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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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resistivity 463 Resonance 260 Rest mass 376 Reversible gate 383 Ricci curvature tensor 109 Ricci — Curbastro, G. 109 Riemann integral 130—131 Riemann — Lebesgue theorem 244 Riemann, G.F.B. 131 192 244 Right-handed circular helix 30 Right-handed triad 18 Rigid pendulum, distributed 82 Rigid pendulum, simple 41 Ritz, W. 405 Rolling 32 Rolling cylinder 419 Root test 207 Roots of complex numbers 184 Rotation vector 51 63 74 Row vector 12 451 Savart, F. 169 scalar 5 Scalar field 121 Scalar potential 351 Scalar product 10 Scalar triple product 23 Schroedinger's equation 356 363 Schroedinger's equation, stationary 364 Schroedinger, E.R.J.A. 361 Schwarz, H.A. 16 Schwarzschild radius 113 415 Schwarzschild's metric 113 Schwarzschild's solution 113 Schwarzschild, K. 113 Second partials test 427 Semi-linear equation 317 Separation constant 325 Separation of variables 300 312 331 339 341 368 Serret, J.A. 31 Sets in 121 186 Shannon, C.E. 266 Shape of the drum 347 Shor's Factorization Algorithm 388 Shor, P.W. 388 Simple eigenvalue 329 Simple pole 219 Singularity 219 Skewed lines 411 Smooth function 124 Solenoid 137 Soliton 448 Solution operator 322 Space-time 99 Spectrum of a signal 256 268 Spectrum of an operator 329 Spectrum, electromagnetic radiation 350 Speed 33 speed of light 98 164 348 Speed, angular, radial 36 Spherical coordinates 142 Spin 376 Stability condition 397 448 Stable dynamical system 287 289 Stable numerical method 393 Standing wave 313 Stationary wave 313 Steady-state solution 305 Steiner, J. 418 Stern — Gerlach experiment 377 Stern, O. 377 Stokes, G.G. 155 Stream function 434 streamline 433 Stress 344 Stress-energy tensor 108 String theory 379 Sturm — Liouville problem 443—446 Sturm, J.C.F. 443 Superconductors 178 Superposition principle 300 362 Surface area element 134 Surface, orientable 133 Surface, piece-wise smooth 133 Surface, simple 123 susceptibility 175 Symmetric operator 328 Tangent line 28 Tangent plane 128 Taylor formula in 426 Taylor series 212 Taylor, B. 212 Telegraph equation 334 Tensor field 175 457 Tensor of inertia 76 81 Tensor of type (p, q) 457 Thomson, W. (Lord Kelvin) 155 337 Time-reversible 357 Toffoli gate 385 Toffoli, T. 385 torque 19 41 Torsion 31 412 Transformation 17 Transformation, Galilean 101 Transformation, linear 17 Transformation, Lorentz 101 348 423 446 Transformation, Moebius 435 Transformation, orthogonal 17 412 Transport equation 292 Travelling wave solution 311 Triangle inequality 15 Triangular pulse 311 Trigonometric polynomial 242 Tukey, J.W. 281 Tumbling box 420 tuning 313 Twin paradox 103 Two-sided Laplace transform 284 Uncertainty principle 358 373 Underwater cable 335—338 Uniform rotation 48 Unique factorization 432 Uniqueness, Fourier series 245 Uniqueness, power series 212 Unit binormal vector 31 Unit tangent vector 27 Unit vector 9 Unitary matrix 382 Universal gate 385 Universal gravitational constant (G) 45 Upper limit 206 Vacuum field equations 113 Vacuum solutions 112 Variation of parameters 294 298 311 315 323 Variational approach 404 Veblen, O. 123 Vector 3 6 Vector algebra 3 Vector analysis 3 vector calculus 3 Vector field 121 Vector fields and analytic functions 433 Vector potential 168 351 Vector product 17 Vector space 6 326 Vectors, linearly dependent 411 Vectors, linearly independent 7 Vectors, orthogonal 10 Vectors, perpendicular 10 Velocity 33 Velocity potential 434 Volume element 135 von Helmholtz, H.L.F. 338 von Neumann, J. 362 Vorticity 433 448 Wallis, J. 184 Wave diffusion 311 Wave function 357 371 Wave vector 349 Weierstrass's M-test 249 Weierstrass's polynomial, approximation theorem 439 Weierstrass, K.T.W. 249 Weight function 443 Weyl, H. 362 World line 103 XOR 384 Yang — Mills equations 178 351 Yang, C-N. 178 Yawing 32 z-transform 284 285 Zeeman effect 376 Zeeman, P. 376 Zhukovsky's airfoil 435 Zhukovsky's function 435 Zhukovsky, N.Y. 435
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