Mathematical Methods for Physics and Engineering - Matematica.NET

IndexWhere the discussion of a topic runs over two consecutive pages, reference is madeonly to the first of these. For discussions spread over three or more pages the first andlast page numbers are given; these references are usually to the major treatment of thecorresponding topic. Isolated refences to a topic, including those appearing on consecutivepages, are listed individually. Some long topics are split, e.g. ‘Fourier transforms’ and‘Fourier transforms, examples’. The letter ‘n’ after a page number indicates that the topicis discussed in a footnote on the relevant page.A, B, one-dimensional irreps, 1090, 1102, 1109Abelian groups, 1044absolute convergence of series, 124, 831absolute derivative, 975–977acceleration vector, 335Adams method, 1024Adams–Moulton–Bashforth, predictor-correctorscheme, 1035addition rule for probabilities, 1125, 1130addition theorem for spherical harmonicsYl m (θ, φ), 594adjoint, see Hermitian conjugateadjoint operators, 559–564adjustment of parameters, 795Airy integrals, 890–894Ai(z), 889algebra ofcomplex numbers, 85functions in a vector space, 556matrices, 251power series, 134series, 131tensors, 938–941vectors, 213in a vector space, 242in component form, 218algebraic equations, numerical methods for, seenumerical methods for algebraic equationsalternating group, 1116alternating series test, 130ammonia molecule, symmetries of, 1042Ampère’s rule (law), 381, 408amplitude modulation of radio waves, 444amplitude-phase diagram, 914analytic (regular) functions, 826angle between two vectors, 221angular frequency, 693nin Fourier series, 419angular momentum, 933, 949and irreps, 1093of particle system, 950–952of particles, 338of solid body, 396, 951vector representation, 238angular momentum operatorcomponent, 658total, 659angular velocity, vector representation, 223, 238,353annihilation and creation operators, 667anti-Hermitian matrices, 271eigenvalues, 276–278imaginary nature, 277eigenvectors, 276–278orthogonality, 277anti-Stokes line, 905anticommutativity of vector or cross product,222antisymmetric functions, 416and Fourier series, 419and Fourier transforms, 445antisymmetric matrices, 2701305