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Blum E.K., Lototsky S.V. — Mathematics of Physics and Engineering
Blum E.K., Lototsky S.V. — Mathematics of Physics and Engineering

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Название: Mathematics of Physics and Engineering

Авторы: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 482

Добавлена в каталог: 10.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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