Index
983
Extremal function, 95
Extremal function theorem of complete
functional, 176
Extremal theorem of function of one variable, 2
Extremal theorem of function of several
variables, 4
Extremal theorem of function of two variables, 3
Extremal (value), 97
Extreme (value), 97
Extremum (value), 97
F
Family of admissible curves, 95
Family of admissible surfaces, 95
Family of extremal curves, 115
Family of sets, 385
Faraday law of electromagnetic induction,
630
Fermat(’s) principle, 254
Field, 8, 203
Field of force, 522
Field without source, 17
Finding limit under the integral sign, 5
Finite constraint, 320, 515
Finite element, 460
Finite set, 385
First boundary value problem for the
Laplace(’s) equation, 430
First boundary value problem for the
Poisson(’s) equation, 430
First boundary value problem of elliptic
equation, 430
First eigenvalue, 490
First Erdmann corner condition, 297
First fundamental differential form, 375
First fundamental form, 375
First integral, 127
First invariant, 66
First kind of fundamental quantity, 375
First Maxwell(’s) equation, 630
First order distance, 93
First order tensor, 60
First variation, 104, 229
First variation of total potential energy, 538
Fixed boundary variational problem, 95
Fixed constraint, 515
Fixed end point variational problem, 95
Flat order operator, 695
Flux, 16, 22
Force field, 522
Force of constraint, 515
Forcing boundary condition, 245
Forcing function, 419
Forth Maxwell(’s) equation, 630
Fourier coefficient, 403
Fourier coefficient set, 403
Fourier series, 403
Fredholm integral equation of the first kind,
198, 800
Fredholm integral equation of the second
kind, 144
Fredholm integral equation of the third kind,
145
Free boundary, 96
Free boundary condition, 96
Free index, 53
Free particle system, 514
Free system, 514
Free term, 404
Friedrichs first inequality, 439
Friedrichs inequality, 439
Friedrichs second inequality, 439
Frontier point, 391
Full energy functional, 696
Function, 8, 387, 404
Functional, 90, 404
Functional determinant, 322
Functional form, 101
Functional of energy, 384
Functional of integral type, 90
Functional of mixed type, 344, 588
Functional variable, 91
Functional with integral, 90
Function class, 90
Function class of continuousn-th derivative
in a closed interval [x 0 ,x 1 ], 90
Function class of continuous n-th derivative
in an open interval (x 0 ,x 1 ), 90
Function space, 389
Fundamental quantity of the first kind, 375
Fundamental sequence, 390
Fundamental set, 386, 389
G
Galerkin coefficient, 474
Galerkin method, 472
Galerkin(’s) equations, 474
Gas particle equation of motion, 634
Gauss formula, 20, 27, 38, 531
Gaussian differential equation, 423
Gauss-Ostrogradsky theorem, 20
Gauss theorem, 20
983
Extremal function, 95
Extremal function theorem of complete
functional, 176
Extremal theorem of function of one variable, 2
Extremal theorem of function of several
variables, 4
Extremal theorem of function of two variables, 3
Extremal (value), 97
Extreme (value), 97
Extremum (value), 97
F
Family of admissible curves, 95
Family of admissible surfaces, 95
Family of extremal curves, 115
Family of sets, 385
Faraday law of electromagnetic induction,
630
Fermat(’s) principle, 254
Field, 8, 203
Field of force, 522
Field without source, 17
Finding limit under the integral sign, 5
Finite constraint, 320, 515
Finite element, 460
Finite set, 385
First boundary value problem for the
Laplace(’s) equation, 430
First boundary value problem for the
Poisson(’s) equation, 430
First boundary value problem of elliptic
equation, 430
First eigenvalue, 490
First Erdmann corner condition, 297
First fundamental differential form, 375
First fundamental form, 375
First integral, 127
First invariant, 66
First kind of fundamental quantity, 375
First Maxwell(’s) equation, 630
First order distance, 93
First order tensor, 60
First variation, 104, 229
First variation of total potential energy, 538
Fixed boundary variational problem, 95
Fixed constraint, 515
Fixed end point variational problem, 95
Flat order operator, 695
Flux, 16, 22
Force field, 522
Force of constraint, 515
Forcing boundary condition, 245
Forcing function, 419
Forth Maxwell(’s) equation, 630
Fourier coefficient, 403
Fourier coefficient set, 403
Fourier series, 403
Fredholm integral equation of the first kind,
198, 800
Fredholm integral equation of the second
kind, 144
Fredholm integral equation of the third kind,
145
Free boundary, 96
Free boundary condition, 96
Free index, 53
Free particle system, 514
Free system, 514
Free term, 404
Friedrichs first inequality, 439
Friedrichs inequality, 439
Friedrichs second inequality, 439
Frontier point, 391
Full energy functional, 696
Function, 8, 387, 404
Functional, 90, 404
Functional determinant, 322
Functional form, 101
Functional of energy, 384
Functional of integral type, 90
Functional of mixed type, 344, 588
Functional variable, 91
Functional with integral, 90
Function class, 90
Function class of continuousn-th derivative
in a closed interval [x 0 ,x 1 ], 90
Function class of continuous n-th derivative
in an open interval (x 0 ,x 1 ), 90
Function space, 389
Fundamental quantity of the first kind, 375
Fundamental sequence, 390
Fundamental set, 386, 389
G
Galerkin coefficient, 474
Galerkin method, 472
Galerkin(’s) equations, 474
Gas particle equation of motion, 634
Gauss formula, 20, 27, 38, 531
Gaussian differential equation, 423
Gauss-Ostrogradsky theorem, 20
Gauss theorem, 20