Bamberg P.G., Sternberg S. — A Course in Mathematics for Students of Physics, Vol. 1 :: Электронная библиотека попечительского совета мехмата МГУ

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Bamberg P.G., Sternberg S. — A Course in Mathematics for Students of Physics, Vol. 1

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Название: A Course in Mathematics for Students of Physics, Vol. 1

Авторы: Bamberg P.G., Sternberg S.

Аннотация:

After the basic theories of differential and integral calculus are explained, they are applied to interesting problems in optics, electronics (networks), electrostatics, wave dynamics and finally, to classical thermodynamics.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 399

Добавлена в каталог: 29.03.2008

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Предметный указатель

Absolute double integrals      281
Absolute line integral      265
Addition of velocities, law of      155
Adjoint transformation      374-7
Affine coordinate function      15
Affine geometry      18
Affine plane      1
Affine space, axioms for      9
Affine transformation      17
Affine transformations as 3 $\times$ 3 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      30 388-99
Determinant, axioms for      389-390
Differentiable      180
Differential form, linear      199 247-61
Differential of a map      180
DIMENSION      347
Directional derivatives      205-9
Dual basis      350-2
Dual space      342-3
Ehrenfest model      78
Eigenvalue      59
Eigenvector      59
Eikonal      324
Elastic collision      161
Energy momentum vector      165
Euclidean scalar product      120-4
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      326-8
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      230-7
Inverse of a matrix      32 33
Isomorphism      40
Kepler motion      195
Kernel      37 358
Kernel, finding a basis of      367
Lagrange multipliers      227-9
Laplace's equation      227
Laplacian      227

Law of Cosines      124
Light cone      152
Line integrals      250-64
Linear dependence      7 34
Linear differential form      199 247-61
Linear independence      7 34 53
Linear optics      328-35
Linear transformation      18 20
Lines, parametrization of      3 4
Lorentz transformation      152
MAP      13
Markov process      66
Mass      161-3
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      137-48
Normal modes as waves      145
Null cone      152
One-dimensional vector space      10
Optical length      325
Orientation      31 285-9
Orthogonal projection      130
Orthonormal basis      127
Oscillator      103-12
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      209-13 289-95
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      360-8
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      148-66
Star shaped      261-2
Steady state solution      110
Stochastic matrix      71
subspace      343-4
Surjective      14
Symmetric matrix      133
Symplectic group      167
Symplectic linear transformation      167
Symplectic scalar product      167
Tangent space      208
Taylor's formula      222-5
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 $\mathbb{R}^{2}$       277
Two forms in $\mathbb{R}^{3}$       296
Undamped oscillator      104
Underdamped oscillator      105
Variation of parameters      109
Vector space      7 341-2
Vector space, axioms for      8
Velocity transformation      160
Wedge product      275

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