Introduction to mathematical physics: methods and concepts
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2013
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XII, 716 S. Ill., graph. Darst. |
| ISBN: | 9780199641390 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to mathematical physics |b methods and concepts |c Chun Wa Wong |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2013 | |
| 300 | |a XII, 716 S. |b Ill., graph. Darst. | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025875664 | ||
Datensatz im Suchindex
| _version_ | 1804150180028612608 |
|---|---|
| adam_text | Titel: Introduction to mathematical physics
Autor: Wong, Chun Wa
Jahr: 2012
Contents
1 Vectors and fields in space 1
1.1 Concepts of space 1
1.2 Vectors in space 4
1.3 Permutation symbols 14
1.4 Vector differentiation of a scalar field 20
1.5 Vector differentiation of a vector field 25
1.6 Path-dependent scalar and vector integrations 31
1.7 Flux, divergence and Gauss s theorem 42
1.8 Circulation, curl and Stokes s theorem 48
1.9 Helmholtz s theorem 53
1.10 Orthogonal curvilinear coordinate Systems 56
1.11 Vector differential Operators in orthogonal curvilinear
coordinate Systems 65
Appendix 1 Tables of mathematical formulas 72
2 Transformations, matrices and Operators 76
2.1 Transformations and the laws of physics 76
2.2 Rotations in space: Matrices 77
2.3 Determinant and matrix inversion 87
2.4 Homogeneous equations 93
2.5 The matrix eigenvalue problem 97
2.6 Generalized matrix eigenvalue problems 104
2.7 Eigenvalues and eigenvectors of Hermitian matrices 108
2.8 The wave equation 114
2.9 Displacement in time and translation in space:
Infinitesimal generators 117
2.10 Rotation Operators 125
2.11 Matrix groups 129
Appendix 2 Tables of mathematical formulas 135
3 Relativistic square-root spaces* 138
3.1 Introduction 138
3.2 Special relativity and Lorentz transformations 139
3.3 Relativistic kinemaücs and the mass-energy equivalence 150
3.4 Quaternions 159
3.5 Dirac equation, spinors and matrices 165
3.6 Symmetries ofthe Dirac equation* 172
Marks an advanced topic in Contents, or a long or difficult problem in the chapters.
Contents
3.7 Weyl and Majorana spinors, symmetry violations* 179
3.8 Lorentz group 188
3.9 Cartan spinors and spin transformations in square-root space 195
3.10 Dyadics 200
3.11 Cartesian tensors 206
3.12 Tensor analysis 217
Appendix 3 Tables of mathematical formulas 232
4 Fourier series and Fourier transforms 244
4.1 Wave-particle duality: Quantum mechanics 244
4.2 Fourier series 247
4.3 Fourier coefficients and Fourier-series representation 250
4.4 Complex Fourier series and the Dirac 8 function 258
4.5 Fourier transform 265
4.6 Green function and convolution 269
4.7 Heisenberg s uncertainty principle 273
4.8 Conjugate variables and Operators in wave mechanics 276
4.9 Generalized Fourier series and Legendre polynomials 280
4.10 Orthogonal functions and orthogonal polynomials 287
4.11 Mean-square error and mean-square convergence 292
4.12 Convergence of Fourier series 295
4.13 Maxwell equations in Fourier spaces 299
4.14 3D Fourier transforms: Helmholtz decomposition theorem 305
Appendix 4A Short table of Fourier cosine series 313
Appendix 4B Short table of Fourier sine series 313
Appendix 4C Short table of Fourier transforms 314
Appendix 4D Short table of 3D and 4D Fourier transforms 314
Appendix 4E Tables of mathematical formulas 315
5 Differential equations in physics 319
5.1 Introduction 319
5.2 Linear differential equations 321
5.3 First-order differential equations 324
5.4 Second-order linear differential equations 328
5.5 The second homogeneous Solution and an inhomogeneous Solution 332
5.6 Green functions 337
5.7 Series Solution of the homogeneous second-order linear differential
equation 342
5.8 Differential eigenvalue equations and orthogonal functions 347
5.9 Partial differential equations of physics 350
5.10 Separation of variables and eigenfunction expansions 351
5.11 Boundary and initial conditions 354
5.12 Separation of variables for the Laplacian 359
5.13 Green functions for partial differential equations 364
Appendix 5 Tables of mathematical formulas 368
Contents xi
6 Nonlinear Systems* 373
6.1 Introduction 373
6.2 Nonlinear instabilities 374
6.3 Logistic map and chaos 382
6.4 Strange attractor 392
6.5 Driven dissipative linear pendula 400
6.6 Chaos in parametrically driven dissipative nonlinear pendula 407
6.7 Solitons 415
6.8 Traveling kinks 424
6.9 Nonlinear superposition of solitons 432
6.10 More general methods for multi-solitons* 440
Appendix 6 Tables of mathematical formulas 451
7 Special functions 458
7.1 Introduction 458
7.2 Generating function for Legendre polynomials 458
7.3 Hermite polynomials and the quantum oscillator 464
7.4 Orthogonal polynomials 469
7.5 Classical orthogonal polynomials* 476
7.6 Associated Legendre polynomials and spherical harmonics 481
7.7 Bessel functions 487
7.8 Sturm-Liouville equation and eigenfunction expansions 495
Appendix 7 Tables of mathematical formulas 498
8 Functions of a complex variable 502
8.1 Introduction 502
8.2 Functions of a complex variable 502
8.3 Multivalued functions and Riemann surfaces 509
8.4 Complex differentiation: Analytic functions and
singularities 521
8.5 Complex integration: Cauchy integral theorem and
integral formula 524
8.6 Harmonie functions in the plane 528
8.7 Taylor series and analytic continuation 533
8.8 Laurent series 540
8.9 Residues 546
8.10 Complex integration: Calculus of residues 550
8.11 Poles on the contour and Green functions 561
8.12 Laplace transform 571
8.13 Inverse Laplace transform 577
8.14 Construction of functions and dispersion relations 584
8.15 Asymptotic expansions* 590
Appendix 8 Tables of mathematical formulas 614
XÜ Contents
Appendix A Tutorials 620
A.l Complex algebra 620
A.2 Vectors 627
A.3 Simple and partial differentiations 630
A.4 Simple and multiple integrals 636
A.5 Matrices and determinants 643
A.6 Infinite series 650
A.7 Exponential functions 662
Appendix B Mathematica and other Computer algebra Systems 670
Appendix C Computer algebra (CA) with Mathematica 677
C.l Introduction to CA 677
C.2 Equation solvers 679
C.3 Drawing figures and graphs 683
C.4 Number-intensive calculations 684
Resources for students
Bibliography 694
Name index 699
Subject index 702
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| discipline | Physik Mathematik |
| edition | 2. ed. |
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| spelling | Wong, Chun Wa 1938- Verfasser (DE-588)1032671955 aut Introduction to mathematical physics methods and concepts Chun Wa Wong 2. ed. Oxford Oxford Univ. Press 2013 XII, 716 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier 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 DE-601 pdf/application http://www.gbv.de/dms/tib-ub-hannover/734535104.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025875664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Introduction to mathematical physics methods and concepts |
| title_auth | Introduction to mathematical physics methods and concepts |
| title_exact_search | Introduction to mathematical physics methods and concepts |
| title_full | Introduction to mathematical physics methods and concepts Chun Wa Wong |
| title_fullStr | Introduction to mathematical physics methods and concepts Chun Wa Wong |
| title_full_unstemmed | Introduction to mathematical physics methods and concepts Chun Wa Wong |
| title_short | Introduction to mathematical physics |
| title_sort | introduction to mathematical physics methods and concepts |
| title_sub | methods and concepts |
| topic | Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Lehrbuch |
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