Mathematical Physics Vol 1

480

INDEX

complete integral, 342 complete solution, 342, 350, 352, 353, 385 completeness of functions, 265 complex field, 93 condition of integrability, 349 conditions Dirichlet, 312 conservative field, 163 continuity, 40 necessary and sufficient condition, 41 vector function, 41 contour problem first, 373 second, 373 third, 373 contravariant tensor of the first order, 212 convergence, 40 mean, 266 mean-square, 266 radius, 225 with respect to norm, 265 convolution, 357 coordinate line, 109, 110 surface, 109, 110 coordinate system, 110 Cartesian, 110 orthogonal, 110, 113 rectangular, 110 coordinates bipolar-bispherical, 117 bipolar-planar, 117 Cartesian, 108, 110, 112, 114 contravariant, 111 covariant, 111

spheroidal-a, 118 toroidal, 118

cosine integral, 254 covariant tensor

of the first order, 213

curve torsion, 74

definite integral

vector function, 47

deformable body, 17 delta operator, 88 delta symbol, 24 derivative

directional, 80, 81, 84 in the direction of tangent, 85 of higher order, 44

determinant

functional, 200

differential

of higher order, 44 vector, 43 vector function, 43–45 Bessel, 227, 231, 234, 241 Legendre, 227, 228 Legendre’s solution, 230 of the vibrating string, 337 partial, 334 solution, 334

differential equation

differential equations classification, 359 partial, 333 formation, 335 series solutions, 227 Dirichlet problem, 373

for a circle, 375 for a sphere, 377

curvilinear, 110 cylindrical, 114 ellipsoid, 116 ellipsoidal, 116 elliptical, 118 elliptical-cylindrical, 116 generalized, 108, 110, 112, 113 orthogonal, 113 parabolical-cylindrical, 115

distributivity

vector product, 58

divergence, 113

element

of arc, 111 of volume, 111, 113

elliptic integrals, 257 incomplete, 258

paraboloid, 116 rectilinear, 110 spherical, 115 spheroid, 116

of the first kind, 258 of the second kind, 258 of the third kind, 258