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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Hassani S. — Mathematical Methods: for Students of Physics and Related Fields |
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| Ïðåäìåòíûé óêàçàòåëü |
Huygens 97 103
Hydrogen atom 677—680 802
Hyperbolic cosine 290
Hyperbolic sine 290
Hypergeometric function 328—330
Hypergeometric function, confluent 332—333
Hypergeometric function, integral representation 329
Identity matrix 180
Indeterminate form 294—297
Index, free 440
Indicial equation 609
Induction, mathematical 265—266
Inductive definition 266
Infinite series 266—274
Inner product 218—222
Inner product matrix 185
Inner product, positive definite 187
Inner product, Riemannian 187
integral 79
Integral as function 317—326
Integral transform 693
Integral transform, kernel 693
Integral, Bessel’s 652
Integral, derivative of 85—86
Integral, function of trigonometric 534—536
Integral, indefinite 87
Integral, line 387—391
Integral, Mellin inversion 722
Integral, rational function 529—531
Integral, rational trigonometric 532—534
integrand 80
Integrating factor 553—555
Integration 77—80
Integration, application, Cartesian coordinates 104—107 112 115—117
Integration, application, cylindrical coordinates 107—109 112—115 118—119
Integration, application, double integrals 115—122
Integration, application, electricity 104—109
Integration, application, general 91—96
Integration, application, gravity 104—109
Integration, application, magnetostatics 109—115
Integration, application, mechanics 101—103
Integration, application, single integral 101—115
Integration, application, spherical coordinates 120—122
Integration, application, triple integrals 122—128
Integration, Cauchy integral formula 508—509
Integration, change of dummy variable 82
Integration, complex function 503—508
Integration, interchange of limits 82
Integration, linearity 82
Integration, parameter 80
Integration, partition of range 82
Integration, point 79
Integration, properties 81—89
Integration, region of 79
Integration, small region 83
Integration, symmetric range 84
Integration, transformation of variable 83
Integration, variable 80
Intersection 783
Inverse Fourier transform 695
Inverse matrix 203 207
Inverse of a matrix 180
Ionic crystal, one-dimensional 145
Ionic crystal, potential energy 164
Ionic crystal, two-dimensional 157
ISOLDE 569
Isoperimetric problem 738
Iterated map 754—763
Iterated map, fixed point 755
Iterated map, orbit 755
jacobi 211 331
Jacobi, Carl Gustav Jacob, biography 326
Jacobian 207—210
Jacobian in probability 804
Jacobian matrix 208
Kaluza 215
Kepler 89 97
Kepler, Johannes, biography 579
Kepler’s first law 582
Kepler’s second law 582
Kepler’s third law 583
Kernel, integral transform 693
Klein — Gordon equation 747
Koch snowflake 777
Kronecker delta 222 442 449 489
Kronecker delta, Euclidean metric 466
Kronecker delta, generalized 452
Lagrange 294 304 326 330 594 617 642
Lagrange identity 572
Lagrange multiplier 360 738
Lagrange, biography 742
Lagrangian 740—745
Lagrangian density 744—745
Lagrangian density, electrodynamics 745
Lagrangian, interacting particles 741
Lagrangian, Klein — Gordon 747
Lagrangian, particle in EM field 746
Lagrangian, single particle 741
Laguerre polynomials 230 679
Laplace 115 304 322 326 744
Laplace transform 712—723
Laplace transform and differential equations 718—721
Laplace transform, Bromwich contour 722
Laplace transform, convolution 716
Laplace transform, cosine 713
Laplace transform, derivative 717—718
Laplace transform, first shift 714
Laplace transform, gamma function 713
Laplace transform, imaginary exponential 713
Laplace transform, integral 717—718
Laplace transform, inverse 721—723
Laplace transform, linearity 714
Laplace transform, Mellin inversion integral 722
Laplace transform, periodic functions 716
Laplace transform, properties 713—717
Laplace transform, second shift 714
Laplace transform, sine 713
Laplace transform, step function 713
Laplace transform, unit function 713
Laplace’s equation 411 542 546
Laplace’s equation, Bessel functions 642—654
Laplace’s equation, Cartesian coordinates 594—603
Laplace’s equation, cylindrical coordinates 639—656
Laplace’s equation, Legendre polynomials 610—617
Laplace’s equation, radial equation 619—622
Laplace’s equation, solution, uniqueness 592
Laplace’s equation, spherical coordinates 607—634
Laplace’s equation, uniqueness of solution 592—593
Laplacian 411
Laplacian and Dirac delta function 412
Laplacian, curvilinear coordinates 435
Laplacian, Green’s function 708—709
Laurent series, complex 518—522
Lavoisier 744
Law of addition of velocities 237
Law of Large Numbers 809
Law of motion, relativistic 253—254
legendre 304 326
Legendre equation 575
Legendre equation, recursion relation 611
Legendre functions, second kind 618
Legendre polynomial 228 614 616
Legendre polynomial, expansion in 628—630
Legendre polynomial, expansion in, physical examples 631—634
Legendre polynomial, generating function 621
Legendre polynomial, Laplace’s equation 610—617
Legendre polynomial, multipole expansion 621
Legendre polynomial, orthogonality 625
Legendre polynomial, parity 622
Legendre polynomial, properties 622—628
| Legendre polynomial, recurrence relation 623
Legendre polynomial, Rodrigues formula 626
Legendre polynomials 229 575
Legendre transformation 54 748
Legendre, Adrien-Marie, biography 617
Leibniz 46 87 90 97 210 272 482
Leibniz, Gottfried Wilhelm, biography 103
Length element, primary 59
Levi-Civita symbol 453
Levi-Civita symbols, cross product 458
Limit cycle 770
Line integral 387—391
linear combination 173
Linear dependence 174
Linear equation 230—234
Linear equation, compatible 231
Linear equation, echelon form 232
Linear equation, homogeneous 234
Linear equation, incompatible 231
Linear independence 174
Linear operator 216
Linear transformation 216—218
Liouville substitution 588
Logistic map 755
Logistic map, second iterate 757
Lorentz gauge 419
Lorentz transformation 243—247
Lorentz transformation in 2 dimensions 245
Lorentz transformation, general 244
Lowering indices 457—459
Lyapunov exponent 763
L’Hopital’s Rule 294—297
Maclaurin 210 272
Maclaurin series 287
Madelung constant 165
Magnetic charge 409
Magnetic dipole moment 410
Magnetic field, moving charge 30
Magnetic force, current loop 420
Magnetic force, moving charge 30
Magnetic monopole 409
Manifold 456 469
Map, iterated 754—763
Marginal probability 786—789
Mathematical induction 265—266
Matrix 177
Matrix, G-orthogonal 191 222
Matrix, G-orthogonal, space 200
Matrix, identity 180
Matrix, inner product 185
Matrix, inverse 180 203 207
Matrix, Jacobian 208
Matrix, metric 185
Matrix, multiplication rule 442
Matrix, orthogonal 190
Matrix, symmetric 182
Matrix, transformation in space 195
Matrix, transpose 181
Matrix, unit 180
Matrix, zero 180
Maxwell 26 369 382
Maxwell — Boltzmann statistics 791
Maxwell, James Clerk, biography 419
Maxwell’s equations 415—419
Maxwell’s equations, derivation of wave equation 417
Maxwell’s equations, relation to relativity 237
Mean 790
Mellin inversion integral 722
Membrane 686—687
Metric connection 465—468
Metric connection, relativity 466
Metric matrix 185
Metric tensor 454—461
Metric tensor, definition 456
Metric tensor, relativity 458
Minimal coupling 749
Minkowski 215
Mode of oscillation 682
Moebius band 366
Moment generating function 790
Moment generating function, binomial distribution 793
Moment generating function, Poisson distribution 799
Moment of inertia 122
Moment, quadrupole 449
Momentum, generalized 748
Momentum, relativistic 249
Momentum, zero mass particle 250
Monge 115 304
Motion, constant of 552
Multipole expansion 297—299
Napoleon 304 593
Natural frequency 586
Neumann function 645
Newton 16 26 43 46 78 87 90 103 122 272 294 317 322 326 330 481 482 548 593
Newton, Isaac, biography 96
NOLDE 575
Nonautonomous 767
Normal distribution 806—809
Normal distribution, sum of two 807
nth iterate 760
ODE 542
ODE and PDEs 542—550
Olbers 641
Operator, angular momentum 412
Operator, angular momentum, spherical coordinates 435
Operator, del 359
Operator, differential 576
Operator, differential, linear 217
Operator, linear 216
Orientable surface 366
Orthogonal matrix 190
Orthogonal polynomial, standardization 227
Orthogonal polynomials 227—230
Orthonormal basis 186
Parabolic coordinates 73
Paraboloidal coordinates 74 437
Parallel translation 465
Parseval relation 654
Parseval’s relation 724
Partial derivative 57—59
Particle in a box 675
Pascal 15 103 481
Passive transformation 178
PDE 542
PDE and ODE 542—550
PDE, separation, Cartesian coordinates 544—546
PDE, separation, cylindrical coordinates 547—548
PDE, separation, spherical coordinates 548—550
Period-doubling 757
Periodic BC 574
Permutation 791
Phase space 764—766
Phase space, diagram 764
Phase space, trajectory 764
Planck 666
Plane, basis 175
Poincare 674
poisson 594
Poisson distribution 797—800
Poisson equation 411 542
Poisson equation, astrophysics 415
Poisson equation, Green’s function 709
Polar coordinates 16
Polar equation 549
Pole of order m 528
Pole, simple 528
Polynomial, Hermite 229 670
Polynomial, Laguerre 230 679
Polynomial, Legendre 228 229 614 616
Polynomial, Legendre, Laplace’s equation 610—617
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