normal Matrices.............................. 319 Additional Readings............................ 328 7 Ordinary Differential Equations 329 7.1 Introduction................................. 329 7.2 First-Order Equations........................... 331 7.3 ODEs with Constant Coefficients..................... 342 7.4 Second-Order Linear ODEs........................ 343 7.5 Series Solutions-Frobenius Method .................. 346 7.6 Other Solutions............................... 358 Contents vii 7.7 Inhomogeneous Linear ODEs....................... 375 7.8 Nonlinear Differential Equations..................... 377 Additional Readings............................ 380 8 Sturm-Liouville Theory 381 8.1 Introduction................................. 381 8.2 Hermitian Operators............................ 384 8.3 ODE Eigenvalue Problems......................... 389 8.4 Variation Method.............................. 395 8.5 Summary, Eigenvalue Problems...................... 398 Additional Readings............................ 399 9 Partial Differential Equations 401 9.1 Introduction................................. 401 9.2 First-Order Equations........................... 403 9.3 Second-Order Equations.......................... 409 9.4 Separation of Variables .......................... 414 9.5 Laplace and Poisson Equations...................... 433 9.6 Wave Equation............................... 435 9.7 Heat-Flow, or Diffusion PDE....................... 437 9.8 Summary .................................. 444 Additional Readings............................ 445 10 Green s Functions 447 10.1 One-Dimensional Problems........................ 448 10.2 Problems in Two and Three Dimensions................. 459 Additional Readings............................ 467 11 Complex Variable Theory 469 11.1 Complex Variables and Functions..................... 470 11.2 Cauchy-Riemann Conditions........................ 471 11.3 Cauchy s Integral Theorem ........................ 477 11.4 Cauchy s Integral Formula ........................ 486 11.5 Laurent Expansion............................. 492 11.6 Singularities................................. 497 11.7 Calculus of Residues............................ 509 11.8 Evaluation of Definite Integrals...................... 522 11.9 Evaluation of Sums............................. 544 11.10 Miscellaneous Topics............................ 547 Additional Readings............................ 550 12 Further Topics in Analysis 551 12.1 Orthogonal Polynomials.......................... 551 12.2 Bernoulli Numbers............................. 560 12.3 Euler-Maclaurin Integration Formula .................. 567 Contents 12.4 Dirichlet Series............................... 571 12.5 Infinite Products .............................. 574 12.6 Asymptotic Series ............................. 577 12.7 Method of Steepest Descents ....................... 585 12.8 Dispersion Relations............................ 591 Additional Readings............................ 598 13 Gamma Function 599 13.1 Definitions, Properties........................... 599 13.2 Digamma andPolygamma Functions................... 610 13.3 The Beta Function ............................. 617 13.4 Stirling s Series............................... 622 13.5 Riemann Zeta Function........................... 626 13.6 Other Related Functions.......................... 633 Additional Readings............................ 641 14 Bessel Functions 643 14.1 Bessel Functions of the First Kind, Jv(x)................. 643 14.2 Orthogonality ............................... 661 14.3 Neumann Functions, Bessel Functions of the Second Kind....... 667 14.4 Hankel Functions.............................. 674 14.5 Modified Bessel Functions, Iv(x) and Kv(x)............... 680 14.6 Asymptotic Expansions .......................... 688 14.7 Spherical Bessel Functions......................... 698 Additional Readings............................ 713 15 Legendre Functions 715 15.1 Legendre Polynomials........................... 716 15.2 Orthogonality................................ 724 15.3 Physical Interpretation of Generating Function............. 736 15.4 Associated Legendre Equation....................... 741 15.5 Spherical Harmonics............................ 756 15.6 Legendre Functions of the Second Kind.................. 766 Additional Readings............................ 771 16 Angular Momentum 773 16.1 Angular Momentum Operators ...................... 774 16.2 Angular Momentum Coupling....................... 784 16.3 Spherical Tensors.............................. 796 16.4 Vector Spherical Harmonics........................ 809 Additional Readings............................ 814 17 Group Theory g!5 17.1 Introduction to Group Theory....................... 815 17.2 Representation of Groups......................... 821 17.3 Symmetry and Physics........................... 826 Contents ix 17.4 Discrete Groups .............................. 830 17.5 Direct Products............................... 837 17.6 Symmetric Group.............................. 840 17.7 Continuous Groups............................. 845 17.8 Lorentz Group ............................... 862 17.9 Lorentz Covariance of Maxwell s Equations............... 866 17.10 Space Groups................................ 869 Additional Readings ............................ 870 18 More Special Functions 871 18.1 Hermite Functions............................. 871 18.2 Applications of Hermite Functions .................... 878 18.3 Laguerre Functions............................. 889 18.4 Chebyshev Polynomials .......................... 899 18.5 Hypergeometric Functions ........................ 911 18.6 Confluent Hypergeometric Functions................... 917 18.7 Dilogarithm................................. 923 18.8 Elliptic Integrals.............................. 927 Additional Readings............................ 932 19 Fourier Series 935 19.1 General Properties............................. 935 19.2 Applications of Fourier Series....................... 949 19.3 Gibbs Phenomenon............................. 957 Additional Readings............................ 962 20 Integral Transforms 963 20.1 Introduction................................. 963 20.2 Fourier Transform............................. 966 20.3 Properties of Fourier Transforms..................... 980 20.4 Fourier Convolution Theorem....................... 985 20.5 Signal-Processing Applications...................... 997 20.6 Discrete Fourier Transform........................ 1002 20.7 Laplace Transforms ............................ 1008 20.8 Properties of Laplace Transforms..................... 1016 20.9 Laplace Convolution Theorem....................... 1034 20.10 Inverse Laplace Transform......................... 1038 Additional Readings ............................ 1045 21 Integral Equations 1047 21.1 Introduction................................. 1047 21.2 Some Special Methods........................... 1053 21.3 Neumann Series............................... 1064 21.4 Hilbert-Schmidt Theory .......................... 1069 Additional Readings ............................ 1079 Contents 22 Calculus of Variations 1081 22.1 Euler Equation............................... 1081 22.2 More General Variations.......................... 1096 22.3 Constrained Minima/Maxima....................... 1107 22.4 Variation with Constraints......................... 1111 Additional Readings............................ 1124 23 Probability and Statistics 1125 23.1 Probability: Definitions, Simple Properties................ 1126 23.2 Random Variables............................. 1134 23.3 Binomial Distribution ........................... 1148 23.4 Poisson Distribution............................ 1151 23.5 Gauss Normal Distribution........................ 1155 23.6 Transformations of Random Variables.................. 1159 23.7 Statistics................................... 1165 Additional Readings............................ 1179 Index 1181
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contents	Mathematical Preliminaries -- Determinants and Matrices -- Vector Analysis -- Tensors and Differential Forms -- Vector Spaces -- Eigenvalue Problems -- Ordinary Differential Equations -- Sturm-Liouville Theory -- Partial Differential Equations -- Green's Functions -- Complex Variable Theory -- Further Topics in Analysis -- Gamma Function -- Bessel Functions -- Legendre Functions -- Angular Momentum -- Group Theory -- More Special Functions -- Fourier Series -- Integral Transforms -- Integral Equations -- Calculus of Variations -- Probability and Statistics
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genre	1\p (DE-588)4143389-0 Aufgabensammlung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content
genre_facet	Aufgabensammlung Lehrbuch
id	DE-604.BV040037768
illustrated	Illustrated
indexdate	2024-12-20T16:07:49Z
institution	BVB
isbn	9780123846549
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-024894503
oclc_num	934655708
open_access_boolean
owner	DE-703 DE-11 DE-92 DE-91G DE-BY-TUM
owner_facet	DE-703 DE-11 DE-92 DE-91G DE-BY-TUM
physical	XIII, 1205 S. graph. Darst.
publishDate	2013
publishDateSearch	2013
publishDateSort	2013
publisher	Elsevier / Academic Press
record_format	marc
spellingShingle	Arfken, George B. 1922- Weber, Hans-Jurgen Harris, Frank E. 1929- Mathematical methods for physicists a comprehensive guide Mathematical Preliminaries -- Determinants and Matrices -- Vector Analysis -- Tensors and Differential Forms -- Vector Spaces -- Eigenvalue Problems -- Ordinary Differential Equations -- Sturm-Liouville Theory -- Partial Differential Equations -- Green's Functions -- Complex Variable Theory -- Further Topics in Analysis -- Gamma Function -- Bessel Functions -- Legendre Functions -- Angular Momentum -- Group Theory -- More Special Functions -- Fourier Series -- Integral Transforms -- Integral Equations -- Calculus of Variations -- Probability and Statistics Mathematical analysis Mathematische Methode (DE-588)4155620-3 gnd Vektorrechnung (DE-588)4062471-7 gnd Physik (DE-588)4045956-1 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Analysis (DE-588)4001865-9 gnd Elektromagnetismus (DE-588)4014306-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Maxwellsche Gleichungen (DE-588)4221398-8 gnd Theorie (DE-588)4059787-8 gnd Physiker (DE-588)4045968-8 gnd Mathematik (DE-588)4037944-9 gnd Quantenmechanik (DE-588)4047989-4 gnd
subject_GND	(DE-588)4155620-3 (DE-588)4062471-7 (DE-588)4045956-1 (DE-588)4053332-3 (DE-588)4001865-9 (DE-588)4014306-5 (DE-588)4037952-8 (DE-588)4221398-8 (DE-588)4059787-8 (DE-588)4045968-8 (DE-588)4037944-9 (DE-588)4047989-4 (DE-588)4143389-0 (DE-588)4123623-3
title	Mathematical methods for physicists a comprehensive guide
title_auth	Mathematical methods for physicists a comprehensive guide
title_exact_search	Mathematical methods for physicists a comprehensive guide
title_full	Mathematical methods for physicists a comprehensive guide George B. Arfken ; Hans J. Weber ; Frank E. Harris
title_fullStr	Mathematical methods for physicists a comprehensive guide George B. Arfken ; Hans J. Weber ; Frank E. Harris
title_full_unstemmed	Mathematical methods for physicists a comprehensive guide George B. Arfken ; Hans J. Weber ; Frank E. Harris
title_short	Mathematical methods for physicists
title_sort	mathematical methods for physicists a comprehensive guide
title_sub	a comprehensive guide
topic	Mathematical analysis Mathematische Methode (DE-588)4155620-3 gnd Vektorrechnung (DE-588)4062471-7 gnd Physik (DE-588)4045956-1 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Analysis (DE-588)4001865-9 gnd Elektromagnetismus (DE-588)4014306-5 gnd Mathematische Physik (DE-588)4037952-8 gnd Maxwellsche Gleichungen (DE-588)4221398-8 gnd Theorie (DE-588)4059787-8 gnd Physiker (DE-588)4045968-8 gnd Mathematik (DE-588)4037944-9 gnd Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Mathematical analysis Mathematische Methode Vektorrechnung Physik Schrödinger-Gleichung Analysis Elektromagnetismus Mathematische Physik Maxwellsche Gleichungen Theorie Physiker Mathematik Quantenmechanik Aufgabensammlung Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024894503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT arfkengeorgeb mathematicalmethodsforphysicistsacomprehensiveguide AT weberhansjurgen mathematicalmethodsforphysicistsacomprehensiveguide AT harrisfranke mathematicalmethodsforphysicistsacomprehensiveguide

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