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Bayin S.S. — Mathematical Methods in Science and Engineering
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Название: Mathematical Methods in Science and EngineeringАвтор: Bayin S.S. Аннотация: An innovative treatment of mathematical methods for a multidisciplinary audience
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 679Добавлена в каталог: 05.12.2009Операции: Положить на полку |
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Предметный указатель
Abel test 444 Abel’s formula 569 Absolute convergence 432 Active and passive views 174 Addition of velocities 201 Addition theorem, sspherical harmonics 264 Advanced Green’s functions 624 Algebra of vectors 164 Alternating series, Leibniz rule 439 Analytic continuation 350 Analytic functions, Cauchy — Riemann conditions 297 Angular momentum operators, eigenvalue equations quantum mechanics 255 Angular momentum operators, matrix elements quantum mechanics 257 Angular momentum, factorization method 143 Angular momentum, quantum mechanics 249 Argument 294 Associated Laguerre polynomials 45 51 Associated Laguerre polynomials, generating function 52 Associated Laguerre polynomials, orthogonality and completeness 53 Associated Laguerre polynomials, recursion relations 53 Associated Laguerre polynomials, Rodriguez formula 53 Associated Legendre equation 13 28 Associated Legendre equation, factorization method 137 Associated Legendre polynomials 30 Associated Legendre polynomials, orthogonality and completeness 31 Asymptotic series 462 Bernoulli numbers 453 Bernoulli periodic function 454 Bernoulli polynomials, generating function 453 Bessel functions, boundary conditions 91 Bessel functions, channel waves tsunamis 93 Bessel functions, factorization method 155 Bessel functions, first kind 86 Bessel functions, flexible chain problem 92 Bessel functions, generating functions 89 Bessel functions, integral definitions 90 Bessel functions, modified Bessel functions 88 Bessel functions, orthogonality and completeness 90 Bessel functions, recursion relations 90 Bessel functions, second kind 87 Bessel functions, spherical 88 Bessel functions, third kind 87 Bessel functions, Wronskians 95 Bessel’s equation 86 Bessel’s equation, Laplace transforms 507 beta function 362 Binomial coefficient 447 Binomial formula, relativistic energy 447 Binomial theorem 447 Bloch equation 640 Bohr energy levels 45 Boosts, Lorentz transformation 244 Boundary conditions, Dirichlet 109 Boundary conditions, Green’s functions 572 594 Boundary conditions, Hermitian operators 110 Boundary conditions, inhomogeneous Green’s functions 575 Boundary conditions, Neumann 109 Boundary conditions, single point Green’s functions 572 Boundary conditions, Sturm — Liouville system 108 Boundary conditions, unmixed mixed 109 Branch cut, Riemann sheet 306 Branch line 306 Branch point 306 Bromwich integral, inverse Laplace transform Laplace transform 492 Caputo derivative 429 Cartesian coordinates 163 Cartesian tensors 178 Cartesian tensors, contraction 179 Cartesian tensors, pseudotensor tensor density 180 Cartesian tensors, rank 178 Cartesian tensors, trace 179 Casimir effect 466 Casimir effect, MEMS 468 Cauchy formula 388 Cauchy integral formula, fractional derivative 390 Cauchy integral theorem 336 Cauchy principal value 365 Cauchy theorem 339 Cauchy theorem, convergence tests 435 Cauchy — Goursat theorem 335 Cauchy — Riemann conditions 297 Chebyshev equation 75 Chebyshev equation, second kind 76 Chebyshev polynomials, another definition 78 Chebyshev polynomials, first kind 75 76 Chebyshev polynomials, Gegenbauer polynomials 76 Chebyshev polynomials, generating function 78 Chebyshev polynomials, orthogonality and completeness 78 Chebyshev polynomials, second kind 76 Chebyshev series, Raabe test 437 Christoffel symbols, first kind 192 Christoffel symbols, second kind 192 Commutation relations, angular momentum 249 Completeness of eigenfunctions 276 Complex algebra 293 Complex conjugate 295 complex derivative 296 Complex functions 295 Complex numbers, argument 294 Complex numbers, conjugate 295 Complex numbers, modulus 294 Complex plane 294 Complex techniques, definite integrals 352 Conditional convergence 432 Conditional convergence, Abel test 444 Condon — Shortley phase 140 Condon — Shortley phase, spherical harmonics 34 Confluent Gauss equation 104 Conformal mappings 313 Conformal mappings, electrostatics 314 Conformal mappings, fluid mechanics 318 Conjugate harmonic functions 299 Continuous groups, generators 278 Continuous groups, Lie groups 224 278 Continuous random walk, fractional derivatives 424 Contour integral techniques 352 Contour integral, complex 335 Contour integrals, special functions 369 Contraction of indices 188 Contravariant/covariant components 186 Convergence tests, Cauchy root test 433 Convergence tests, comparison 433 Convergence tests, Gauss test 436 Convergence tests, integral test 434 Convergence tests, Raabe test 435 Convergence tests, ratio test 433 Convergence, absolute conditional 432 Convolution theorem, Fourier transforms 485 Convolution theorem, Laplace transforms 498 Covariance 197 Covariant divergence 194 Covariant/contra variant components 182 Curl 193 Cut line 306 De Moivre’s Formula 295 Derivative and integral, unification for integer orders 385 Derivative, n-fold 382 Differential equations, conversion to integral equations 550 Differentiation of vectors 166 Differintegrals, composition 400 Differintegrals, CTRW Brownian motion 424 Differintegrals, dependence on the lower limit 408 Differintegrals, evaluation of definite integrals 421 Differintegrals, extraordinary differential equations 417 Differintegrals, Fokker — Planck equation 427 Differintegrals, heat transfer equation 415 Differintegrals, homogeneity 399 Differintegrals, Leibniz rule 407 Differintegrals, linearity 399 Differintegrals, properties 399 Differintegrals, right and left handed 407 Differintegrals, scale transformation 400 Differintegrals, semidifferential equations 419 Differintegrals, series 400 Differintegrals, some examples 409 Differintegrals, special functions 424 Differintegrals, techniques 413 Diffusion equation 379 Diffusion equation, Brownian motion path integrals 633 Diffusion equation, Feynman — Kac formula 639 Diffusion equation, Fourier transforms 488 Diffusion equation, propagator 610 Dipoles 23 Dirac — Delta function 481 Direction cosines 167 Divergence 194 Divergent series 465 Divergent series, Casimir effect 466 Divergent series, quantum vacuum energyy 467 Doppler shift 208 Dot product 165 Double factorial 377 Dual field strength tensor 212 d’Alembert operator 72 209 215 473 619 Eigenvalue problems Green’s functions 579 Einstein summation convention 188 Elastic beam, deformation 527 Electrostatics, Green’s functions 604 Entire function 297 347 Equivalent representations 246 ESKC relation 635 Essential singular point 347 Euler angles 172 Euler equation 518 Euler equation, another form 520 Euler — Maclaurin sum formula 454 Euler — Masheroni constant 471 Euler’s theorem 228 Expansion theorem 113 Expansion theorem, eigenfunctions 276 Extension, prolongation generators 282 Extraordinary differential equations 417 Factorization method, associated Legendre equation 137 Factorization method, Bessel functions 155 Factorization method, Gegenbauer polynomials 153 Factorization method, harmonic oscillator 156 Factorization method, single electron atom 151 Factorization method, solutions 130 Factorization method, spherical harmonics 141 Factorization method, Sturm — Liouville equation 123 Factorization method, symmetric top problem 154 Factorization method, technique and categories 132 Factorization method, theory 124 Feynman path integral, momentum space 659 Feynman path integral, quadratic momentum dependence 661 Feynman path integral, Schroedinger equation 655 Feynman — Kac formula 639 Feynman — Kac formula, derivation 641 Fick’s equation 380 Field strength tensor 212 First canonical form, self-adjoint differential operator Sturm — Liouville operator 108 Flexible chain, Bessel’s equation 84 Flow around an obstacle, conformal mappings 319 Fokker-Planck equation, fractional derivatives 427 Four-momentum, conservation 205 Four-scalars 204 Four-tensors 202 Four-vector space 274 Four-vectors 204 Four-velocity 204 Fourier integral 479 Fourier transforms 481 Fourier transforms in three dimensions 486 Fourier transforms, convolution theorem 485 Fourier transforms, cosine sine 482 Fourier transforms, diffusion equation 488 Fourier transforms, existence 486 Fourier transforms, Parceval theorems 487 Fourier transforms, partial differential equations 484 Fourier transforms, transform of a derivative 484 Fractional derivatives, Caputo definition 429 Fractional derivatives, Cauchy integral formula 390 Fractional derivatives, Gruenwald definition differintegrals 385 Fractional derivatives, Laplace transforms 396 Fractional derivatives, notation 381 Fractional derivatives, Riemann formula 395 Fractional derivatives, Riemann — Liouville definition 387 Fredholm equation 548 Frobenius method 13 16 Function spaces, Hilbert space 274 Fundamental tensor 184 Galilean transformation 215 Gamma function 360 462 Gamma function, infinite product 471 Gauss equation, special functions 104 Gegenbauer equation 75 Gegenbauer equation, factorization method 153 Gegenbauer polynomials 75 Gegenbauer polynomials, Bessel functions 89 Gegenbauer polynomials, Chebyshev polynomials 78 Gegenbauer polynomials, commutation relations 227 Gegenbauer polynomials, cosmology 72 Gegenbauer polynomials, differential 228 Gegenbauer polynomials, extension prolongation 282 Gegenbauer polynomials, generating function 75 Gegenbauer polynomials, Hermite polynomials 60 Gegenbauer polynomials, Laguerre polynomials 46 Gegenbauer polynomials, Legendre polynomials 19 Gegenbauer polynomials, normal form 280 Gegenbauer polynomials, orthogonality and completeness 75 Gegenbauer polynomials, R(3) 227 Gegenbauer polynomials, transformations 279 Generalized Fourier series 114 Generating function, associated Laguerre polynomials 52 Generators, continuous groups Lie groups 278 Geodesics 197 Gradient 193 Green’s functions 10 Green’s functions, advanced and retarded 621 Green’s functions, all space 584 Green’s functions, boundary conditions 568 Green’s functions, compounding propagators 609 Green’s functions, construction 569 Green’s functions, defining equation 572 Green’s functions, differential equations 572 Green’s functions, Dirac-delta function 583 Green’s functions, eigenfunction expansions 579 Green’s functions, first-order time dependence 606 Green’s functions, general boundary conditions 604 Green’s functions, harmonic oscillator 591 Green’s functions, Helmholtz equation 582 Green’s functions, inhomogeneous boundary conditions 575 Green’s functions, integral equations 568 Green’s functions, Laplace operator 597 Green’s functions, Lippmann-Schwinger equation 603 Green’s functions, one-dimensional 567 Green’s functions, point source 609 Green’s functions, Poisson equation 597 Green’s functions, propagators 609 Green’s functions, Schroedinger’s equation 597 Green’s functions, second-order time dependence 616 Green’s functions, three-dimensional 593 Green’s functions, three-dimensional continuum limit 594 Green’s functions, wave equation 618 Griinwald 385 Group invariants 231 Group representations 246 Group representations, R(3) 248 Group representations, SU(2) 269 Group spaces 272
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