990
Index
Slope, 201
Slope function, 201
Smallest eigenvalue, 490
Solenoidal field, 17
Solution of a variational problem, 95
Source-free field, 17
Space, 389
Space structure, 389
Special isoperimetric problem, 333
Specific strain energy, 519
Specific work, 519
Spectrum, 490
Spectrum of operator equation, 490
Sphere, 391
Spherical center, 391
Spherical surface, 391
Square-summable sequence space, 393
Stationary curve, 115
Stationary function, 115
Stationary value, 115
Steady constraint, 515
Stokes formula, 36, 39
Stokes theorem, 36
Strain energy, 519, 521
Strain energy density, 519
Strain tensor, 517
Strengthened Legendre condition, 216
Stress boundary, 529
Stress energy density, 544
Strong δ neighborhood, 93
Strong extremum, 97
Strong maximum, 97
Strong minimum, 97
Strong neighborhood, 93
Strong relative maximum, 97
Strong relative minimum, 97
Strong variation, 98
Sturm-Liouville second order differential
equation, 422
Sturm-Liouville 2 n-th order differential
equation, 422
Subset, 386
Subspace, 389
Substitution operator, 53
Substitution tensor, 53
Sum norm, 394
Superior arc, 128
Supremum, 386
Surface function, 91
Surjection, 387
Surjective, 387
Surmorphism, 387
Symmetric(al) tensor of (the) second order,
61
Symmetric bilinear functional, 104
Symmetric operator, 409
Symmetry, 389
System, 514
System of elasticity, 516
System of Euler equations, 177
System of free particles, 514
System of particles, 514
System of unfree particles, 514
T
Taking limit under the integral sign, 5
Tautochrone (curve), 136
Tayler series expansion, 1
Taylor formula, 1
Taylor mean value theorem, 1
Taylor mean value theorem of function of
several variables, 3
Taylor mean value theorem of function of
two variables, 2
Taylor theorem, 1
Telegraph equation, 632
Tensor decomposition theorem, 62
Tensor field, 8
Tensor function, 8
Tensor of second order, 61
Tensor recognition theorem, 65
Third boundary value problem for the
Laplace(’s) equation, 430
Third boundary value problem for the
Poisson(’s) equation, 430
Third boundary value problem of elliptic
equation, 430
Third invariant, 66
Third Maxwell(’s) equation, 630
Three-dimensional Laplace operator, 412
Three-dimensional Laplace(’s) equation, 32
Three-dimensional Laplacian operator, 412
Topological space, 389
Topological structure, 389
Total complementary energy, 546
Total complementary energy functional, 587
Total energy functional, 696
Total kinetic energy, 548
Total potential energy, 556
Total potential energy functional, 697
Total potential energy of an elastic body, 537
Total set, 386
Total variation, 99, 101, 243
Total variation notation, 99
Index
Slope, 201
Slope function, 201
Smallest eigenvalue, 490
Solenoidal field, 17
Solution of a variational problem, 95
Source-free field, 17
Space, 389
Space structure, 389
Special isoperimetric problem, 333
Specific strain energy, 519
Specific work, 519
Spectrum, 490
Spectrum of operator equation, 490
Sphere, 391
Spherical center, 391
Spherical surface, 391
Square-summable sequence space, 393
Stationary curve, 115
Stationary function, 115
Stationary value, 115
Steady constraint, 515
Stokes formula, 36, 39
Stokes theorem, 36
Strain energy, 519, 521
Strain energy density, 519
Strain tensor, 517
Strengthened Legendre condition, 216
Stress boundary, 529
Stress energy density, 544
Strong δ neighborhood, 93
Strong extremum, 97
Strong maximum, 97
Strong minimum, 97
Strong neighborhood, 93
Strong relative maximum, 97
Strong relative minimum, 97
Strong variation, 98
Sturm-Liouville second order differential
equation, 422
Sturm-Liouville 2 n-th order differential
equation, 422
Subset, 386
Subspace, 389
Substitution operator, 53
Substitution tensor, 53
Sum norm, 394
Superior arc, 128
Supremum, 386
Surface function, 91
Surjection, 387
Surjective, 387
Surmorphism, 387
Symmetric(al) tensor of (the) second order,
61
Symmetric bilinear functional, 104
Symmetric operator, 409
Symmetry, 389
System, 514
System of elasticity, 516
System of Euler equations, 177
System of free particles, 514
System of particles, 514
System of unfree particles, 514
T
Taking limit under the integral sign, 5
Tautochrone (curve), 136
Tayler series expansion, 1
Taylor formula, 1
Taylor mean value theorem, 1
Taylor mean value theorem of function of
several variables, 3
Taylor mean value theorem of function of
two variables, 2
Taylor theorem, 1
Telegraph equation, 632
Tensor decomposition theorem, 62
Tensor field, 8
Tensor function, 8
Tensor of second order, 61
Tensor recognition theorem, 65
Third boundary value problem for the
Laplace(’s) equation, 430
Third boundary value problem for the
Poisson(’s) equation, 430
Third boundary value problem of elliptic
equation, 430
Third invariant, 66
Third Maxwell(’s) equation, 630
Three-dimensional Laplace operator, 412
Three-dimensional Laplace(’s) equation, 32
Three-dimensional Laplacian operator, 412
Topological space, 389
Topological structure, 389
Total complementary energy, 546
Total complementary energy functional, 587
Total energy functional, 696
Total kinetic energy, 548
Total potential energy, 556
Total potential energy functional, 697
Total potential energy of an elastic body, 537
Total set, 386
Total variation, 99, 101, 243
Total variation notation, 99