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| Авторизация |
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| Поиск по указателям |
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| Shankar R. — Basic Training In Mathematics |
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| Предметный указатель |
 operator 284
Absolute convergence 80 118
Absolute value 92
action 309
Active transformation 208
Adjoint matrix 220
Adjoint operation 254
Ampere’s Law 198
Analytic continuation 142
Analytic function 107 109
Analytic function, analytic continuation of 142
Analytic function, branch points of 113
Analytic function, Cauchy — Riemann Equations for (CRE) 1
Analytic function, derivative of 114
Analytic function, diagnostic for 109
Analytic function, domain of analyticity of 110
Analytic function, essential singularities of 113
Analytic function, exp(z) 119
Analytic function, harmonic functions—relation to 114
Analytic function, hyperbolic functions 119
Analytic function, integrals of 128
Analytic function, Laplace’s equation, relation to 115
Analytic function, ln(z) 121
Analytic function, meromorphic functions 113
Analytic function, permanence of functional relations 143
Analytic function, poles of 111
Analytic function, power series definition of 116
Analytic function, removable singularity of 113
Analytic function, residue theorem for 132 134
Analytic function, singularities of 111
Analytic function, Taylor series for 139
Analytic function, trigonometric functions 115
Anti-analytic functions 109
Antiderivative 37
Antihermitian 221
Antilinearity of inner product 240
Antisymmetric tensor 297
Area vector 155
Axioms of vector space 230
Bernoulli’s equation 318 327
Bessel functions 335
Bessel’s equation 327
Binomial theorem 18
Box product 155 (see also “Scalar triple product”)
Bra 239 253
Branch point 113
Branch point of ln function 124
Cauchy — Riemann Equations (CRE) 109
Cauchy’s Theorem 132 134
Cayley — Hamilton theorem 263
Chain rule 3
Characteristic polynomial 257
Circulation 172
Cofactor matrix 215
Column vector 206
Commutator 210
Comparison test for series 77
Complementary function 103 313
complex numbers 89
Complex numbers, absolute value of 92
Complex numbers, application to LCR circuit 98
Complex numbers, argument of 96
Complex numbers, cartesian form of 90
Complex numbers, complex conjugate of 91
Complex numbers, Euler’s identity for 95
Complex numbers, imaginary part of 90
Complex numbers, phase of 96
Complex numbers, polar form of 94
Complex numbers, purely imaginary 90
Complex numbers, real part of 90
Complex numbers, unimodular 97
Complex variable 107 (see also “Analytic function”)
Complimentary function 313
components of vector 236
Conditional convergence 80
Conservative field 162
Constraints 55
Continuity equation for charge 193
Continuity equation for heat 336
Continuity of function in one variable 1
Continuity of function in two variables 107
Contraction of tensors 296
Contravariant tensor 299
Convergence of series 75
Convergence of series, absolute convergence 80 118
Convergence of series, complex series 116
Convergence of series, conditional convergence 80
Convergence of series, radius of 118
Coupled mass problem 267
Covariant tensor 299
Cross product 153
Cross product, as a determinant 217
Cross product, in terms of components 156
Curl 172 174 177
Curl, as a determinant 217
Curl, in noncartesian coordinates 181
Current density 162
Cylindrical coordinates 66
D operator 187 279
D operator, eigenbasis of -iD 279
D operator, Fourier series 281
Dagger 220
De Moivre’s Theorem 98
Definite integral 34
Definite integral, lower limit of 24
Definite integral, upper limit of 24
Degeneracy 263
Dependent variable 1
Derivative 2
Determinant 212 214
Determinants 214
Determinants and cross product 217
Determinants and curl 217
Differential calculus 1
Differential calculus, chain rule 3
Differential calculus, dependent variable 1
Differential calculus, differentials 29
Differential calculus, exponential and log functions 5
Differential calculus, hyperbolic functions 13
Differential calculus, implicit differentiation 28
Differential calculus, independent variable 1
Differential calculus, inverse hyperbolic functions 18
Differential calculus, inverse trigonometric functions 22
Differential calculus, linearity of derivative 3
Differential calculus, ln(1+y) 15
Differential calculus, L’Hopital’s rule 24
Differential calculus, plotting functions 23
Differential calculus, radian measure 19
Differential calculus, series for hyperbolic functions 19
Differential calculus, Taylor series 8
Differential calculus, trigonometric functions 19
Differential equations 305
Differential equations, for damped oscillator 311
Differential equations, Frobenius method 318
Differential equations, Green’s function method for 344
Differential equations, heat equations 336
Differential equations, linear 306
Differential equations, nonlinear 306
Differential equations, order of 306
Differential equations, ordinary 305 (see also “Ordinary differential equations”)
Differential equations, partial 305 (see also “Partial differential equations”)
Differential equations, superposition principle for 306
Differential equations, wave equations 329
Differential operators 187
Differentials 29
Dimensionality 235 246
Dirac delta function 197 288
Dirac matrices 227
Displacement current 199
Divergence 182
| Divergence, in other coordinates 186
Domain of analyticity 110
Domain of integration 61
Domain, simply connected 129
Dot product 151
Dot product, and inner product 237
Dot product, in terms of components 151
Drum, circular 332
Drum, square 330
Dual spaces 253
Dummy variable 43
e - the base of natural logs, power series definition 7
e - the base of natural logs, second definition 12
Eigenfunction 280
Eigenvalue problem 255
Eigenvalue problem, characteristic polynomial 257
Eigenvalue problem, degenerate case 263
Eigenvalue problem, of operator 284
Eigenvalue problem, of -iD operator 279
Eigenvalue problem, of coupled masses 263
Eigenvalue problem, of D operator 310
Eigenvalue problem, of quadratic forms 274
Eigenvalues 255
Eigenvectors 255
Einstein convention 296
Electrodynamics 193
Electrodynamics, Ampere’s law 198
Electrodynamics, continuity equation 193
Electrodynamics, displacement current 199
Electrodynamics, Lorentz force law 194
Electrodynamics, Maxwell’s equations 200
Electrodynamics, scalar potential 201
Electrodynamics, vector potential 201
Electrodynamics, wave equation 200 202
Epsilon neighborhood 110
Essential singularity 113
Essential singularity, relation to Taylor series 142
Euler’s identity 94
Exponential function, exp(elephant) 94
Exponential function, exp(x) 5 12
Exponential function, exp(z) 119
Field of vector space 231
Field, scalar and vector 158
Field, vector space 231
First order ordinary differential equation 315
Flux 163
Fourier integrals 287
Fourier series 281
Fourier series, coefficients of 281
Fourier series, completeness of 292
Fourier series, convergence of 286
Fourier series, exponential form 281
Fourier series, trigonometric 285
Fourier series, uniform convergence of 286
Fourier transform 287
Frobenius method 318
Frobenius method, indicial equation 325
Frobenius method, recursion relation in 318
Frobenius method, with singular coefficients 324
Function spaces 277
Function spaces, eigenvalue problem of 284
Function spaces, eigenvalue problem of -iD 279
Function spaces, inner product in 278
Function spaces, orthonormal basis for 279
Gamma function 43
Gauge transformation 202
Gaussian integral 71
Gauss’s theorem 184
Gibbs’ oscillation 338
Gradient 167
Gradient, and Lagrange multipliers 170
Gradient, in noncartesian coordinates 177
Gram — Schmidt Theorem 240 244
Gram — Schmidt Theorem, applied to Legendre polynomials 324
Green’s function method 344
Green’s Theorem 174
Hamiltonian 273
Harmonic function 115
Heat equation 336
Heat equation, derivation of 337
Heat equation, in d = 2 340
Heat equation, in d= 1 337
Heat equation, in polar coordinates 343
Hermite polynomials 323
Hermitian 221
Hermitian operators, and coupled masses 267
Hermitian operators, and orthogonal functions 279
Hermitian operators, and quadratic forms 274
Hermitian operators, diagonalization of 294
Hermitian operators, orthogonality of eigenvectors 260
Hermitian operators, reality of eigenvalues 260
Higher derivative vector operators 189
Hilbert space 278
Homology 191
Hyper complex numbers 125
Hyperbolic functions 13
Hyperbolic functions, in complex plane 119
Hyperbolic functions, Power series for 19
Hyperbolic functions, relation to trigonometric functions 121
Imaginary part 90
Impedance 101
Implicit differentiation 28
Indefinite integral 39
Independent variable 1
Indicial equation 325
Inner product spaces 237 239
Inner product spaces, postulates of 239
Integral calculus 28
Integral calculus, in many variables 61
Integral test for series 78
Integrals, analytical way 36
Integrals, and evaluation of areas 37 40
Integrals, antiderivative 37
Integrals, basics 33
Integrals, change of variables in 44
Integrals, composition law for 41
Integrals, definite 34
Integrals, dummy variables in 43
Integrals, in cylindrical coordinates 66
Integrals, in polar coordinates 64
Integrals, in spherical coordinates 66
Integrals, integrand 34
Integrals, integration by parts 42
Integrals, Jacobian 45
Integrals, linearity of 41
Integrals, lower limit of 32
Integrals, multiple 61
Integrals, numerical way 36
Integrals, of gaussian function 71
Integrals, of solid angle 70
Integrals, parametric differentiation 46
Integrals, primitive 37
Integrals, scale factor 65
Integrals, tricks of the trade 44
Integrals, upper limit of 34
Integrals, variable of 34
integrand 34
Integration by parts 42
Integration variable 34
Interval of convergence 10 81
Inverse hyperbolic functions 18
Inverse hyperbolic functions, miscellaneous problems in 25
Inverse matrix 211 212 216
Inverse trigonometric functions 22
Jacobian 45 65
Jacobian as a determinant 71 218
Lagrange multipliers 55
Lagrange multipliers and gradients 170
Laguerre’s equation 328
Laplace’s equation 115 340 344
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