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Blum E.K., Lototsky S.V. — Mathematics of Physics and Engineering
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Название: Mathematics of Physics and EngineeringАвторы: Blum E.K., Lototsky S.V. Аннотация: Aimed at scientists and engineers, this book is an exciting intellectual journey through the mathematical worlds of Euclid, Newton, Maxwell, Einstein, and Schrodinger-Dirac. While similar books present the required mathematics in a piecemeal manner with tangential references to the relevant physics and engineering, this textbook serves the interdisciplinary needs of engineers, scientists and applied mathematicians by unifying the mathematics and physics into a single systematic body of knowledge but preserving the rigorous logical development of the mathematics. The authors take an unconventional approach by integrating the mathematics with its motivating physical phenomena and, conversely, by showing how the mathematical models predict new physical phenomena.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 482Добавлена в каталог: 10.04.2010Операции: Положить на полку |
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A priori analysis 297 299 309 312 Abel, N.H. 182 Absolutely integrable 264 Acceleration 33 Acceleration, angular, radial 36 Acceleration, centripetal 35 Acceleration, normal 34 Acceleration, tangential 34 Aliasing error 278 279 Ampere's law 166 Ampere, A-M 165 Amsler, J. 151 Analytic function 190 Anderson, C.D. 378 Annulus 216 Approximation error, local vs. global 392 Arc length 29 Area element 133 Argand diagram 184 Argand, J.-R. 184 Atmospheric winds 59 Average value 130 Azimuthal number 372 Ballot, C.H.D.B. 59 Band-limited 265 279 Basis 7 Berkeley, G. 3 43 97 Bessel's differential equation 236 342 Bessel's function 342 441 Bessel's inequality 244 Bessel, F.W. 236 Bijection 383 Binary star 72 Biot — Savart law 169 Biot, J.B. 169 Birkhoff, G.D. 115 Black hole 115 Bohr orbit 372 Bohr radius 368 Bohr's correspondence principle 367 Bohr's model 372 Bohr, N.H.D. 359 Boolean operations 384 Born, M. 361 Bound current 176 boundary conditions 160 300 Boundary value problem 160 Brahe, T. 44 Branch 215 Branching point 219 Bunyakovsky, V.Ya. 16 Burgers equations 355 Burgers, J.M. 355 Caloric 296 Calorie 296 Cantor, G.F.L.P. 179 Cardano, G. 181 Carleson, L. 247 Cartesian basis 7 Cauchy problem 292 Cauchy — Riemann equations 192 Cauchy — Schwartz inequality 15 327 Cauchy's inequality 201 Cauchy, A.L. 16 Cavendish, H. 45 Cayley, A. 433 Center of mass 66 80 Change of variables 144 149 Characteristic 293 Characteristic curve 318 Characteristic equation 320 Characteristic function 284 Characteristic system 318 Chebyshev's differential equation 238 Chebyshev, P.L. 239 Christoffel symbol 109 Christoffel, E.B. 109 Clairaut's theorem 126 Clairaut, A.C. 126 Classical solution 291 292 297 300 316 Column vector 12 451 Complete orthonormal system 328 Complex analysis 190 Complex flop 280 Complex function 190 Complex impedance 189 Complex potential 434 Complex power 215 Component 11 Compton, A.H. 360 Computer algebra system 28 Confluent hypergeometric differential equation 239 conformal 204 Conjugate harmonic 193 Conservative field 131 Continuous complex function 190 continuous curve 25 Continuous scalar field 123 Continuous vector field 123 Continuous vector function 25 Contravariant valence 457 Controller 288 Convergence, absolute, conditional 206 Convergence, mean-square 245 Convergence, uniform 248 Convolution 268 Cooley, J.W. 281 Coordinate curve 142 Copernicus, N. 44 Copy 384 Coriolis acceleration 52 Cosmological red shift 119 Coulomb's gauge 169 352 Coulomb's law 164 Courant — Friedrichs — Lewy condition 399 Courant, R. 399 Covariant valence 457 Crank — Nicolson scheme 396 397 Crank, J. 396 Critical point 129 Critical point, numerical computation 129 Cross product 17 Curl 138 Curvature, curve 30 412 Curvature, Ricci 109 Curvature, scalar 109 Curve 25 Curve, canonical parametrization 30 Curve, closed 25 Curve, continuous 25 Curve, Jourdan 123 Curve, piece-wise smooth 28 Curve, planar 32 Curve, rectifiable 28 Curve, simple 25 Cylindrical coordinates 141 d'Alembert's solution 310 D'Alembert, J. 310 Damping 188 260 Davisson, C.L. 360 de Broglie wave length 360 de Broglie, L-V.P.R. 360 de Coriolis, G-G. 49 de Coulomb, C.A. 164 de Lavoisier, A-L. 296 de Moivre's formula 185 de Moivre, A. 185 de Vries, G. 448 Decoherence 364 390 Dedekind, J.W.R. 179 Delta function 275 Descartes, R. 7 182 Detectable state 363 Determinant 452 Deutsch gate 386 Deutsch-Jozsa algorithm 380 387 Diagonal matrix 451 Diamagnetic 177 Dicke, R.H. 46 dielectric constant 175 Differentiable complex function 190 Differentiable field 124 Differentiable vector function 25 Differentiation formulas 26 125 139 140 Diffusion equation 295 Dipole moment 171 173 Dirac's bra-ket notations 362 Dirac's equation 375 Dirac, P.A.M. 275 Direction vector of a line 8 127 Directional derivative 123 Dirichlet Laplacian 330 338—343 Dirichlet principle 406 Dirichlet's principle 161 Dirichlet, J.P.G.L. 121 241 Disk of convergence 209 Dissipative 306 Divergence 137 Divergence theorem 151 Dot product 10 Du Bois-Reymond, P.D.G. 247 Dynamics 39 Eddington, A.S. 117 Eigenfunction 329 Eigenstate 363 Eigenstates 380 Eigenvalue 329 Eigenvector 329 EINSTEIN's summation convention 107 456 Einstein's tensor 110 Einstein, A. 3 98 107—119 294 416 Electric Dipole 170 429 Electric displacement 175 Electrical permittivity 164 Electron-volt 368 Elliptic equation 319 Elliptic integral 417 Energy of the string 312 Entangled states 381 Entire function 191 Enumerating finite rectangular array 280 Enumerating infinite rectangular array 339 Enumerating infinite triangular array 437 Eoetvoes, R. 46 Equation of continuity 154 Equation of plane 13 Equipotential line 434 Euclid 1 Euclid's postulates 1 Euclidean geometry 1 Euler — Lagrange equations 112 Euler's angles 418 Euler's equations, fluids 355 Euler's equations, rigid system 79 Euler's formula 184 214 Euler, L. 79 84 182 355 Evolution equation 322 Exact discretization 396 400 403 Explicit Euler scheme 392 396 Faraday's law 165 Faraday, M. 165 Fast Fourier transform (FFT) 280 449 Fejer kernel 438 Fejer, L. 438 Ferrel, W. 59 Ferromagnetics 178 Fick's law of diffusion 294 Fick, A.E. 294 Field, conservative, potential 131 156 Field, irrotational 141 156 433 Field, salar, vector 121 Field, smooth 124 Field, solenoidal 137 433 Fine structure constant 373 Finite difference approximation 394 448 Finite element approximation 404 Finite elements vs. finite differences 406—407 Fizeau, A.H.L. 348 Flat Minkowski metric 105 113 Flux 134 force 43 Force, central 46 413 Force, centrifugal 49 53 66 Force, conservative 88 Force, Coriolis 49 53—61 66 Force, inertial 47 Foucault 57 348 Foucault pendulum 57 Fourier coefficients, continuous 243 Fourier coefficients, discrete 279 Fourier cosine transform 273 Fourier integral 263 272 Fourier series 245 Fourier sine transform 273 Fourier transform 263 Fourier transform, other definitions 264 Fourier, J-B.J. 241 Frame 4 Frame, accelerating 61 Frame, inertial 43 46 Frame, primary inertial 43 Frame, principal axes 77 Free motion 287 Frenet's formulas 31 Frenet's trihedron 32 Frenet, J.F. 31 Friction coefficient 420 Friedrichs, K.O. 399 Frobenius, G. 231 Fuchs, L. 231 Fully nonlinear equation 318 Function 121 Functional 111 161 275 405 Fundamental mode 313 Fundamental solution, heat equation 298 Fundamental theorem of algebra 181 201 Galerkin's method 404 449 Galerkin, B.G. 404 Galilean transformation 96 Galilei, G. 42 45 101 Galileo's Principle 40 Galois, E. 182 Gate 383 Gauge 351 Gauge fixing 351 Gauge transform 351 Gauss, C.F. 152 192 281 Generalized cylindrical coordinates 135 Generalized Fourier series 328 Generalized polar coordinates 133 Generalized solution 304 310 315 Generalized spherical coordinates 135 Geodesic 110 Gerlach, W. 377 Germer, L.H. 360 Gibbs phenomenon 254 Gibbs, J.W. 3 163 254 Gordon, W. 378 Goursat, E 198 Gradient 124
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