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Carroll R.W. — Mathematical physics
Carroll R.W. — Mathematical physics

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Название: Mathematical physics

Автор: Carroll R.W.

Аннотация:

An introduction to the important areas of mathematical physics, this volume starts with basic ideas and proceeds (sometimes rapidly) to a more sophisticated level, often to the context of current research. All of the necessary functional analysis and differential geometry is included, along with basic calculus of variations and partial differential equations (linear and nonlinear). An introduction to classical and quantum mechanics is given with topics in Feynman integrals, gauge fields, geometric quantization, attractors for PDE, Ginzburg-Landau Equations in superconductivity, Navier-Stokes equations, soliton theory, inverse problems and ill-posed problems, scattering theory, convex analysis, variational inequalities, nonlinear semigroups, etc. Contents: 1. Classical Ideas and Problems. Introduction. Some Preliminary Variational Ideas. Various Differential Equations and Their Origins. Linear Second Order PDE. Further Topics in the Calculus of Variations. Spectral Theory for Ordinary Differential Operators, Transmutation, and Inverse Problems. Introduction to Classical Mechanics. Introduction to Quantum Mechanics. Weak Problems in PDE. Some Nonlinear PDE.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 410

Добавлена в каталог: 22.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{1}$-norm      7
$m$-accretive      276
$r$-matrix      211
$s$-accretive      274
$\Gamma$-regularization      266 268
$\varepsilon$-approximate solution      275
Abelian gauge      296
Absolute continuity      7 272 337
Absorbing set      84 315
Accretive      236 272 343
Acoustic waves      90
Action functional      55 78
Action-angle variables      199 200
Adjoint functions      206
Adjoint system      34
Affine function      266
Affine minorant      266
AKNS system      192
Alaoglu’s theorem      271 279 323
Algebra of operators      60
Almost everywhere      236 337
Alternating      355
Annihilation operator      60 287
Anticausal      152 154
Antiderivation      368
Antidual      70
Approximate eigenvector      103
Arzela — Ascoli theorem      95 320 260
Asplund’s theorem      273
Asymptotic states      104
Attractor      83
Autocorrelation      47 155
B-complete continuity      237
Backlund transformation      191 216
Backward heat problem      25
Baire space      317
Banach theorem homomorphisms      324
Banach — Steinhaus theorem      239 317 320
Bang-bang control      34
Barrel      317
Barreled space      317
Barrier      60
BBM equation      76
Bianchi identity      301 305
Bispinor      297
Blowup      228
Bogomolny formula      79
Bound state      38 61 120
Boundary operator      52
Bounded map      229
Bounded set      316 318
Bra      63
Brachistochrone problem      2
Brouwer fixed point theorem      247 253 259
Brownian motion      291
Burger’s Equation      76
Canonical equations      56
Canonical form PDE      17 18
Canonical transformation      55 201
Casimir operator      65
Category      252 361
Catenary      30
Cauchy data      14
Cauchy net      313
Cauchy Peano theorem      74
Cauchy problem      12 14 56 151
Cauchy Schwartz inequality      325
Cauchy — Kowalevsky theorem      87
Causal      141 146 152 154
cell      52 366
Chain      52 53 366
Chain rule      354
Characteristic strip      56
Characteristics      10 12 18 56
Charge      293
Charts      351
Chern class      309
Chern number      78
Christoffel symbol      298
Closed form      359
Closed graph theorem      325
Closed map      262
Closure      313
Cluster point      241
Coercive      67 280 282 283
Coimitation relations      59 60 287
COLOR      298
Compact homotopy      264
Compact operator      233
Compactness      233 319
Compensated compactness      285
Complete continuity      229 233 237
Complete space      313
Completely integrable      200 218
Completeness      63 204 220
Concave function      268
Cone condition      345
Conjugate fields      296
Conjugate function      29 265 267
Conjugate linear      67 69
Conjugate point      31
Conjugate variables      199
Connected      256
Connected Green’s function      294 295
Connection      78 211 217 290 303
Conservation of energy      24 53
Conserved quantity      188
Continuous spectrum      103 108
Continuous subspace      105
Contractible      253
Contraction      301
Contraction map theorem      230
Contravariant      287
Convex disced envelope      317 332
Convex functional      243 265
Convex hul      1 254 264
Convolution      12
Cost optimization      27
Cotangent bundle      51 63 355 365
Cotangent space      64 353
Countable at infinity      351
Coupling constant      211
Covariant      287 296
Covariant derivative      78 218 296 298 304
Crandall — Liggett theorem      277
Creation operator      60 287
Critical point      228 245
Critical Sobolev exponent      285 286
Crum transform      191
Current      80 292 296
Curvature      78 217 290 304 212
CYCLE      366
D-monotone      236 343
Darboux transformation      191
Darboux — Christoffel formula      203
De Rham cohomology      366
de Rham complex      366
Deconvolution      45
Degenerate Cauchy problem      18
Degree      256 257
Delta function      12 42 149
Demicontinuous      228 235 236
Derivation      354
Derrick’s theorem      80
Determining sequence      332
Diatomic molecule      64
Differential form      357
Differential ideal      216
Differentiation      22 330 334 348
Dirac equation      295
Directional derivative      29
Dirichlet functional      5
Dirichlet problem      5 15 66 270
Disced set      315
Discrete spectrum      102
Discretization      275
dispersion relation      209 214
Dissipative PDE      84
distribution      329
Divergence form      234
Domain      263
Domain of dependence      13 47
Domain of influence      13
Dominated convergence      236 337
Du Bois Reymond      4 5
Dual functions      206
Dual inverse problem      202
Dual problem      26 267
Dual space      313
Dual variable      26
Duality      316
Duality map      273
Duffing’s equation      75
Dynamical variables      59
d’Alembert solution      10 13
Effective domain      265
Eigenfunction      11 39
Eigenfunction expansion      12 39 146
Eigenstate      59
Eigenvalue      11
Elliptic equation      15 17 234 240 242 282
Embedding theorems      346
Energy      23
Energy-momentum tensor      288 301
Epigraph      265 284
Equicontinuous      95 319
Equilibrium      27
Equivalence class      236
Essential      255 263
Essential spectrum      103 108
Essentially selfadjoint      58 109
Euler — Poisson — Darboux equation      18 22
Euler’s equations      4 49 74
Euler’s trick      3 30
Evolution equation      12 197 248
Exact form      359
Excision      253 395
Expectation      57
Exponential map      374
Extension by continuity      321
Exterior product      355
Extrapolation      47
Factorization      152 154
Fadeev — Popov ansatz      300
Fermat’s principle      2
Feynman integral      290
Feynman propagator      295
Feynman — Kac formula      292
Field strength      304
Finest topology      333
Finite dimensional map      258
Finite intersection property      234
Finitely continuous      242
Fixed point index      264
Flavor      298
Flow      218
Forcing      220
Forms extension      104
Forward scattering amplitude      138
Fourier method      12
Fourier transform      12 337
Fourier type operator      123 153 181
Fractal dimension      84
Frechet derivative      174 198 209 229 362
Frechet space      313
Fredholm operator      216 234
Free boundary      285
Friedrich’s extension      82
Frobenius theorem      216
Functionally invariant set      83
functor      252 361
Fundamental solution      19
Fundamental system NBH      312
Galerkin method      240 283
Gateaux derivative      229
Gauge      302
Gauge algebra      306
Gauge fixing      299
Gauge invariance      81
Gauge potential      9 81 305
Gauge transformation      9 81 211 216 292 296 306
Gaussian integral      295
Gelfand — Levitan equation      41 92 123 129 151 152 160
Generalized eigenfunctions      110 118 148
Generalized Galerkin      240 248
Generalized inverse      87
Generalized momentum      49
Generalized Radon transform      140
Generalized solution      249
Generalized translation      152
Generating functional      293 298
Germ      353
Ghost field      300
Ginzburg — Landau equations      76—79 82
Global analysis      77
Global attractor      85
Goldstone boson      81
Gopinath — Sondhi equation      166 167
Goursat problem      151 1 94 220
Graded abelian groups      252
Gradient      287
Gradient map      232
Graph topology      250
Green’s function      39 97 114 116 162 163 290
Green’s operator      122
Green’s Theorem      5 66
Gribov ambiguity      299
Gronwall lemma      75
Grothendieck topologies      348
Ground state      288
H-compact operator      110
Haar measure      299
Hademard example      19
Hahn — Banach theorem      238 313 316
Hamilton — Jacobi equation      54 56 285
Hamiltonian      29 34
Hamiltonian vector field      52
Hamilton’s equations      51 198
Hamilton’s principle      8 49
Hammerstein operator      26
Hanging cable      26
Hankel kernel      162
Harmonic function      20
harmonic oscillator      59
Hausdorff dimension      83
Hausdorff measure      83
Hausdorff space      311 336
Heat equation      13
Heat kernel      14
Heini — Borel property      234
Heisenberg uncertainty      58 59
Heisenbert picture      63
Hemicontinuity      236
Hermite polynomials      60
Hermitian line bundle      308
Hermitian operator      60
Higgs field      78 300
Higgs mechanism      81
Hilbert integral      31 55
Hilbert space      325
1 2 3
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