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| Hassani S. — Mathematical Methods: for Students of Physics and Related Fields |
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| Предметный указатель |
Abel 331 503 675
Abel, Niels Henrik, biography 326
Absolute differential 463
Acceleration 44
Acceleration, components, spherical coordinates 353
Active transformation 178
Addition of velocities, relativistic law of 246
Adjoint DO 571—573
Advanced Green’s function 712
Affine connection 462—464 470
Algebra, fundamental theorem 478 511
Amplitude, complex 486
Angle as integral 345
Angle, solid 344—350
Angle, solid, total 349
Angle, total 346
Angular momentum operator 412
Angular momentum operator, spherical coordinates 435
Angular momentum, conservation 351
Angular momentum, conservation, central force 354
Antisymmetric tensor 452
Arago 321
Archimedes 47
Archimedes, of Syracuse biography 81
Area element, primary 60
Astragalus 781
Astrophysics 415
Astrophysics, Poisson equation 415
Attractor 766
Attractor, strange 778
Autonomous 767
Average 790 801
Azimuth 12
Azimuthal angle 12
Azimuthal equation 549
Azimuthal symmetry 607
Barrow 87 96 97 481
Barrow, Isaac, biography 47
Basin of attraction 766
Basis 16
Basis for plane 175
Basis, orthonormal 186
Basis, standard 216
Bayes’ Theorem 788
Beltrami identity 731
bernoulli 272 294 320 321 326 642
Bernoulli’s FODE 560
bessel 322
Bessel differential equation 548 641
Bessel differential equation, recursion relation 644
Bessel equation, Liouville substitution 589
Bessel function 333—335 644
Bessel function, addition theorem 651
Bessel function, confluent hypergeometric 652
Bessel function, expansion in 653—654
Bessel function, expansion in, physical examples 654—656
Bessel function, generating function 651
Bessel function, integral representation 652
Bessel function, Laplace’s equation 642—654
Bessel function, order, negative integer 646
Bessel function, orthogonality relation 649
Bessel function, properties 646—652
Bessel function, recurrence relation 646
Bessel function, second kind 645
Bessel, Friedrich Wilhelm, biography 641
Bessel’s integral 652
beta function 320
bezout 210
Bianchi identity 470
Bifurcation 757
Bifurcation, Hopf 770
Bifurcation, period-doubling 757
Binding energy 582
Binomial probability distribution 792—797
Binomial theorem 265
Biography, Abel, Niels Henrik 326
Biography, Archimedes, of Syracuse 81
Biography, Barrow, Isaac 47
Biography, Bessel, Friedrich Wilhelm 641
Biography, Biot, Jean-Baptiste 115
Biography, Cauchy, Augustin-Louis 503
Biography, Cavalieri, Bonaventura 90
Biography, Cavendish, Henry 23
Biography, Cayley, Arthur 192
Biography, Coulomb, Charles 23
Biography, de Fermat, Pierre 15
Biography, de Laplace, Pierre Simon 593
Biography, Descartes, Rene 15
Biography, Dirac, Paul Adrien Maurice 151
Biography, d’Alembert, Jean Le Rond 548
Biography, Euler, Leonhard 321
Biography, Fourier, Joseph 304
Biography, Gauss, Johann Carl Friedrich 330
Biography, Gibbs, Josiah Willard 381
Biography, Hamilton, William R. 10
Biography, Heaviside, Oliver 382
Biography, Hermite, Charles 674
Biography, Jacobi, Carl Gustav Jacob 326
Biography, Kepler, Johannes 579
Biography, Legendre, Adrien-Marie 617
Biography, Leibniz, Gottfried Wilhelm 103
Biography, Maxwell, James Clerk 419
Biography, Newton, Isaac 96
Biography, Savart, Felix 115
Biography, Stokes, George Gabriel 398
Biography, Sylvester, James Joseph 210
Biography, Taylor, Brook 294
Biography, Wallis, John 90
Biot — Savart law 30
Biot — Savart law, circuit 111
Biot — Savart law, general 110
Biot, Jean-Baptiste, biography 115
Bipolar coordinates 73
Bipolar coordinates, three-dimensional 74 438
Boltzmann 419
Bose — Einstein statistics 792
Boundary condition 542
Boundary condition, Dirichlet 593
Boundary condition, Neumann 593
Boundary conditions, periodic 574
Boundary conditions, separated 574
Brachistochrone 731
Bromwich contour 722
Butterfly effect 771
Calculus of residues 525—536
Calculus, fundamental theorem 87
Canonical equations 749
Cantor set 776
Cardan 481
Cartesian vector 216
Cartesian vector, component 216
Cauchy 279 326 331 594
Cauchy criterion 261
Cauchy integral formula 508—509
Cauchy — Goursat theorem 505
Cauchy — Riemann conditions 500
Cauchy — Riemann theorem 501
Cauchy, Augustin-Louis, biography 503
Cavalieri, Bonaventura, biography 90
Cavendish, Henry, biography 23
Cayley 192 211
Cayley, Arthur, biography 192
Center of mass 21
Central force 354 579—583
Central force, eccentricity 581
Central limit theorem 809
Centrifugal potential 581
Chain rule 55—57
Champollion 304
Chaos 753
| Chaos, theory, systems obeying DE 770—773
Chaos, theory, systems obeying iterated map 763
Chaos, universality 113—118
Coefficient 173
Cofactor 205
Collision, relativistic 250—253
Column vector 177
Combination 791
Complement 783
Complex amplitude 486
Complex conjugate 479
Complex function 497—511
Complex function, analytic 499
Complex function, continuous 499
Complex function, derivative 499—503
Complex function, derivative as integral 509—511
Complex function, integration 503—508
Complex function, regular point 499
Complex function, singular point 499
Complex function, singularity 499
Complex integral, positive sense 507
Complex number 478
Complex number, absolute value 479
Complex number, argument 483
Complex number, Cartesian form 478
Complex number, Fourier series 489
Complex number, imaginary part 478
Complex number, polar form 482
Complex number, real part 478
Complex number, roots 486
complex numbers 471—488
Complex numbers, Cartesian form 471—481
Complex numbers, Fourier series 488—491
Complex numbers, polar form 482—488
Complex plane 478
Complex power series 516
Complex power series, analyticity 517
Complex power series, convergence circle 517
Complex power series, differentiation 517
Complex power series, integration 517
Complex power series, uniform convergence 517
Complex series, absolute convergence 516
Component 176
Compton wavelength 253
Conditional probability 186—189
Conducting cylindrical can 655
Conductor electrical 594
Conductor heat 598
Confluent hypergeometric function 332—333
Connection, affine 462—464 470
Connection, metric 465—468
Constraints 360 738
Continuity equation 318—381
Continuity equation, differential form 380
Continuity equation, integral form 380
contour 505
Contour, Bromwich 722
Contour, simple closed 505
Contractible to zero 400
Contraction 451
Contravariant vector 445—447
Convergence test 261—212
Convolution 716
Coordinate system 11—15
Coordinate system, bipolar 73
Coordinate system, bipolar, three-dimensional 74 438
Coordinate system, cartesian 11 12
Coordinate system, cylindrical 12
Coordinate system, elliptic 73 213
Coordinate system, elliptic cylindrical 73 213 436
Coordinate system, parabolic 73
Coordinate system, paraboloidal 74 437
Coordinate system, polar 11
Coordinate system, prolate spheroidal 74 213 437
Coordinate system, spherical 12
Coordinate system, toroidal 74 213 437
Coordinate system, unit vector 31—36
Coordinate system, vector 16—31
Coordinate time 239—240
Coordinate, generalized 741
Copernicus 97 417 580
Correlation, probability 803
Cosine transform 697
Coulomb 744
Coulomb, Charles, biography 23
Coulomb’s law 22 24
Covariance in probability 803
Covariant derivative 464—465
Covariant differential 462—464
Covariant vector 445—447
Cramer 210
Crelle 326
Cross product 7 28—31
Cross product as a tensor 447
Cross product, Levi-Civita symbols 458
Cross product, parallelepiped volume 10
Cross product, parallelogram area 9
Curl, curvilinear coordinates 431-435
Curl, vector field 391—398
Current density 379
Current density and flux 379
Curvature 468—471
Curvature, scalar 470
Curve, parametric equation 61
Curve, primary 59
Curvilinear coordinates, curl 431—435
Curvilinear coordinates, divergence 437—431
Curvilinear coordinates, gradient 425—427
Curvilinear coordinates, Laplacian 435
Curvilinear vector analysis 433—435
Cycloid 732
Damping factor 311
de Broglie 666
de Fermat, Pierre, biography 15
de Laplace, Pierre Simon, biography 593
De Moivre theorem 485
DE, first-order 551—561
DE, first-order, integrating factor 553—555
DE, first-order, linear 556—561
DE, second-order 563—570
Del operator 359
Delta function, and Laplacian 412
Delta function, cylindrical 160
Delta function, derivative 147 159
Delta function, Legendre expansion 630
Delta function, limit of sequence 492
Delta function, one-variable 139—151
Delta function, point sources 144
Delta function, polar 156
Delta function, representation 431—432
Delta function, spherical 160
Delta function, three-variable 159—165
Delta function, two-dimensional 155
Delta function, two-variable 154—159
Delta, Kronecker 442
density 45
Density function, surface 154
Density of states 677
Density, current 379
Density, flux 371—381
Density, probability 801
Derivative 44—46
Derivative, covariant 464—465
Derivative, functional 730
Derivative, mixed 52
Derivative, normal 593
Derivative, partial 47—59
Derivative, time, vector 350—355
Derivative, total 86
Descartes 46 97 103 215 417 481 482
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