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| Авторизация |
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| Shankar R. — Basic Training In Mathematics |
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| Предметный указатель |
Laplacian 192
LCR circuit 98
LCR circuit, impedance 101
LCR circuit, mechanical analogy 104
LCR circuit, transients in 103
Legendre polynomial 324
Legendre’s equation 324
Level surface 168
Line integral 159
linear combination 3
Linear dependence 233
Linear independence 233
Linear operators 247
Linear operators, adjoint of 252
Linear operators, D and -iD operators 279
Linear operators, definition of 248
Linear operators, eigenvalue problem of 255
Linear operators, matrix elements of 249
Linear operators, product of 251 252
Linear transformation 209
Linear vector spaces 229
Linear vector spaces, adjoint operation 254
Linear vector spaces, axioms of 230
Linear vector spaces, basis for 235
Linear vector spaces, dimension of 235 246
Linear vector spaces, dual spaces 253
Linear vector spaces, eigenvalue problem 255
Linear vector spaces, examples 239
Linear vector spaces, expansion of vectors in 242 243
Linear vector spaces, expansion of vectors in orthonoimal basis 242
Linear vector spaces, field of 231
Linear vector spaces, function spaces 277
Linear vector spaces, generation of basis for 279
Linear vector spaces, Gram — Schmidt procedure for 244
Linear vector spaces, inner product for 237 239
Linear vector spaces, linear operators acting on 247
Linear vector spaces, over complex field 231
Linear vector spaces, real 231
Linear vector spaces, Schwarz inequality 246
Linear vector spaces, Triangle inequality 246
ln, branch point of 124
ln, branches of 124
ln, ln(x) 15
ln, ln(z) 121
LOG see “ln”
Lorentz force law 194
Lorentz gauge condition 202
L’HopitaFs rule 24
Matrix inverse 211 212 216
Matrix product 206
Matrix sum 206
Matrix transpose 215
Matrix, adjoint 220 225
Matrix, analogy to numbers 225
Matrix, antihermitian 221
Matrix, antisymmetric 220
Matrix, commutator of 210
Matrix, dagger 220
Matrix, determinant of 211
Matrix, Dirac 227
Matrix, elements 205
Matrix, for rotation 208
Matrix, functions of 222
Matrix, hermitian 221
Matrix, inverse 211 216
Matrix, null 209
Matrix, orthogonal 222
Matrix, Pauli 226
Matrix, product of 206
Matrix, simultaneous equations 212
Matrix, sum of 206
Matrix, symmetric 220
Matrix, table of properties 222
Matrix, trace of 227
Matrix, transpose 215
Matrix, unit 209
Matrix, unitary 221
Maxima, minima and saddle points 274
Maxwell’s equations 200
Meromorphic functions 113
Mixed derivative 52
Modulus 90
Moment of inertia tensor 298
Natural logarithm 7 8
Norm of a vector 149
Normal modes 267 272
Normal modes, in quantum mechanics 273
Normal modes, of coupled masses 267
Normal modes, of string 289
Null vector 149 230
Ohm’s Law 295
Ordinary differential equation (ODE) 307
Ordinary differential equation (ODE), Bessel’s equation 327
Ordinary differential equation (ODE), classical oscillator 311
Ordinary differential equation (ODE), complimentary function 313
Ordinary differential equation (ODE), Frobenius method 318 324
Ordinary differential equation (ODE), Hermite’s equation 322
Ordinary differential equation (ODE), initial conditions 308
Ordinary differential equation (ODE), integration constants 307
Ordinary differential equation (ODE), Laguerre’s equation 328
Ordinary differential equation (ODE), Legendre’s equation 324
Ordinary differential equation (ODE), particular solution 313
Ordinary differential equation (ODE), quantum oscillator 320
Ordinary differential equation (ODE), with constant coefficients 307
Ordinary differential equation (ODE), with variable coefficients (first order) 315
Ordinary differential equation (ODE), with variable coefficients (second order) 318
Orthogonal coordinates 65
Orthogonal matrix 221
Orthonormal basis 149 239
Orthonormal basis, expansion of a vector in 242
Oscillator, action for 309
Oscillator, analogies to LCR circuit 104
Oscillator, equations for 104 311
Oscillator, quantum 320
Oscillator, types of behavior 311
Outer product 297
Parseval’s theorem 293
Partial derivative 51
Partial differential equation (PDE) 329
Partial differential equation (PDE), heat equation in d = 1, 2 336
Partial differential equation (PDE), polar coordinates 334 343
Partial differential equation (PDE), separation of variables 329
Partial differential equation (PDE), solution by Green’s functions 344
Partial differential equation (PDE), wave equation in d = 1, 2 329
Particular solution 103 313
Passive transformation 208
Pauli matrices 226
Permanence of relations 143
Permeability of free space 172
Permittivity of free space 166
Pi ( ) 20
Planck’s constant 288
Plotting functions 23
Poisson’s solution 344
Polar coordinates 64
Polar form 94
Polarizability tensor 299
Poles, n-th order 113
Poles, residue at 112
Poles, simple 112
Position vector 156
| Potential 175
Power series, absolute convergence 80 116
Power series, hyperbolic functions 19 119
Power series, in x 80
Power series, in z 116
Power series, interval of convergence of 10 81
Power series, ln(1 + x) 15 85
Power series, radius of convergence 118
Power series, tests for convergence 80
Power series, tricks for expansion in 83
Power series, trigonometric functions 22 119
primitive 37
Principal axes 298
Projection operator 210
Propagator 271
Quadratic forms 274
Quadratic forms, diagonalization of 274
Quantum oscillator 320
RADIANS 19
Radius of convergence 118
Rank of tensor 296
Rapidity 27
Ratio test for series 10 78
Real part 90
Reciprocal vectors 219
Recursion relation 319
Recursion relation for Bessel functions 327
Recursion relation for Hermite polynomials 322
Recursion relation for quantum oscillator 322
Removable singularity 113
Residue 112
Residue Theorem (Cauchy) 132 134
Right-hand rule 154
Right-handed coordinates 151
Roots in complex plane 122
Rotation matrix 208
Row vector 206
Saddle point 54
Saddle point of quadratic forms 274 276
Scalar field 158
Scalar field, gradient of 167
Scalar potential 201
Scalar triple product 155 (see also “Box”)
Scale factor 65
Schwarz inequality 246
Screened Poisson equation 345
Screw rule 156
Second Order ODE 318
Separation of variables 329
Series 75
Series, absolute convergence 80 117
Series, comparison test 77
Series, conditional convergence 80
Series, geometric 76
Series, in complex variable 117
Series, integral test 78
Series, ratio test 78
Series, tests for convergence 77
Simultaneous equations 212
Singularities 111
Solid angle 68 70
Space-time interval 26
Spherical coordinates 66
Spin 265
State vector 269
Stationary point 53
Stationary point, and quadratic forms 274
Stationary point, with constraints 55
Steady state response 104
Stokes’ Theorem 179
String 289
String, normal modes of 289
String, separation of variables for 329
Superposition principle 100 195 306
Surface integral 159 162 164
Surface term in integrals 42
Taylor series, and essential singularities 83 141
Taylor series, in a complex variable 139
Taylor series, single variable 8 10
Taylor series, two variables 52
Tensors 294
Tensors, antisymmetric tensor 297
Tensors, conductivity 296
Tensors, contraction 296
Tensors, moment of inertia 298
Tensors, outer product 297
Tensors, polarizability 299
Tensors, rank of 296
Time derivatives of vectors 156
torque 154
Trace of matrix 227
Transients 103
Transpose of a product 220
Transpose of matrix 215
Triangle inequality 246
Trigonometric functions, and hyperbolic functions 121
Trigonometric functions, in x 19
Trigonometric functions, in z 115
Trigonometric functions, power series for 22
Uncertainty principle 288
Unit matrix 209
Unit vector 149
Unitary matrix 221
Unitary operators 260
vector calculus 149
Vector calculus, applications to electrodynamics 193 (see also “Electrodynamics”)
Vector calculus, conservative field 162
Vector calculus, curl of vector field 172
Vector calculus, digression on integral theorems 190
Vector calculus, digression on vector identities 190
Vector calculus, divergence of vector field 182
Vector calculus, gradient of scalar field 167
Vector calculus, Green’s theorem 174
Vector calculus, higher derivatives 189
Vector calculus, integral theorems in 188
Vector calculus, Laplacian 192
Vector calculus, line and surface integrals 159
Vector calculus, potential of conservative field 175
Vector calculus, Stokes’ theorem 179
Vector calculus, vector analysis review 149
Vector field 158
Vector field, circulation of 172
Vector field, curl of 172
Vector field, divergence of 182
Vector field, Gauss’s Law for 184
Vector field, Green’s Theorem for 174
Vector field, line integral of 159
Vector field, Stokes’ Theorem for 179
Vector field, surface integral of 162
Vector potential 201
Vectors, cross product for 153
Vectors, dot product for 151
Vectors, in polar coordinates 157
Vectors, introduction 149
Vectors, time derivative of 154
Velocity vector 156
Wave equation 200
Wave equation, circular drum 332
Wave equation, d= 1, 2 329
Wave equation, separation of variables 329
Wave equation, square drum 328
Zero matrix 209
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