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| Hassani S. — Mathematical Methods: for Students of Physics and Related Fields |
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| Предметный указатель |
Descartes, Rene, biography 15
Determinant 202—207 222—227
Determinant, parallelepiped volume 10
Differential 53—54
Differential equation, Bessel 548 641
Differential equation, Bessel, recursion relation 644
Differential equation, Bessel, second solution 645—646
Differential equation, Bessel, solutions 642—645
Differential equation, confluent hypergeometric 332
Differential equation, Hermite, recursion relation 668
Differential equation, hypergeometric 328
Differential equation, Legendre 608
Differential equation, Legendre, second solution 617—619
Differential equation, order of 556
Differential equation, ordinary 542
Differential equation, partial 542
Differential equation, second-order linear, adjoint 572
Differential equation, second-order linear, integrating factor 571
Differential operator 217 576
Differential, absolute 463
Differential, covariant 462—464
Differential, exact 553
Diffusion equation 661
Diffusion equation, time-dependent 663
DIMENSION 176
Dimension, fractal 775—778
Dipole moment 298
Dipole potential 299
Dipole, approximation 298
Dipole, magnetic 410
Dirac 26
Dirac delta function in variational problems 730
Dirac delta function, step function 153
Dirac, biography 151
Dirac, Paul Adrien Maurice, biography 151
Disjoint sets 783
Distance, spacetime 240—242
distribution 146
Distribution, normal 806—809
Distribution, normal, sum of two 807
Divergence 371—381
Divergence, curvilinear coordinates 425—431
Divergence, spherical coordinates 430
Divergence, Theorem 374—378
Divergence, vector field 374
Doppler shift, relativistic 255
Dot product 5 21
Double del operation 407—412
Double factorial 319
Dummy index 262
Dynamical system, autonomous 767
Dynamical system, nonautonomous 767
D’Alembert 273 303 743
d’Alembert, Jean Le Rond, biography 548
Eccentricity 581
Eigenvalue 224
Eigenvalue equation 224
Eigenvector 224
Einstein 215 666
Einstein curvature tensor 471
Einstein equation 471
Einstein, summation convention 441
electric field 104
Electric field, point charge 25
Electrical conductor 594
Electrodynamics, Lagrangian density 745
Electrodynamics, tensors 459—461
Element, area 59—68
Element, Cartesian 60—62
Element, cylindrical 65—68
Element, length 59—68
Element, spherical 62—64
Element, volume 59—68
Elliptic coordinates 73 213
Elliptic cylindrical coordinates 73 213 436
Elliptic functions 322—326
Elliptic integral, complete 324
Elliptic integral, first kind 323
Elliptic integral, second kind 323
Empty set 782
Energy momentum tensor 471
Energy, relativistic 249
Energy, zero mass particle 250
Equation, canonical 749
Equation, Klein — Gordon 747
Error function 322 806
Euclid 47 80 90
Euler 272 303 326 330 503 642 743
Euler angles 201
Euler equation 483
Euler — Lagrange equation 729—731 734—736 738 739
Euler, Leonhard, biography 321
Euler’s equation 414
Event 784
Event, compound 784
Event, elementary 784
Event, random 781
Exact differential 553
expectation value 790
Extremum problem 727
Extremum problem, gradient 359—361
Factorial function 99 318
Factorial, double 319
Faraday 26
Feigenbaum alpha 774
Feigenbaum delta 773
Feigenbaum numbers 113—115
Fermi energy 677
Fermi — Dirac statistics 791
Feynman 26
Field 21—28 343
Field point 25 78
Field, electric 104
Field, scalar 343
Field, spinor 343
Field, tensor 343
Field, vector 343
Fine structure constant 679
Finite constraint problem 739
Fixed point, iterated map 755
Fixed point, stable 756
Flat space 470
Florence Nightingale 210
Fluid dynamics 413—415
Flux 365—369
Flux, density 311—381
Flux, vector field 365—369
FODE 551—561
FODE, Bernoulli 560
FODE, homogeneous 560
FODE, integral of 552
FODE, integrating factor 553—555
FODE, Lagrange 561
FODE, linear 556—561
FODE, normal 551
FOLDE 556—561
FOLDE, explicit solution 557
Force density 414
Force, central 354
Form factor 702
Four-acceleration 248
Four-momentum 241—250
Four-vector 243
Four-velocity 241—250
FOURIER 115 279 322
Fourier series 299—303
Fourier series, complex numbers 488—491
Fourier series, to Fourier transform 693—696
Fourier transform 693—112
Fourier transform and derivatives 102—103
| Fourier transform and quark model 702
Fourier transform, application to DEs 102—104
Fourier transform, convolution theorem 724
Fourier transform, Coulomb potential, charge distribution 701
Fourier transform, Coulomb potential, point charge 700
Fourier transform, definition 695
Fourier transform, examples 698—102
Fourier transform, Gaussian 699
Fourier transform, Green’s functions 105—112
Fourier transform, heat equation, one-dimensional 704
Fourier transform, higher dimensions 696
Fourier transform, inverse 695
Fourier transform, of delta function 698
Fourier transform, properties 696
Fourier — Bessel series 655
Fourier, Joseph, biography 304
Fractal 777
Fractal dimension 115—118
Free index 440
Frequency, natural 586
Frobenius method 608—610 693
Function, analytic, isolated singularity 525
Function, analytic, principal part 528
Function, antiderivative 87
Function, as integral 311—326
Function, as power series 321—335
Function, Bessel 333—335 644
Function, Bessel, Laplace’s equation 642—654
Function, Beta 320
Function, complex 491—511
Function, complex hyperbolic 502
Function, complex trigonometric 502
Function, complex, derivative 499—503
Function, complex, residue 526
Function, confluent hypergeometric 332
Function, delta, point sources 144
Function, elliptic 322—326
Function, error 322
Function, even 84
Function, factorial 318
Function, gain 586
Function, Gamma 318—319
Function, gamma, Stirling approximation 319
Function, harmonic 501
Function, homogeneous 51—59
Function, hypergeometric 328—330
Function, hypergeometric, integral representation 329
Function, iterated map 755
Function, linear density 143
Function, logistic map 755
Function, odd 84
Function, periodic 299
Function, piecewise continuous 82
Function, primitive 87
Function, rational, integral 529—531
Function, sequence 274—279
Function, series 274—279
Function, special 550
Function, transfer 586
Functional 728
Functional derivative 730
Fundamental theorem of algebra 478
Fundamental theorem of calculus 87
G-orthogonal 187 219
G-orthogonal, matrix 191 222
G-orthogonal, matrix, space 200
G-orthogonal, vector, in space 199
Gain function 586
Galileo 26 90 97 325
Gamma function 318—319
Gamma function, Stirling approximation 319
Gauge transformation 418
Gauss 279 321 326 503 617 641
Gauss elimination 231
Gauss, Johann Carl Friedrich, biography 330
Gaussian, Fourier transform of 699
Gauss’s law 369
Gauss’s law, differential form 378
Gauss’s law, integral form 377
Gay-Lussac 594
Generalized coordinates 741
Generalized momentum 748
Generating function, Hermite polynomials 673
Geodesic 465
Geodesic relativity 466
Geodesic sphere 466
Geometric series 271
Geometry and metric tensor 456
Geometry, distance formula 241
Gibbs 370
Gibbs, Josiah Willard, biography 381
Gibb’s phenomenon 302
Goldbach 320
Gradient 355—361 445
Gradient, components 440
Gradient, curvilinear coordinates, normal to surface 358
Gradient, three dimensions 357
Gradient, two dimensions 357
Gram — Schmidt process 221
Gram — Schmidt process for space 199
Grassmann 382
Green 210
Green’s function, advanced 712
Green’s function, differebtial eq. for 707
Green’s function, heat equation 709—710
Green’s function, Laplacian 708—709
Green’s function, Poisson equation 709
Green’s function, retarded 712
Green’s function, wave equation 711—712
Green’s functions 705—712
Gregory 272 294
Guided wave 682—686
Guided wave, TE 684
Guided wave, TEM 685
Guided wave, TM 684
Halley 641
Hamilton 369 382
Hamilton, William R., biography 10
Hamiltonian 747—749
Harmonic oscillator, quantum 667
Harmonic oscillator, quantum, Hermite DE 668
Heat conductor 598
Heat equation 543 661—665
Heat equation, Green’s function 709—710
Heat equation, one-dimensional 704
Heat transfer, time-dependent 663
Heat-conducting plate, circular 664—665
Heat-conducting plate, rectangular 663—664
Heat-conducting rod 662—663
Heaviside 370
Heaviside, Oliver, biography 382
Heisenberg 26 151 675
Heisenberg uncertainty relation 699
Helmholtz coil 291—293
Helmholtz free energy 54
Hermite DE, recursion relation 668
Hermite polynomial 670
Hermite polynomial, orthogonality 672
Hermite polynomials 229 575
Hermite polynomials, generating function 673
Hermite, Charles, biography 674
HNOLDE 575
HNOLDE, characteristic polynomial 576
Homogeneous function 57—59
Homogeneous SOLDE, exact 571
Homogeneous, function 57
Hooke 97
Hopf bifurcation 770
HSOLDE 564
HSOLDE, second solution 568
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