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| Bamberg P.G., Sternberg Sh. — A Course in Mathematics for Students of Physics: Volume 1 |
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| Предметный указатель |
Absolute double integrals 281
Absolute line integral 265
Addition of velocities, law of 155
Adjoint transformation 374—377
Affine coordinate function 15
Affine geometry 18
Affine plane 1
Affine space, axioms for 9
Affine transformation 17
Affine transformations as  matrices 50
Annihilator 356
Arc length 265
Areas and determinants 26
Basis 39 348
Basis, change of 41
Beats 141
Big “oh”, little “oh” 178
Bijective 14
Bilinear 123 272
Born expansion 194
Cartan xiii
Cayley — Hamilton theorem 61
Chain rule 184
Change of basis matrix 41 349
Characteristic equation 59
Characteristic polynomial 59
Closed forms 262
Cofactor matrix 398
Collision 161
Column reduction 367
composition 15
Conditional probability 67
Conformal linear transformation 57
Conjugate planes 318
Conservation of energy 161
Conservation of energy momentum 165
Conservation of momentum 161
Constant rank theorem 368
Coordinate function 15
Coupled oscillators 138
Critically damped oscillator 105
De Moivre’s Theorem 58
Determinant 30 388—399
Determinant, axioms for 389—390
Differentiable 180
Differential form, linear 199 247—261
Differential of a map 180
DIMENSION 347
Directional derivatives 205—209
Dual basis 350—352
Dual space 342—343
Ehrenfest model 78
Eigenvalue 59
Eigenvector 59
Eikonal 324
Elastic collision 161
Energy momentum vector 165
Euclidean scalar product 120—124
Euclidean transformation 16
Exact forms 250
Exponential of a matrix 83
Exponential series 82
Extending a basis 349
Exterior derivative 275 276 305
Exterior product 275
Fermat’s principle 326—328
Fibonacci sequence 80
Focal length 319
Force field 248
Forced oscillator 108
Formal power series 82
Forward region 151
Fundamental theorem of affine geometry 43
Fundamental theorem of projective geometry 54
Galilean transformation 160
Gauss decomposition 322
Gibbs xii
Gram — Schmidt process 124—131
Grassmann xiii
Green’s Theorem 298—303
hessian 225
Image 37 358
Image, finding a basis of 367
Implicit function theorem 238
Inelastic collision 161
Injective 13
Inverse function theorem 230—237
Inverse of a matrix 32 33
Isomorphism 40
Kepler motion 195
Kernel 37 358
Kernel, finding a basis of 367
Lagrange multipliers 227—229
Laplace’s equation 227
Laplacian 227
| Law of Cosines 124
Light cone 152
Line integrals 250—264
Linear dependence 7 34
Linear differential form 199 247—261
Linear independence 7 34 53
Linear optics 328—335
Linear transformation 18 20
Lines, parametrization of 3 4
Lorentz transformation 152
MAP 13
Markov process 66
Mass 161—163
Matrix addition 24
Matrix multiplication 22 25 26
Matrix of a linear transformation 21
Matrix of a rotation 22
Mean value theorem 219—222
Momentum in Newtonian mechanics 163
Momentum in special relativity 165
Morse index theorem 328
Newton’s method 231
Nilpotent matrix 38 39
Non-singular 20
Normal forms for matrices 60 62 63
Normal modes 137—148
Normal modes as waves 145
Null cone 152
One-dimensional vector space 10
Optical length 325
Orientation 31 285—289
Orthogonal projection 130
Orthonormal basis 127
Oscillator 103—112
Overdamped oscillator 106
Perspective 51
Phase portrait 95—103
Phase shift 112
Picard’s method 233
Piecewise differentiable path 251
Poincare’ transformation 154
Point characteristic 324
Positive definite 123
Principal planes 322
probability 66 67
Projection 38
Projective plane 53
Proper Lorentz transformation 152
Pullback 209—213 289—295
Quadratic form 133
Quotient space 354
Rank-nullity theorem 358
Regular 20
Resonance 112 141
Response curve 112
Rest mass 165
Reverse triangle inequality 157
Riemann xv
Row reduction 360—368
Saddle point 135
Scalar product, axioms for 123 131
Simultaneity 154
Singular linear transformation 20
Snell’s law 313
Snell’s law, linearized version 317 318
Solution set theorem 371
Spacetime 149
Special relativity 148—166
Star shaped 261—262
Steady state solution 110
Stochastic matrix 71
subspace 343—344
Surjective 14
Symmetric matrix 133
Symplectic group 167
Symplectic linear transformation 167
Symplectic scalar product 167
Tangent space 208
Taylor’s Formula 222—225
Thin lens 318
Thin lens, matrix of 319
Time, Newton’s concept of 11—13
Trace of a matrix 38
Transition probability 68
Translation 18
TRANSPOSE 133
Twin paradox 157
Two forms in  277
Two forms in  296
Undamped oscillator 104
Underdamped oscillator 105
Variation of parameters 109
Vector space 7 341—342
Vector space, axioms for 8
Velocity transformation 160
Wedge product 275
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