Mathematical methods for physicists:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Acad. Press
1985
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 985 S. graph. Darst. |
| ISBN: | 0120598205 0120598108 |
Staff View
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Record in the Search Index
| _version_ | 1804117247513329664 |
|---|---|
| adam_text | CONTENTS
Chapter 1 VECTOR ANALYSIS 1
1.1 Definitions, Elementary Approach 1
1.2 Advanced Definitions 7
1.3 Scalar of Dot Product 13
1.4 Vector or Cross Product 18
1.5 Triple Scalar Product, Triple Vector Product 26
1.6 Gradient 33
1.7 Divergence 37
1.8 Curl 42
1.9 Successive Applications of 47
1.10 Vector Integration 51
1.11 Gauss s Theorem 57
1.12 Stokes s Theorem 61
1.13 Potential Theory 64
1.14 Gauss s Law, Poisson s Equation 74
1.15 Hemholtz s Theorem 78
Chapter 2 COORDINATE SYSTEMS 85
2.1 Curvilinear Coordinates 86
2.2 Differential Vector Operations 90
2.3 Special Coordinate Systems—Rectangular Cartesian
Coordinates 94
2.4 Circular Cylindrical Coordinates (p,cp,z) 95
2.5 Spherical Polar Coordinates (;•, 0. p) 102
2.6 Separation of Variables 111
Chapter 3 TENSOR ANALYSIS 118
3.1 Introduction, Definitions 118
3.2 Contraction, Direct Product 124
vii
viii CONTENTS
3.3 Quotient Rule 126
3.4 Pseudotensors, Dual Tensors 128
3.5 Dyadics 137
3.6 Theory of Elasticity 140
3.7 Lorentz Covariance of Maxwell s Equations 150
3.8 Noncartesian Tensors, Covariant Differentiation 158
3.9 Tensor Differential Operations 164
Chapter 4 DETERMINANTS, MATRICES, AND GROUP
THEORY 168
4.1 Determinants 168
4.2 Matrices 176
4.3 Orthogonal Matrices 191
4.4 Oblique Coordinates 206
4.5 Hermitian Matrices, Unitary Matrices 209
4.6 Diagonalization of Matrices 217
4.7 Eigenvectors, Eigenvalues 229
4.8 Introduction to Group Theory 237
4.9 Discrete Groups 243
4.10 Continuous Groups 251
4.11 Generators 261
4.12 SU(2), SU(3), and Nuclear Particles 267
4.13 Homogeneous Lorentz Group 271
Chapter 5 INFINITE SERIES 277
5.1 Fundamental Concepts 277
5.2 Convergence Tests 280
5.3 Alternating Series 293
5.4 Algebra of Series 295
5.5 Series of Functions 299
5.6 Taylor s Expansion 303
5.7 Power Series 313
5.8 Elliptic Integrals 321
5.9 Bernoulli Numbers, Euler Maclaurin Formula 327
5.10 Asymptotic or Semiconvergent Series 339
5.11 Infinite Products 346
Chapter 6 FUNCTIONS OF A COMPLEX VARIABLE I 352
6.1 Complex Algebra 353
6.2 Cauchy Riemann Conditions 360
CONTENTS ix
6.3 Cauchy s Integral Theorem 365
6.4 Cauchy s Integral Formula 371
6.5 Laurent Expansion 376
6.6 Mapping 384
6.7 Conformal Mapping 392
Chapter 7 FUNCTIONS OF A COMPLEX VARIABLE II: Calculus
of Residues 396
7.1 Singularities 396
7.2 Calculus of Residues 400
7.3 Dispersion Relations 421
7.4 The Method of Steepest Descents 428
Chapter 8 DIFFERENTIAL EQUATIONS 437
8.1 Partial Differential Equations or Theoretical
Physics 437
8.2 First Order Differential Equations 440
8.3 Separation of Variables—Ordinary Differential
Equations 448
8.4 Singular Points 451
8.5 Series Solutions—Frobenius Method 454
8.6 A Second Solution 467
8.7 Nonhomogeneous Equation—Green s Function 480
8.8 Numerical Solutions 491
Chapter 9 STURM LIOUVILLE THEORY—ORTHOGONAL
FUNCTIONS 497
9.1 Self Adjoint Differential Equations 497
9.2 Hermitian (Self Adjoint) Operators 510
9.3 Gram Schmidt Orthogonalization 516
9.4 Completeness of Eigenfunctions 523
Chapter 10 THE GAMMA FUNCTION (FACTORIAL
FUNCTION) 539
10.1 Definitions, Simple Properties 539
10.2 Digamma and Polygamma Functions 549
10.3 Stirling s Series 555
10.4 The Beta Function 560
10.5 The Incomplete Gamma Functions and Related
Functions 565
x CONTENTS
Chapter 11 BESSEL FUNCTIONS 573
11.1 Bessel Functions of the First Kind, Jv(x) 573
11.2 Orthogonality 591
11.3 Neumann Functions, Bessel Functions of the Second
Kind, Nv{x) 596
11.4 Hankel Functions 603
11.5 Modified Bessel Functions, Iv(x) and Kv{x) 610
11.6 Asymptotic Expansions 616
11.7 Spherical Bessel Functions 622
Chapter 12 LEGENDRE FUNCTIONS 637
12.1 Generating Function 637
12.2 Recurrence Relations and Special Properties 645
12.3 Orthogonality 652
12.4 Alternate Definitions of Legendre Polynomials 663
12.5 Associated Legendre Functions 666
12.6 Spherical Harmonics 680
12.7 Angular Momentum Ladder Operators 685
12.8 The Addition Theorem for Spherical Harmonics 693
12.9 Integrals of the Product of Three Spherical
Harmonics 698
12.10 Legendre Functions of the Second Kind, Qn(x) 701
12.11 Vector Spherical Harmonics 707
Chapter 13 SPHERICAL FUNCTIONS 712
13.1 Hermite Functions 712
13.2 Laguerre Functions 721
13.3 Chebyshev (Tsebyscheff) Polynomials 731
13.4 Chebyshev Polynomials—Numerical
Applications 740
13.5 Hypergeometric Functions 748
13.6 Confluent Hypergeometric Functions 753
Chapter 14 FOURIER SERIES 760
14.1 General Properties 760
14.2 Advantages, Uses of Fourier Series 766
14.3 Applications of Fourier Series 770
14.4 Properties of Fourier Series 778
14.5 Gibbs Phenomenon 783
14.6 Discrete Orthogonality—Discrete Fourier
Transform 787
CONTENTS xi
Chapter 15 INTEGRAL TRANSFORMS 794
15.1 Integral Transforms 794
15.2 Development of the Fourier Integral 797
15.3 Fourier Transforms—Inversion Theorem 800
15.4 Fourier Transform of Derivatives 807
15.5 Convolution Theorem 810
15.6 Momentum Representation 814
15.7 Transfer Functions 820
15.8 Elementary Laplace Transforms 824
15.9 Laplace Transform of Derivatives 831
15.10 Other Properties 838
15.11 Convolution or Faltung Theorem 849
15.12 Inverse Laplace Transformation 853
Chapter 16 INTEGRAL EQUATIONS 865
16.1 Introduction 865
16.2 Integral Transforms, Generating Functions 873
16.3 Neumann Series, Separable (Degenerate) Kernals 879
16.4 Hilbert Schmidt Theory 890
16.5 Green s Functions—One Dimension 897
16.6 Green s Functions—Two and Three Dimensions
Chapter 17 CALCULUS OF VARIATIONS 925
17.1 One Dependent and One Independent Variable 925
17.2 Applications of the Euler Equation 930
17.3 Generalizations, Several Dependent Variables 937
17.4 Several Independent Variables 942
17.5 More Than One Dependent, More Than One
Independent Variable 944
17.6 Lagrangian Multipliers 945
17.7 Variation Subject to Constraints 950
17.8 Rayleigh Ritz Variational Technique 957
Appendix 1 REAL ZEROS OF A FUNCTION 963
Appendix 2 GAUSSIAN QUADRATURE 968
Index 976
|
| any_adam_object | 1 |
| author | Arfken, George B. 1922- |
| author_GND | (DE-588)137142188 |
| author_facet | Arfken, George B. 1922- |
| author_role | aut |
| author_sort | Arfken, George B. 1922- |
| author_variant | g b a gb gba |
| building | Verbundindex |
| bvnumber | BV002955942 |
| classification_rvk | SK 900 SK 950 |
| classification_tum | PHY 011f |
| ctrlnum | (OCoLC)611554102 (DE-599)BVBBV002955942 |
| discipline | Physik Mathematik |
| edition | 3. ed. |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Aufgabensammlung Lehrbuch |
| id | DE-604.BV002955942 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:51:22Z |
| institution | BVB |
| isbn | 0120598205 0120598108 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001850603 |
| oclc_num | 611554102 |
| open_access_boolean | |
| owner | DE-384 DE-91 DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-20 DE-824 DE-29T DE-188 DE-11 DE-210 |
| owner_facet | DE-384 DE-91 DE-BY-TUM DE-703 DE-19 DE-BY-UBM DE-20 DE-824 DE-29T DE-188 DE-11 DE-210 |
| physical | XXII, 985 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Acad. Press |
| record_format | marc |
| spelling | Arfken, George B. 1922- Verfasser (DE-588)137142188 aut Mathematical methods for physicists George Arfken 3. ed. Boston [u.a.] Acad. Press 1985 XXII, 985 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Maxwellsche Gleichungen (DE-588)4221398-8 gnd rswk-swf Physiker (DE-588)4045968-8 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Elektromagnetismus (DE-588)4014306-5 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Physik (DE-588)4045956-1 s Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 Mathematik (DE-588)4037944-9 s Physiker (DE-588)4045968-8 s 2\p DE-604 Theorie (DE-588)4059787-8 s 3\p DE-604 Schrödinger-Gleichung (DE-588)4053332-3 s 4\p DE-604 Maxwellsche Gleichungen (DE-588)4221398-8 s 5\p DE-604 Analysis (DE-588)4001865-9 s 6\p DE-604 Elektromagnetismus (DE-588)4014306-5 s 7\p DE-604 Vektorrechnung (DE-588)4062471-7 s 8\p DE-604 Quantenmechanik (DE-588)4047989-4 s 9\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001850603&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 |
| spellingShingle | Arfken, George B. 1922- Mathematical methods for physicists Vektorrechnung (DE-588)4062471-7 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Physik (DE-588)4037952-8 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Maxwellsche Gleichungen (DE-588)4221398-8 gnd Physiker (DE-588)4045968-8 gnd Quantenmechanik (DE-588)4047989-4 gnd Theorie (DE-588)4059787-8 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Analysis (DE-588)4001865-9 gnd Elektromagnetismus (DE-588)4014306-5 gnd |
| subject_GND | (DE-588)4062471-7 (DE-588)4037944-9 (DE-588)4037952-8 (DE-588)4053332-3 (DE-588)4221398-8 (DE-588)4045968-8 (DE-588)4047989-4 (DE-588)4059787-8 (DE-588)4045956-1 (DE-588)4155620-3 (DE-588)4001865-9 (DE-588)4014306-5 (DE-588)4143389-0 (DE-588)4123623-3 |
| title | Mathematical methods for physicists |
| title_auth | Mathematical methods for physicists |
| title_exact_search | Mathematical methods for physicists |
| title_full | Mathematical methods for physicists George Arfken |
| title_fullStr | Mathematical methods for physicists George Arfken |
| title_full_unstemmed | Mathematical methods for physicists George Arfken |
| title_short | Mathematical methods for physicists |
| title_sort | mathematical methods for physicists |
| topic | Vektorrechnung (DE-588)4062471-7 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Physik (DE-588)4037952-8 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Maxwellsche Gleichungen (DE-588)4221398-8 gnd Physiker (DE-588)4045968-8 gnd Quantenmechanik (DE-588)4047989-4 gnd Theorie (DE-588)4059787-8 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Analysis (DE-588)4001865-9 gnd Elektromagnetismus (DE-588)4014306-5 gnd |
| topic_facet | Vektorrechnung Mathematik Mathematische Physik Schrödinger-Gleichung Maxwellsche Gleichungen Physiker Quantenmechanik Theorie Physik Mathematische Methode Analysis Elektromagnetismus Aufgabensammlung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001850603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT arfkengeorgeb mathematicalmethodsforphysicists |