Mathematical Methods for Physics and Engineering - Matematica.NET

INDEXvolume integrals, 396and divergence theorem, 401volume ofcone, 75ellipsoid, 207parallelepiped, 225rhomboid, 237tetrahedron, 192volumesas surface integrals, 397, 401in many dimensions, 210of regions, using multiple integrals, 191–193volumes of revolution, 75and surface area & centroid, 195–197zero-order tensors, 932–935zeros of a function of a complex variable, 839location of, 879–882, 921order, 839, 856principle of the argument, 880Rouché’s theorem, 880, 882zeros of Sturm-Liouville eigenfunctions, 573zeros, of a polynomial, 2zeta series (Riemann), 128, 129z-plane, see Argand diagramwave equation, 676, 688, 790boundary conditions, 693–695characteristics, 704from Maxwell’s equations, 373in one dimension, 689, 693–695in three dimensions, 695, 714, 737standing waves, 693wave number, 437, 693nwave packet, 436wave vector, k, 437wavefunction of electron in hydrogen atom, 208Weber functions Y ν (x), 607wedge product, see vector productweightof relative tensor, 964of variable, 477weight function, 555, 790Wiener–Kinchin theorem, 450WKB methods, 895–905accuracy, 902general solutions, 897phase memory, 895the Stokes phenomenon, 903work doneby force, 381vector representation, 220Wronskianand Green’s functions, 527for second solution of ODE, 544, 580from ODE, 532test for linear independence, 491, 532X-ray scattering, 237Yl m (θ, φ), see spherical harmonicsY ν (x), Bessel functions of second kind, 607Young’s modulus, 677, 953z, as a complex number, 84z ∗ , as complex conjugate, 89–91zero (null)matrix, 254, 255operator, 249unphysical state |∅〉, 650vector, 214, 242, 5561333