Mathematical Methods for Physicists: A concise introduction - Site Map

INDEX
curvilinear coordinates, 27
damped oscillations, 80
De Moivre's formula, 237
del, 22
formulas involving del, 27
delta function, Dirac, 183
Fourier integral, 183
Green's function and, 192
point source, 193
determinants, 538±547
di€erential equations, 62
®rst order, 63
exact 67
integrating factors, 69
separable variables 63
homogeneous, 63
numerical solutions, 469
second order, constant coecients, 72
complementary functions, 74
Frobenius and Fuchs theorem, 86
particular integrals, 77
singular points, 86
solution in power series, 85
direct product
matrices, 139
tensors, 50
direction angles and direction cosines, 3
divergence
cartesian, 22
curvilinear, 30
cylindrical, 33
spherical polar, 35
dot product of vectors, 5
dual vectors and dual spaces, 211
eigenvalues and eigenfunctions of Sturm±
Liouville equations, 340
hermitian matrices, 124
orthogonality, 129
real, 128
an operator, 217
entire functions, 247
Euler's linear equation, 83
Fourier series, 144
convergence and Dirichlet conditions, 150
di€erentiation, 157
Euler±Fourier formulas, 145
exponential form of Fourier series, 156
Gibbs phenomenon, 150
half-range Fourier series, 151
integration, 157
interval, change of, 152
orthogonality, 162
Parseval's identity, 153
vibrtating strings, 157
Fourier transform, 164
convolution theorem, 188
delta function derivation, 183
Fourier integral, 164
Fourier series (contd)
Fourier sine and cosine transforms, 172
Green's function method, 192
head conduction, 179
Heisenberg's uncertainty principle, 173
Parseval's identity, 186
solution of integral equation, 421
transform of derivatives, 190
wave packets and group velocity, 174
Fredholm integral equation, 413 see also integral
equations
Frobenius' method see series solution of
di€erential equations
Frobenius±Fuch's theorem, 86
function
analytic,
entire,
harmonic, 247
function spaces, 226
gamma function, 94
gauge transformation, 411
Gauss' law, 391
Gauss' theorem, 37
generating function, for
associated Laguerre polynomials, 320
Bessel functions, 330
Hermite polynomials, 314
Laguerre polynomials, 317
Legendre polynomials, 301
Gibbs phenomenon, 150
gradient
cartesian, 20
curvilinear, 29
cylindrical, 33
spherical polar, 35
Gram±Schmidt orthogonalization, 209
Green's functions, 192,
construction of
one dimension, 192
three dimensions, 405
delta function, 193
Green's theorem, 43
in the plane, 44
group theory, 430
conjugate clsses, 440
cosets, 439
cyclic group, 433
rotation matrix, 234, 252
special unitary group, SU(2), 232
de®nitions, 430
dihedral groups, 446
generator, 451
homomorphism, 436
irreducible representations, 442
isomorphism, 435
multiplication table, 434
Lorentz group, 454
permutation group, 438
orthogonal group SO(3)
552