986
Index
L
Lagrange density function, 549
Lagrange function, 101, 549, 566
Lagrange function density, 549
Lagrange multiplier, 287, 320
Lagrange principle, 597
Lagrange principle of least action, 597
Lagrange problem, 326, 345
Lagrange(’s) action, 596
Lagrange(’s) equation, 485
Lagrange(’s) equations for conservative
system, 554
Lagrange’s remainder, 2
Lagrange theorem, 320, 326
Lagrange transformation, 112
Lagrangian density function, 549
Lagrangian form of D’Alembert’s principle,
547
Lagrangian function, 101, 549, 566
Lagrngian function density, 549
Laplace operator, 19, 32
Laplace(’s) equation, 32, 167, 430, 641
Laplace(’s) integral, 337
Laplacian, 19, 32
Law of reflection of light, 300
Law of refraction of light, 302
Least drag problem on gas flow, 138
Least square method, 489
Least upper bound, 386
Left adjoint operator, 408, 409
Left and right mixed self-adjoint operator,
409
Left and right mixed self-conjugate operator,
409
Left conjugate operator, 408, 409
Left hamiltonian operator train, 706
Left self-adjoint operator, 408, 409
Left self-conjugate operator, 408, 409
Legendre condition, 115, 216
Legendre strong condition, 216
Leibniz formula, 6
Length of vector, 8
Limit, 389
Linear combination, 400
Linear correlation, 400
Linear dependence, 400
Linear differential operator, 412
Linear functional, 103, 405
Linear independence, 400
Linearity, 394
Linearization of a functional, 104
Linear kinematic constraint, 515
Linearly independent, 400
Linear normal space, 393
Linear operation, 392
Linear operator, 405
Linear operator bounded below, 407
Linear operator space, 407
Linear set, 386
Linear space, 389, 392
Linear space structure, 389, 392
l ∞ -norm, 394
Lipschitz boundary, 437
Lipschitz condition, 438
Lipschitz continuous, 438
Lipschitzian, 437
Local extremum, 97
Local maximum, 97
Local minimum, 97
l 1 -norm, 394
Lorentz condition, 631
Lower bound, 385
l 2 -norm, 394
l p -norm, 394
M
Major arc, 128
Map, 387
Mapping, 387, 404
Mass-energy relation, 599
Mass point, 514
Maupertuis-Lagrange principle of least
action, 596
Maupertuis(’) principle, 596
Maupertuis(’) principle of least action, 596
Maximizing sequence, 457
Maximum norm, 394
Maxwell-Ampère circulation law, 630
Maxwell(’s) equations, 630, 631
Mayer problem, 345
Mean curvature, 351
Mechanical principle, 513
Mechanical system, 514
Mechanics principle, 513
Meet, 385
Member, 384
Membrane contact problem, 291
Method of least squares, 489
Method of variation, 85
Metric, 389
Metric axioms, 389
Metric space, 389
Metric subspace, 389
Metric tensor, 375
Minimal eigenvalue, 490
Index
L
Lagrange density function, 549
Lagrange function, 101, 549, 566
Lagrange function density, 549
Lagrange multiplier, 287, 320
Lagrange principle, 597
Lagrange principle of least action, 597
Lagrange problem, 326, 345
Lagrange(’s) action, 596
Lagrange(’s) equation, 485
Lagrange(’s) equations for conservative
system, 554
Lagrange’s remainder, 2
Lagrange theorem, 320, 326
Lagrange transformation, 112
Lagrangian density function, 549
Lagrangian form of D’Alembert’s principle,
547
Lagrangian function, 101, 549, 566
Lagrngian function density, 549
Laplace operator, 19, 32
Laplace(’s) equation, 32, 167, 430, 641
Laplace(’s) integral, 337
Laplacian, 19, 32
Law of reflection of light, 300
Law of refraction of light, 302
Least drag problem on gas flow, 138
Least square method, 489
Least upper bound, 386
Left adjoint operator, 408, 409
Left and right mixed self-adjoint operator,
409
Left and right mixed self-conjugate operator,
409
Left conjugate operator, 408, 409
Left hamiltonian operator train, 706
Left self-adjoint operator, 408, 409
Left self-conjugate operator, 408, 409
Legendre condition, 115, 216
Legendre strong condition, 216
Leibniz formula, 6
Length of vector, 8
Limit, 389
Linear combination, 400
Linear correlation, 400
Linear dependence, 400
Linear differential operator, 412
Linear functional, 103, 405
Linear independence, 400
Linearity, 394
Linearization of a functional, 104
Linear kinematic constraint, 515
Linearly independent, 400
Linear normal space, 393
Linear operation, 392
Linear operator, 405
Linear operator bounded below, 407
Linear operator space, 407
Linear set, 386
Linear space, 389, 392
Linear space structure, 389, 392
l ∞ -norm, 394
Lipschitz boundary, 437
Lipschitz condition, 438
Lipschitz continuous, 438
Lipschitzian, 437
Local extremum, 97
Local maximum, 97
Local minimum, 97
l 1 -norm, 394
Lorentz condition, 631
Lower bound, 385
l 2 -norm, 394
l p -norm, 394
M
Major arc, 128
Map, 387
Mapping, 387, 404
Mass-energy relation, 599
Mass point, 514
Maupertuis-Lagrange principle of least
action, 596
Maupertuis(’) principle, 596
Maupertuis(’) principle of least action, 596
Maximizing sequence, 457
Maximum norm, 394
Maxwell-Ampère circulation law, 630
Maxwell(’s) equations, 630, 631
Mayer problem, 345
Mean curvature, 351
Mechanical principle, 513
Mechanical system, 514
Mechanics principle, 513
Meet, 385
Member, 384
Membrane contact problem, 291
Method of least squares, 489
Method of variation, 85
Metric, 389
Metric axioms, 389
Metric space, 389
Metric subspace, 389
Metric tensor, 375
Minimal eigenvalue, 490