980
Index
Boundary, 391
Boundary condition, 96
Boundary inner product, 473
Boundary method, 473
Boundary point, 391
Boundary residual, 472
Boundary weighted function, 473
Bounded below linear operator, 407
Bounded below operator, 492
Bounded linear functional, 406
Bounded linear operator, 406
Bounded linear operator space, 407
Bounded operator, 405
Bounded set, 391
Brachistochrone problem, 86, 134
Broken curve, 295
Broken extremal curve, 295
Broken line, 295
Broken point, 295
Bubnov-Galerkin method, 472
Bunjakovski inequality, 48
C
Calculus of variations, 85
Canonical equations, 582
Canonical form, 581
Capillarity, 349
Capillary phenomena, 349
Capillary tube, 349
Capillary tube problem, 349
Cartesian base (basis), 52
Cartesian first order tensor, 60
Cartesian product, 387
Cartesian second order tensor, 60
Cartesian space, 387
Catenary equation, 138, 340
Catenoid, 138
Cauchy equations, 517, 528
Cauchy inequality, 71, 74
Cauchy-Schwarz inequality, 396
Cauchy sequence, 390
Center, 201
Center of a ball, 391
Center of sphere, 391
Central curve field, 202
Central field of extremal curves, 203
Characteristic direction, 65
Characteristic element, 490
Characteristic equation, 490
Characteristic function, 490
Characteristic value, 65, 490, 852
Characteristic value problem, 490
Characteristic vector, 490
Chebyshev equation, 423
Chord oscillation equation, 555
Circulation, 29
Circulation surface density, 29
Clairaut theorem, 186
Class function, 90
Classical theory in the calculus of variations,
214, 455
Classical variational methods, 214, 455
Class of admissible curves, 95
Class of admissible surfaces, 95
Class of functions, 90
Class of sets, 385
Closed ball, 391
Closed domain, 400
Closed set, 392
Closure, 392
Cluster point, 391
Coefficient of transformation, 58
Collection of sets, 385
Comma convention, 57
Comparison curve, 110
Compatibility condition, 518
Compatibility equation, 518
Complementary energy, 544
Complementary energy density, 544
Complementary energy density function,
544
Complementary set, 386
Complementary strain energy, 521, 544
Complementary strain energy density, 544
Complementary virtual energy, 546
Complementary virtual strain energy, 521,
544
Complementary virtual work, 544
Complete, 391
Complete functional, 172
Complete inner product, 613
Complete inner product space, 397
Completely generalized variational principle, 384
Complete metric space, 390
Complete normed linear space, 394
Complete set, 392
Complete space, 391
Complete system of Euler equations, 177
Complex inner product space, 394
Complex linear space, 392
Component, 60, 386
Composite mapping, 388
Conditional extremum, 319
Conditional extremum problem, 88
Index
Boundary, 391
Boundary condition, 96
Boundary inner product, 473
Boundary method, 473
Boundary point, 391
Boundary residual, 472
Boundary weighted function, 473
Bounded below linear operator, 407
Bounded below operator, 492
Bounded linear functional, 406
Bounded linear operator, 406
Bounded linear operator space, 407
Bounded operator, 405
Bounded set, 391
Brachistochrone problem, 86, 134
Broken curve, 295
Broken extremal curve, 295
Broken line, 295
Broken point, 295
Bubnov-Galerkin method, 472
Bunjakovski inequality, 48
C
Calculus of variations, 85
Canonical equations, 582
Canonical form, 581
Capillarity, 349
Capillary phenomena, 349
Capillary tube, 349
Capillary tube problem, 349
Cartesian base (basis), 52
Cartesian first order tensor, 60
Cartesian product, 387
Cartesian second order tensor, 60
Cartesian space, 387
Catenary equation, 138, 340
Catenoid, 138
Cauchy equations, 517, 528
Cauchy inequality, 71, 74
Cauchy-Schwarz inequality, 396
Cauchy sequence, 390
Center, 201
Center of a ball, 391
Center of sphere, 391
Central curve field, 202
Central field of extremal curves, 203
Characteristic direction, 65
Characteristic element, 490
Characteristic equation, 490
Characteristic function, 490
Characteristic value, 65, 490, 852
Characteristic value problem, 490
Characteristic vector, 490
Chebyshev equation, 423
Chord oscillation equation, 555
Circulation, 29
Circulation surface density, 29
Clairaut theorem, 186
Class function, 90
Classical theory in the calculus of variations,
214, 455
Classical variational methods, 214, 455
Class of admissible curves, 95
Class of admissible surfaces, 95
Class of functions, 90
Class of sets, 385
Closed ball, 391
Closed domain, 400
Closed set, 392
Closure, 392
Cluster point, 391
Coefficient of transformation, 58
Collection of sets, 385
Comma convention, 57
Comparison curve, 110
Compatibility condition, 518
Compatibility equation, 518
Complementary energy, 544
Complementary energy density, 544
Complementary energy density function,
544
Complementary set, 386
Complementary strain energy, 521, 544
Complementary strain energy density, 544
Complementary virtual energy, 546
Complementary virtual strain energy, 521,
544
Complementary virtual work, 544
Complete, 391
Complete functional, 172
Complete inner product, 613
Complete inner product space, 397
Completely generalized variational principle, 384
Complete metric space, 390
Complete normed linear space, 394
Complete set, 392
Complete space, 391
Complete system of Euler equations, 177
Complex inner product space, 394
Complex linear space, 392
Component, 60, 386
Composite mapping, 388
Conditional extremum, 319
Conditional extremum problem, 88