Авторизация
Поиск по указателям
Bayin S.S. — Mathematical Methods in Science and Engineering
Обсудите книгу на научном форуме Нашли опечатку?
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 |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Group theory, group character 248 Group theory, Holder inequality 442 Group theory, invariants 231 Group theory, Lorentz group 232 241 Group theory, Poincare group 241 Group, definition 224 Group, terminology 224 Hamilton’s principle 533 Hankel function 87 Harmonic functions 299 Harmonic oscillator, damped Laplace transforms 505 Harmonic oscillator, factorization method 156 Harmonic oscillator, Green’s functions 591 Harmonic oscillator, quantum mechanical Hermite polynomials 57 Harmonic oscillator, three dimensional 56 Harmonic series 432 Heat transfer equation, differintegrals 415 Helmholtz equation 9 Helmholtz equation, continuum limit 584 Helmholtz equation, Green’s functions 582 Helmholtz equation, three dimensions 593 Hermite equation 58 60 Hermite polynomials 59 Hermite polynomials, contour integral 373 Hermite polynomials, dipole calculations 64 Hermite polynomials, Gaussian 63 Hermite polynomials, generating function 60 Hermite polynomials, harmonic oscillator 57 Hermite polynomials, orthogonality and completeness 62 Hermite polynomials, recursion relations 62 Hermite polynomials, Rodriguez formula 61 Hermitian operators, boundary conditions 110 Hermitian operators, eigenvalues eigenfunctions 110 Hermitian operators, quantum mechanics 116 Hermitian operators, Sturm — Liouville operator 110 Hilbert space, function spaces 274 Hilbert space, inner product 117 Hilbert space, quantum mechanics 277 Hilbert — Schmidt theory 560 Hilbert — Schmidt theory, completeness of eigenfunctions 563 Hilbert — Schmidt theory, nonhermitian operators 564 Homogeneous Lorentz group 241 Hypergeometric equation 99 Hypergeometric functions 99 Improper transformations 170 Incomplete beta function 364 Incomplete gamma function 364 Indicial equation 14 Indicial equation, double root 45 Indicial equation, roots 16 Infinite products 468 Infinite products, cosine function 471 Infinite products, gamma function 471 Infinite products, sine function 470 Infinite series, convergence 431 Infinitesimal ring, Lie algebra 226 Infinitesimal transformations, orthogonal transformations 175 Inhomogeneous boundary conditions, Green’s functions 575 Inhomogeneous Lorentz group 241 Inner product space 273 Inner product, Hilbert space 117 Integral equations via integral transforms 559 Integral equations vs. differential equations 548 Integral equations, Cauchy formula 549 Integral equations, classification 548 Integral equations, eigenvalue problems Hilbert — Schmidt theory 560 Integral equations, Fredholm equation 548 Integral equations, Green’s functions 568 Integral equations, homogeneous 548 Integral equations, methods of solution Neumann series 554 Integral equations, nonhermitian kernels 564 Integral equations, separable kernels 556 Integral equations, successive iterations 554 Integral equations, Volterra equation 548 Integral transforms 10 Integral transforms, Fourier transforms 478 Integral transforms, general 477 Integral transforms, Hankel transform Fourier — Bessel transform 479 Integral transforms, integral equations 559 Integral transforms, Laplace transforms 478 Integral transforms, Mellin transform 479 Integral transforms, Mellin transform, relations 511 Integral, n-fold 384 Invariance 197 Inverse Laplace transforms, Bromwich integral 492 Inverse Laplace transforms, Lerch theorem 491 Inversion of power series 451 Irreducible representation 247 Isolated singular point 297 347 Isomorphism 239 Isoperimetric problems 529 Jacobi polynomials 41 Jacobi polynomials, contour integral 375 Jacobian of transformation 190 Jordan’s lemma 357 Kronecker delta 179 Kummer formula 106 Ladder operators step up/down operators 124 125 Laguerre equation 45 Laguerre polynomials 46 Laguerre polynomials, contour integral 371 372 Laguerre polynomials, generating function 46 Laguerre polynomials, orthogonality and completeness 48 Laguerre polynomials, recursion relations 50 Laguerre polynomials, Rodriguez formula 47 Laguerre polynomials, special values 50 Laguerre series 46 Laplace equation 9 Laplace equation, variational analysis 525 Laplace transforms 490 Laplace transforms in n dimensions 511 Laplace transforms, basic 492 Laplace transforms, Bessel’s equation 507 Laplace transforms, damped oscillator 505 Laplace transforms, definite integrals 502 Laplace transforms, derivatives 503 Laplace transforms, differintegrals 413 Laplace transforms, electromagnetic waves 506 Laplace transforms, fractional derivatives 396 Laplace transforms, inverses Bromwich integral 492 Laplace transforms, Mellin transforms 511 Laplace transforms, partial fractions 501 Laplace transforms, theorems 494 Laplacian, covariant 194 Laurent series 341 Laurent series, short cut 346 Legendre equation 13 Legendre polynomials 18 Legendre polynomials, generating function 19 Legendre polynomials, normalization constant 26 Legendre polynomials, orthogonality and completeness 24 Legendre polynomials, recursion relations 21 Legendre polynomials, rodriguez formula 19 Legendre polynomials, Schlofli formula 370 Legendre polynomials, special integrals 23 Legendre polynomials, special values 22 Legendre series 15 Legendre series, convergence Gauss test 436 Leibniz formula 25 Letnikov 385 Levi — Civita symbol 180 Lie algebra, generators of SU(2) differential 240 Lie algebra, group differential operators 228 Lie algebra, infinitesimal ring 226 Lie algebra, rotation group R(3) 227 Lie algebra, SU(2) 237 Lie groups, continuous groups 224 Line element 184 199 Linear independence, Wronskian 41 Lorentz contraction, length contraction 201 Lorentz group, commutation relations 244 Lorentz group, generators 244 Lorentz group, homogeneous inhomogeneous 241 Lorentz transformation 199 Lorentz transformation, boost 244 Lorentz transformation, group invariants 232 Lorentz transformation, orientation of axis 209 M-test, Weierstrass M-test 444 Maclaurin series 446 Mappings 300 Mappings, conformal 313 Mappings, inversion 301 302 Mappings, many-to-one 306 Mappings, one-to-one 304 Mappings, one-to-two 306 Mappings, rotation 301 Mappings, Schwarz-Christoffel transformations 322 Mappings, translation 300 Mappings, two-to-one 304 Maxwell’s equations 211 Maxwell’s equations, potentials 214 Maxwell’s equations, transformations 213 Mean square displacement 380 Mellin transforms 512 MEMS, Casimir effect 468 Metric tensor 184 Metric tensor, covariant derivative 194 Minkowski metric 202 Minkowski spacetime 198 Minkowski’s inequality 442 Mittag-Leffler theorem, infinite products 470 Mlittag — Leffler functions 418 Modified Bessel functions 88 Modulus 294 Multipole expansion 267 Neumann function 87 Neumann series, error calculation 556 Newton’s equations, covariant 215 Normal form, generators 280 Orthogonal transformations 167 170 Orthogonality and completeness, associated Laguerre polynomials 53 Orthogonality and completeness, associated Legendre polynomials 31 Orthogonality and completeness, Bessel functions 90 Orthogonality and completeness, Chebyshev polynomials 78 Orthogonality and completeness, Gegenbauer polynomials 75 Orthogonality and completeness, Hermite polynomials 62 Orthogonality and completeness, Laguerre polynomials 48 Orthogonality and completeness, Legendre polynomials 24 Orthogonality and completeness, Sturm — Liouville operators 111 Outer product 179 189 Parceval theorems 487 Partial fractions, Laplace transforms 501 Partial sum 431 Path integrals, Bloch formula 640 Path integrals, ESKC relation 635 649 Path integrals, Feynman path integral 655 Path integrals, Feynman phase space path integral 659 Path integrals, Feynman — Kac formula 639 Path integrals, finite elements method 650 Path integrals, interpretation 643 Path integrals, methods of calculation 646 Path integrals, Schrodinger equation 658 Path integrals, semiclassical method 650 Path integrals, time slice method 647 Path integrals, Wiener path integral 635 Pauli spin matrices 236 Permutation symbol 190 Pinned Wiener measure 637 Poincare group 241 Point groups 278 Point source initial condition, Green’s functions 609 Poisson equation, Green’s functions 597 Power series 449 Prolongation, extension generators 282 Propagators 609 Proper time 204 205 Proper transformations 170 Pseudo — Euclidean 199 Pseudotensor 180 Quantum mechanics, Hermitian operators 116 Quotient theorem 189 Quotient theorem, R(3) and SU(2) 269 Quotient theorem, R(3) relation to SU(2) 269 Rank 178 Rayleigh-Ritz method, variational integrals 539 Recursion relation, associated Laguerre polynomials 53 Recursion relation, Bessel functions 90 Recursion relation, Hermite polynomials 62 Recursion relation, Laguerre polynomials 50 Recursion relation, Legendre polynomials 21 Reducible representation 247 Regular singular point, Probenius method 16 Regularization, Renormalization 465 Relativistic energy, binomial formula 447 Relativistic mass 207 Renormalization 465 Representation space 246 Residue theorem 347 Rest mass 205 Retarded Green’s functions 624 Riemann curvature scalar 195 Riemann curvature tensor 195 Riemann formula 395 Riemann sheets, branch cuts 308 Riemann Theorem 440 Riemann zeta function 434 Riemann-Liouville, derivative 387 Rodriguez formula, associated Laguerre polynomials 53 Rodriguez formula, Hermite polynomials 61 Rodriguez formula, Laguerre polynomials 47 Rodriguez formula, Legendre polynomials 19 Rotation group, representation 248 Rotation group, spherical harmonics 249 Rotation matrix, differential equation 262 Rotation matrix, evaluation 260 Rotation matrix, inverse 261 Rotation matrix, orthogonal transformations 170 Rotation matrix, spherical harmonics 258 Rotation operator, Euler angles 251 Schlofli formula 370 Schlofli integral formula, Legendre polynomials 370 Schroedinger equation 10 43 Schroedinger equation, bound states 601 Schroedinger equation, factorization method single electron atom 151 Schroedinger equation, Feynman path integral 658 Schroedinger equation, Green’s function 615 Schroedinger equation, propagator free particle 615 Schur’s lemma 247 Schwartz inequality 118 Schwarz — Cauchy inequality 442 Schwarz-Christoffel transformations 324 Schwarz-Christoffel transformations, fringe effects 325 Second canonical form, Sturm — Liouville operator 122 Self-adjoint differential operator 107 Semi-infinite parallel plate, mappings fringe fields 325 Semi-integrals 413 Semiderivatives 413 Semidifferential equations 419 Separation of variables 10 Series, algebra 439 Series, inequalities 442 Series, rearrangement 440 Similarity transformations 175 Simple pole 347 Single-electron atom models 44 Singular points, classification 347 Singular points, essential 347 Singular points, isolated 347 Singular points, simple pole 347 Soap film 521
Реклама
|
|
О проекте