Навигация
Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
ОбложкаGbur G. Mathematical methods for optical physics and engineering. - Cambridge; New York: Cambridge University Press, 2011. - xvii, 800 p.: ill. - Ref.: p.787-792. - Ind.: p.793-800. - ISBN 978-0-521-51610-5
Шифр: (И/В34-G29) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
Preface ........................................................ xv
1  Vector algebra ............................................... 1
   1.1  Preliminaries ........................................... 1
   1.2  Coordinate system invariance ............................ 4
   1.3  Vector multiplication ................................... 9
   1.4  Useful products of vectors ............................. 12
   1.5  Linear vector spaces ................................... 13
   1.6  Focus: periodic media and reciprocal lattice vectors ... 17
   1.7  Additional reading ..................................... 24
   1.8  Exercises .............................................. 24
2  Vector calculus ............................................. 28
   2.1  Introduction ........................................... 28
   2.2  Vector integration ..................................... 29
   2.3  The gradient, fig.2 ........................................ 35
   2.4  Divergence, fig.2 .......................................... 37
   2.5  The curl, fig.2x ........................................... 41
   2.6  Further applications of fig.2 .............................. 43
   2.7  Gauss' theorem (divergence theorem) .................... 45
   2.8  Stokes' theorem ........................................ 47
   2.9  Potential theory ....................................... 48
   2.10 Focus: Maxwell's equations in integral and
        differential form ...................................... 51
   2.11 Focus: gauge freedom in Maxwell's equations ............ 57
   2.12 Additional reading ..................................... 60
   2.13 Exercises .............................................. 60
3  Vector calculus in curvilinear coordinate systems ........... 64
   3.1  Introduction: systems with different symmetries ........ 64
   3.2  General orthogonal coordinate systems .................. 65
   3.3  Vector operators in curvilinear coordinates ............ 69
   3.4  Cylindrical coordinates ................................ 73
   3.5  Spherical coordinates .................................. 76
   3.6  Exercises .............................................. 79
4  Matrices and linear algebra ................................. 83
   4.1  Introduction: Polarization and Jones vectors ........... 83
   4.2  Matrix algebra ......................................... 88
   4.3  Systems of equations, determinants, and inverses ....... 93
   4.4  Orthogonal matrices ................................... 102
   4.5  Hermitian matrices and unitary matrices ............... 105
   4.6  Diagonalization of matrices, eigenvectors, and
        eigenvalues ........................................... 107
   4.7  Gram-Schmidt orthonormalization ....................... 115
   4.8  Orthonormal vectors and basis vectors ................. 118
   4.9  Functions of matrices ................................. 120
   4.10 Focus: matrix methods for geometrical optics .......... 120
   4.11 Additional reading .................................... 133
   4.12 Exercises ............................................. 133
5  Advanced matrix techniques and tensors ..................... 139
   5.1  Introduction: Foldy-Lax scattering theory ............. 139
   5.2  Advanced matrix terminology ........................... 142
   5.3  Left-right eigenvalues and biorthogonality ............ 143
   5.4  Singular value decomposition .......................... 146
   5.5  Other matrix manipulations ............................ 153
   5.6  Tensors ............................................... 159
   5.7  Additional reading .................................... 174
   5.8  Exercises ............................................. 174
6  Distributions .............................................. 177
   6.1  Introduction: Gauss'law and the Poisson equation ...... 177
   6.2  Introduction to delta functions ....................... 181
   6.3  Calculus of delta functions ........................... 184
   6.4  Other representations of the delta function ........... 185
   6.5  Heaviside step function ............................... 187
   6.6  Delta functions of more than one variable ............. 188
   6.7  Additional reading .................................... 192
   6.8  Exercises ............................................. 192
7  Infinite series ............................................ 195
   7.1  Introduction: the Fabry-Perot interferometer .......... 195
   7.2  Sequences and series .................................. 198
   7.3  Series convergence .................................... 201
   7.4  Series of functions ................................... 210
   7.5  Taylor series ......................................... 213
   7.6  Taylor series in more than one variable ............... 218
   7.7  Power series .......................................... 220
   7.8  Focus: convergence of the Born series ................. 221
   7.9  Additional reading .................................... 226
   7.10 Exercises ............................................. 226
8  Fourier series ............................................. 230
   8.1  Introduction: diffraction gratings .................... 230
   8.2  Real-valued Fourier series ............................ 233
   8.3  Examples .............................................. 236
   8.4  Integration range of the Fourier series ............... 239
   8.5  Complex-valued Fourier series ......................... 239
   8.6  Properties of Fourier series .......................... 240
   8.7  Gibbs phenomenon and convergence in the mean .......... 243
   8.8  Focus: X-ray diffraction from crystals ................ 246
   8.9  Additional reading .................................... 249
   8.10 Exercises ............................................. 249
9  Complex analysis ........................................... 252
   9.1  Introduction: electric potential in an infinite
        cylinder .............................................. 252
   9.2  Complex algebra ....................................... 254
   9.3  Functions of a complex variable ....................... 258
   9.4  Complex derivatives and analyticity ................... 261
   9.5  Complex integration and Cauchy's integral theorem ..... 265
   9.6  Cauchy's integral formula ............................. 269
   9.7  Taylor series ......................................... 271
   9.8  Laurent series ........................................ 273
   9.9  Classification of isolated singularities .............. 276
   9.10 Branch points and Riemann surfaces .................... 278
   9.11 Residue theorem ....................................... 285
   9.12 Evaluation of definite integrals ...................... 288
   9.13 Cauchy principal value ................................ 297
   9.14 Focus: Kramers-Rronig relations ....................... 299
   9.15 Focus: optical vortices ............................... 302
   9.16 Additional reading .................................... 308
   9.17 Exercises ............................................. 308
10 Advanced complex analysis .................................. 312
   10.1 Introduction .......................................... 312
   10.2 Analytic continuation ................................. 312
   10.3 Stereographic projection .............................. 316
   10.4 Conformal mapping ..................................... 325
   10.5 Significant theorems in complex analysis .............. 332
   10.6 Focus: analytic properties of wavefields .............. 340
   10.7 Focus: optical cloaking and transformation optics ..... 345
   10.8 Exercises ............................................. 348
11 Fourier transforms ......................................... 350
   11.1 Introduction: Fraunhofer diffraction .................. 350
   11.2 The Fourier transform and its inverse ................. 352
   11.3 Examples of Fourier transforms ........................ 354
   11.4 Mathematical properties of the Fourier transform ...... 358
   11.5 Physical properties of the Fourier transform .......... 365
   11.6 Eigenfunctions of the Fourier operator ................ 372
   11.7 Higher-dimensional transforms ......................... 373
   11.8 Focus: spatial filtering .............................. 375
   11.9 Focus: angular spectrum representation ................ 377
   11.10 Additional reading ................................... 382
   11.11 Exercises ............................................ 383
12 Other integral transforms .................................. 386
   12.1 Introduction: the Fresnel transform ................... 386
   12.2 Linear canonical transforms ........................... 391
   12.3 The Laplace transform ................................. 395
   12.4 Fractional Fourier transform .......................... 400
   12.5 Mixed domain transforms ............................... 402
   12.6 The wavelet transform ................................. 406
   12.7 The Wigner transform .................................. 409
   12.8 Focus: the Radon transform and computed axial
        tomography (CAT) ...................................... 410
   12.9 Additional reading .................................... 416
   12.10 Exercises ............................................ 416
13 Discrete transforms ........................................ 419
   13.1 Introduction: the sampling theorem .................... 419
   13.2 Sampling and the Poisson sum formula .................. 423
   13.3 The discrete Fourier transform ........................ 427
   13.4 Properties of the DFT ................................. 430
   13.5 Convolution ........................................... 432
   13.6 Fast Fourier transform ................................ 433
   13.7 The z-transform ....................................... 437
   13.8 Focus: z-transforms in the numerical solution of
        Maxwell's equations ................................... 445
   13.9 Focus: the Talbot effect .............................. 449
   13.10 Exercises ............................................ 456
14 Ordinary differential equations ............................ 458
   14.1 Introduction: the classic ODEs ........................ 458
   14.2 Classification of ODEs ................................ 459
   14.3 Ordinary differential equations and phase space ....... 460
   14.4 First-order ODEs ...................................... 469
   14.5 Second-order ODEs with constant coefficients .......... 474
   14.6 The Wronskian and associated strategies ............... 476
   14.7 Variation of parameters ............................... 478
   14.8 Series solutions ...................................... 480
   14.9 Singularities, complex analysis, and general
        Frobenius solutions ................................... 481
   14.10 Integral transform solutions ......................... 485
   14.11 Systems of differential equations .................... 486
   14.12 Numerical analysis of differential equations ......... 488
   14.13 Additional reading ................................... 501
   14.14 Exercises ............................................ 501
15 Partial differential equations ............................. 505
   15.1 Introduction: propagation in a rectangular waveguide .. 505
   15.2 Classification of second-order linear PDEs ............ 508
   15.3 Separation of variables ............................... 517
   15.4 Hyperbolic equations .................................. 519
   15.5 Elliptic equations .................................... 525
   15.6 Parabolic equations ................................... 530
   15.7 Solutions by integral transforms ...................... 534
   15.8 Inhomogeneous problems and eigenfunction solutions .... 538
   15.9 Infinite domains; the d'Alembert solution ............. 539
   15.10 Method of images ..................................... 544
   15.11 Additional reading ................................... 545
   15.12 Exercises ............................................ 545
16 Bessel functions ........................................... 550
   16.1 Introduction: propagation in a circular waveguide ..... 550
   16.2 Bessel's equation and series solutions ................ 552
   16.3 The generating function ............................... 555
   16.4 Recurrence relations .................................. 557
   16.5 Integral representations .............................. 560
   16.6 Hankel functions ...................................... 564
   16.7 Modified Bessel functions ............................. 565
   16.8 Asymptotic behavior of Bessel functions ............... 566
   16.9 Zeros of Bessel functions ............................. 567
   16.10 Orthogonality relations .............................. 569
   16.11 Bessel functions of fractional order ................. 572
   16.12 Addition theorems, sum theorems, and product
         relations ............................................ 576
   16.13 Focus: nondiffracting beams .......................... 579
   16.14 Additional reading ................................... 582
   16.15 Exercises ............................................ 582
17 Legendre functions and spherical harmonics ................. 585
   17.1 Introduction: Laplace's equation in spherical
        coordinates ........................................... 585
   17.2 Series solution of the Legendre equation .............. 587
   17.3 Generating function ................................... 589
   17.4 Recurrence relations .................................. 590
   17.5 Integral formulas ..................................... 592
   17.6 Orthogonality ......................................... 594
   17.7 Associated Legendre functions ......................... 597
   17.8 Spherical harmonics ................................... 602
   17.9 Spherical harmonic addition theorem ................... 605
   17.10 Solution of PDEs in spherical coordinates ............ 608
   17.11 Gegenbauer polynomial ................................ 610
   17.12 Focus: multipole expansion for static electric
         fields ............................................... 611
   17.13 Focus: vector spherical harmonics and radiation
         fields ............................................... 614
   17.14 Exercises ............................................ 618
18 Orthogonal functions ....................................... 622
   18.1 Introduction: Sturm-Liouville equations ............... 622
   18.2 Hermite polynomials ................................... 627
   18.3 Laguerre functions .................................... 641
   18.4 Chebyshev polynomials ................................. 650
   18.5 Jacobi polynomials .................................... 654
   18.6 Focus: Zernike polynomials ............................ 655
   18.7 Additional reading .................................... 662
   18.8 Exercises ............................................. 662
19 Green's functions .......................................... 665
   19.1 Introduction: the Huygens-Fresnel integral ............ 665
   19.2 Inhomogeneous Sturm-Liouville equations ............... 669
   19.3 Properties of Green's functions ....................... 674
   19.4 Green's functions of second-order PDEs ................ 676
   19.5 Method of images ...................................... 685
   19.6 Modal expansion of Green's functions .................. 689
   19.7 Integral equations .................................... 693
   19.8 Focus: Rayleigh-Sommerfeld diffraction ................ 701
   19.9 Focus: dyadic Green's function for Maxwell's
        equations ............................................. 704
   19.10 Focus: scattering theory and the Born series ......... 709
   19.11 Exercises ............................................ 712
20 The calculus of variations ................................. 715
   20.1 Introduction: principle of Fermat ..................... 715
   20.2 Extrema of functions and functionals .................. 718
   20.3 Euler's equation ...................................... 721
   20.4 Second form of Euler's equation ....................... 727
   20.5 Calculus of variations with several dependent
        variables ............................................. 730
   20.6 Calculus of variations with several independent
        variables ............................................. 732
   20.7 Euler's equation with auxiliary conditions: Lagrange
        multipliers ........................................... 734
   20.8 Hamiltonian dynamics .................................. 739
   20.9 Focus: aperture apodization ........................... 742
   20.10 Additional reading ................................... 745
   20.11 Exercises ............................................ 745
21 Asymptotic techniques ...................................... 748
   21.1 Introduction: foundations of geometrical optics ....... 748
   21.2 Definition of an asymptotic series .................... 753
   21.3 Asymptotic behavior of integrals ...................... 756
   21.4 Method of stationary phase ............................ 763
   21.5 Method of steepest descents ........................... 766
   21.6 Method of stationary phase for double integrals ....... 771
   21.7 Additional reading .................................... 772
   21.8 Exercises ............................................. 773
Appendix A The gamma function ................................. 775
   A.l  Definition ............................................ 775
   A.2  Basic properties ...................................... 776
   A.3  Stirling's formula .................................... 778
   A.4  Beta function ......................................... 779
   A.5  Useful integrals ...................................... 780
Appendix В Hypergeometric functions ........................... 783
   B.1  Hypergeometric function ............................... 784
   B.2  Confluent hypergeometric function ..................... 785
   B.3  Integral representations .............................. 785
References .................................................... 787
Index ......................................................... 793


Архив выставки новых поступлений | Отечественные поступления | Иностранные поступления | Сиглы
 

[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск | English]
  Пожелания и письма: www@prometeus.nsc.ru
© 1997-2017 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Mon Mar 14 16:56:42 2016. Размер: 21,121 bytes.
Посещение N 259 c 22.03.2016