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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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Graves, J.T. 433 Gravitational deflection of light 117 Gravitational red shift 117 Green's formulas 159 Green, G. 150 Ground state 372 Grover's Search Algorithm 388 Grover, L.K. 388 Habilitation 131 Hadamard gate 385 Hadamard matrix 386 Hadamard, J.S. 182 385 Half-range expansion 255 Hamilton's equations 94 Hamilton, W.R. 84 433 Hamiltonian 94 363 Harmonic function 157 193 harmonic oscillator 188 259—261 365 Harmonic vector field 433 Heat kernel 298 Heaviside's function 283 Heaviside, O. 4 163 282 Heisenberg, W.K. 358 Hermite's differential equation 239 Hermite, C. 239 Hermitian matrix 328 382 Hermitian operator 328 Heron of Alexandria 181 Herschel, W. 73 Herts, H.R. 348 Hesse, L.O. 427 Hessian matrix 427 Hilbert space 327 Homogeneous boundary conditions 300 324 Homogeneous equation 317 Homogeneous space, medium 1 Hooke's law 365 462 Hooke, R. 462 Hubble, E.P 119 Huygens — Steiner theorem 418 Huygens's principle 345 Huygens, C. 42 348 418 Hydrogen atom 367—373 446 Hyperbolic equation 319 Hypergeometric differential equation 237 Ideal cable 335 Identity matrix 451 Implicit Euler scheme 392 396 Incompressibility condition 355 Indicial equation 234 Infinite propagation speed 299 Initial value problem 292 296 309 323 324 344 357 Initial-boundary value problem 300 306 312 335 336 Inner product 9 327 Inner product space 327 Instantaneous smoothing 299 Integers on a circle 340 Integral formula of Cauchy 199 Integral theorem of Cauchy 197 International system of units 163 Inverse Fourier transform 263 Isometry 17 412 Isotropic space, medium 1 Jacobi's differential equation 239 Jacobi, C.G.J. viii 148 Jacobian 148 203 Jordan curve 123 Jordan's lemma 436 Joule, J.P. 296 Jourdan, M.E.C. 123 Jozsa, R. 387 KdV equation 448 Kepler's laws 44 Kepler, J. 44 Kinematics 39 Klein — Gordon equation 378 Klein, O. 378 Kolmogorov, A.N. viii 247 Korteweg, D.J. 448 Kronecker symbol 107 457 Kronecker, L. 179 Kummer's differential equation 239 Kummer, E.E. 239 Lagrange's equations 87 Lagrange's identity 410 Lagrange, J-L. 84 Lagrangian 89 Laguerre's polynomial 238 Landau, L.D. viii Laplace transform 281 Laplace's equation 158 Laplace, P-S. 158 Laplacian 139 338 Laquerre, E. 238 Laurent series expansion 216 245 Laurent, P.A. 216 Law of inertia 40 Lebesque, H.L. 244 Legendre polynomial 370 Legendre polynomials 370 430 Legendre's differential equation 239 370 Legendre, A.M. 239 Length 14 Level set 126 Levi-Civita, T. 109 Lewy, H. 399 Line element 29 105 107 144 459 Line integral 131 Linear operator 328 Linear-fractional function 435 Lines of force 167 429 Liouville's formula 235 Liouville's theorem 201 Liouville, J. 180 443 Logical operations 384 Lorentz, H.A. 101 Lorenz's gauge 352 Lorenz, E.N 61 Lorenz, L. 352 Lower limit 206 Mach, E. 3 376 Maclaurin series 212 Maclaurin, C. 212 Magnetic field strength 176 Magnetic number 372 Magnetic permeability 164 magnetic susceptibility 177 Mass, gravitational 45 Mass, inertial 45 Mass, relativistic 102 Mass, rest 101 Mathieu's differential equation 416 Mathieu, C.L. 416 Matrix 451 Maxwell's equations 164 178 347 446 Maxwell, J.C. 163 Mean-square convergence 245 Mean-value property 200 Method of characteristics 318—321 Method of reflection 335 Method of steepest descent 129 Method of weighted residuals 404 Metric 2 105 Metric tensor 105 106 Metric, flat 105 Metric, flat Minkowski 105 Michelson — Morley experiment 97 424 Michelson, A.A. 97 254 Millennium Problems 178 356 Mills, R.L. 178 Minkowski space 105 Minkowski, H. 105 Moebius strip 136 Moebius, A.F. 435 Moment arm 19 Moment generating function 284 Momentum, angular 40 68 70 Momentum, generalized 93 Momentum, linear 40 68 Momentum, relativistic 102 Moore's law 384 Moore, G.E. 384 Morera, G. 198 Morley, E.W. 97 Multiple eigenvalue 329 Multiplicity of an eigenvalue 329 NAND 384 Natural logarithm 214 Navier — Stokes equations. 355 Navier, C.L.M.H. 355 Neighborhood 121 Neumann, C.G. 161 Neumann, F.E 161 Newton's law of cooling 295 305 Newton's law of gravitation 45 Newton's laws of motion 39 Newton, I. 3 40 97 Nicolson, P. 396 Nodal line 339 343 nodes 313 Non-Euclidean geometry 2 NOR 384 Norm 14 411 Normal derivative 158 Normal line 127 Normal mode 313 Normal vector of the plane 13 Numbers 180—183 Numerical quadrature 391 Nyquist — Shannon sampling theorem 265 278 Nyquist, H. 266 Observable state 363 Observable states 380 ODE, ordinary differential equation 231 259 Ohm's law 173 463 Ohm, G.S. 173 Open ball 121 Open disk 121 Operational calculus 282 283 Operator 322 Orbital number 372 ORSTED, H.C. 165 Orthogonal elements 327 Orthogonal projection 11 Orthogonality, Bessel's functions 343 Orthogonality, continuous 242 246 Orthogonality, discrete 278 Orthonormal basis 10 15 453 Orthonormal set 10 Orthonormal system 328 Osculating circle 412 Ostrogradsky, M.V. 152 overtones 313 Parabolic equation 319 Parallel axis theorem 417 Parallelogram law 15 Paramagnetic 177 Parseval des Chenes, M-A. 244 Parseval's identity 244 267 Partial derivative 125 316 Partial sum 243 Pauli matrices 376 Pauli, W.E. 376 PDE 291 Pendulum 41 57 82 Perfect insulation 306 Perihelion 415 Perihelion precession 415 periodic extension 255 Permeability 177 Permittivity 175 Permutation symbol 461 Photon 359 Pitching 32 Planar wave 349 Plancherel's Theorem 267 Plancherel, M. 267 Planck's constant 348 359 Planck, M.K.E. 359 Plane, binormal 32 Plane, normal 32 Plane, normal vector 13 128 Plane, osculating 32 Plane, rectifying 32 Plane, tangent 128 Planimeter 151 Point at infinity 202 222 237 Point dipole, electic 172 Point dipole, magnetic 173 Point mass 24 Points, co-planar 24 Points, collinear 22 Poisson's equation 158 168 427 Poisson's summation formula 266 Poisson, S.D. 158 Polarization 350 Polynomial 179 Positive operator 328 Positive orientation 135 Positron 378 Potential 89 potential energy 132 Potential field 131 Pound — Rebka — Snider experiment 118 Power series 208 Power series, uniqueness 212 Poynting theorem 353 Poynting vector 353 Poynting, J.H. 353 principal quantum number 372 Principal unit normal vector 31 Principal value of the argument 183 Pseudo-Riemannian geometry 105 Quantum 359 Quantum computer 363 379 Quantum electrodynamics 178 379 quantum mechanics 358 Quantum oscillator 365—367 Quasi-linear equation 317 Quaternion 432 Qubit 380 Radius of convergence 209 213 Ratio Test 207 Rational function 190 191 Rayleigh (J.W. Strutt) 405 Rayleigh — Ritz method 405 Reactance 189 Rectangular pulse 271 Rectangular wave 256 Reduced Planck's constant 357 Regular singular point 233 237 Relative permittivity 175 Relativistic space-time 103 Relativity, dynamics 423 Relativity, general 45 105 415 Relativity, special 109 Representations of curve 127 Representations of surface 127 Residual 404 Residue 222
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