Mathematical methods for physicists: a comprehensive guide
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier / Academic Press
2013
|
| Ausgabe: | 7. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 1205 S. graph. Darst. |
| ISBN: | 9780123846549 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804149037492862976 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Arfken, George B. 1922- Weber, Hans-Jurgen Harris, Frank E. 1929- |
| author_GND | (DE-588)137142188 (DE-588)137143370 (DE-588)1023818930 |
| author_facet | Arfken, George B. 1922- Weber, Hans-Jurgen Harris, Frank E. 1929- |
| author_role | aut aut aut |
| author_sort | Arfken, George B. 1922- |
| author_variant | g b a gb gba h j w hjw f e h fe feh |
| building | Verbundindex |
| bvnumber | BV040037768 |
| classification_rvk | SK 950 |
| classification_tum | PHY 011f |
| 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 |
| ctrlnum | (OCoLC)934655708 (DE-599)OBVAC08818772 |
| discipline | Physik Mathematik |
| edition | 7. ed. |
| format | Book |
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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 | 2024-07-10T00:16:40Z |
| 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 |
| spelling | Arfken, George B. 1922- Verfasser (DE-588)137142188 aut Mathematical methods for physicists a comprehensive guide George B. Arfken ; Hans J. Weber ; Frank E. Harris 7. ed. Amsterdam [u.a.] Elsevier / Academic Press 2013 XIII, 1205 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 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 rswk-swf Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Elektromagnetismus (DE-588)4014306-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Maxwellsche Gleichungen (DE-588)4221398-8 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Physiker (DE-588)4045968-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content 2\p (DE-588)4123623-3 Lehrbuch gnd-content Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s DE-604 Mathematik (DE-588)4037944-9 s Physiker (DE-588)4045968-8 s 3\p DE-604 Mathematische Physik (DE-588)4037952-8 s 4\p DE-604 Theorie (DE-588)4059787-8 s 5\p DE-604 Schrödinger-Gleichung (DE-588)4053332-3 s 6\p DE-604 Maxwellsche Gleichungen (DE-588)4221398-8 s 7\p DE-604 Analysis (DE-588)4001865-9 s 8\p DE-604 Elektromagnetismus (DE-588)4014306-5 s 9\p DE-604 Vektorrechnung (DE-588)4062471-7 s 10\p DE-604 Quantenmechanik (DE-588)4047989-4 s 11\p DE-604 Weber, Hans-Jurgen Verfasser (DE-588)137143370 aut Harris, Frank E. 1929- Verfasser (DE-588)1023818930 aut HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 8\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 9\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 10\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 11\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |