Mathematical Physics Vol 1

483

INDEX

Mittag-Leffler function, 255 with four parameters, 256 three parameters, 255 two-parameter, 255 mixed contour problem, 373 mixed integral, 342 mixed product geometric interpretation, 63 mixed solution, 342 modulus of the elliptic integral, 304

partial derivative, 44

of a vector function, 44 partial differential equations elliptic type, 359 homogeneous linear, 356 hyperbolic, 359 linear second order, 355 of second order classification, 357 parabolic, 359 partial gradient, 86 partial sum, 223 particular solution, 342 period fundamental, 308 non-fundamental, 308 Pfaffian equation, 347 Pochhammer symbol, 256

moment of force, 25 Monge notation, 335

nabla operator

properties, 87 natural trihedron, 73 Neumann problem, 373

Newton’s potential, 103 nonorientable surface, 51 norm, 33, 264 normal main, 73, 74 normal elliptic integral of the first kind, 304 notation Monge, 335 one-sided surface, 51 operator delta, 88 Hamilton, 87

point coordinates, 14 Poisson bracket, 353 Poisson integral, 377 poluprecˇnik krivine, 75 polynomial Hermit, 243 Laguerre, 244

Legendre, 228, 230, 231, 266, 271

potential, 107

logarithmic, 104 Newton’s, 103, 104 of force, 103

scalar, 108 vector, 108 primitive function, 47, 48 principal function, 267 principal value, 267 principle of superposition, 241 problem Dirichlet, 373 Neumann in a plane, 379 Sturm–Liouville, 266 product mixed, 26 vector, 24, 25 projection, 20, 21 normal, 20, 21

inverse, 35 Laplace, 88 linear, 34, 35, 86 nabla, 87 properties, 87 nonsingular, 35

orientation

curve, 48 of a closed curve, 49 of a surface, 51

oriented curve

partition, 49 origin of the coordinate system, 14 orthogonal basis, 36

orthonormalized basis, 37 oscillatory movement, 299

of a point on a plane, 21 of a vector on a plane, 21

Parseval’s identity, 321