Principle of relativity, classical 31 703
Principle of stationary action 69ff
Principle of virtual work 18 345
Principle of virtual work and the principle of virtual power 18
Principle principle of virtual power 16ff 50
Principle stationary potential energy 190
Principle turning point 821
Principles, list of important 956
Probability of presence for particles 114
Production of entropy 435
Production of mass 423
Production of momentum 435
Projection operator 1766
Projection-iteration method 254
Propagation of action 81
Propagation velocity 100
Proper map I173ff 551
Proper time in general relativity 732
Proper time in special relativity 718
Pseudomonotone operators definition of see “Part II”
Pseudomonotone operators in elasticity 322ff
Pseudomonotone operators in hydrodynamics 481ff
Pseudosphere 660
Pseudotensor 628
Pseudotensor density 630
Pseudotensor dual 629
Pull-back 670
Pulsars 778
Quantization 98ff
Quantization general approach to see “Part V”
Quantization of classical mechanics in the sense of Heisenberg 78
Quantization of classical mechanics in the sense of Schroedinger 112
Quantization of the phase space 126
Quantum cosmology 750
Quantum of action 78 102 108 126 366 884
Quantum statistics (see also “Part V”
Quantum statistics, basic ideas of 401
Quantum statistics, Bose statistics 402 408
Quantum statistics, Fermi statistics 402 408
Quasars 778
Quasi-classical approximations in general relativity 735
Quasi-classical approximations in quantum mechanics 129
Quasi-concave 1456
Quasi-convex 1456
Quasi-eigen vector 869
Quasi-equilibrium states 372ff 374 379ff
Quasi-statical plastic material 257
Quasi-variational inequality 807
Radiation problem of Carleman 422ff
Rankine — Hugoniot jump condition in gas dynamics 444 (see also “PartV”)
Rayleigh number 508
Reaction probability 107
Reaction velocity 389
Red limit of the cosmos 778
Red shift and the expansion of the universe 57 742
Red shift in gravitational fields 766
Red shift in the spectrum of galaxies 57 742
Region 1758
Regular minimum 51
Regular point 552
Regular solution curve 819
Regular space I596 537
Regular state space 380
Regular value 552
Relatively compact set 1756
Relativity principle of Einstein 32 695
Relativity principle of Galilei 31 703
Representatives (local coordinates) of a cotangent vector 545
Representatives (local coordinates) of a map 537
Representatives (local coordinates) of a point of a manifold 534
Representatives (local coordinates) of a point of the tangent bundle 543
Representatives (local coordinates) of a tangent vector 539
Residual set 570 829
retract 150
Reversible process 381
Reynolds number 440 479 485 495 520
Ricci tensor 731
Riemannian manifold 651
Riemannian manifold proper 651
Riemannian manifold pseudo- 651
Rigid body 52ff 54
Ritz method 252
Rod equation 315ff
Rubberlike material of Ogden 208
Rutherford’s scattering formula 139
Saint Venant — Kirchhoffmaterial 208
Scalar curvature 731
Scales equilibrium of a pair of 14ff
Scales motion of a pair of 19ff
Scales stability of a pair of 14ff
Scattering of particles 106 138ff
Schauder estimates 460
Schrodinger equation 112ff
Schwarzschild solution 756
Section of a bundle 544
Section of a vector bundle 590
Sectorial operator see “Part II”
Semiflow 547
Semigroup see “Part II”
Sets, fundamental properties of 1893
Shell theory 325
Shift operator 847ff
Similarity in mathematical physics 439 484
Simple contra variant tensor 619
Simple covariant tensor 619
Simplicial algorithms 812
Simplicial methods 794ff
Simplicial methods basic ideas of 798
Singular homology groups 688 (see also “PartV”)
Singular perturbation problems 519
Singular point 552
Singular point, nondegenerate 561
Singular value 552
Sinking of a space ship 773
Sinusoidal waves 466ff
Skew-symmetric see “Antisymmetric”
Slow deformation processes 349
Small oscillations 96
Sobolev spaces see “Part II”
Solitary waves 466ff
Solitons 468ff
Spacelike events 715
Specific densities 442
Specific entropy 376
Specific heat capacity 376
Specific inner energy 376
Spectrum 1795
Spectrum does not surround the origin 849
Sperner simplex 798 814
Spherical waves 103
Spin 125
Spin and statistics 125
Splitting of spaces 1766 531 550
Splitting of spaces of maps 531
Stability basic ideas of 16 20
Stability dynamical (in the sense of Ljapunov) 20 842
Stability inelasticity 193 217
Stability of dynamical systems 841
Stability of equilibrium points 841
Stability of mechanical systems 16 50
Stability of orbits 852
Stability of periodic solutions 851
Stability of solutions of ordinary differential equations 841
Stability of the planetary system 42
Stability of thermodynamical states 389
Stability orbital 852
Stability principle in mechanics 16 50ff
Stability principle in mechanics, basic idea of the 16
Stable equilibrium dynamically 20 842
Stable equilibrium statically 16 50
| Star models classical 412
Star models relativistic 790
Star, death of a 777ff
State 371
State equation of 372 377 414
State equilibrium 373 387ff
State quasi-equilibrium 372ff 387ff
State strictly stable 193
State strongly stable 218 244
Statical 16 50
Stationary flow 438
Statistical physics (see also “Part V”)
Statistical physics classical 417 420
Statistical physics, basic ideas of 396ff
Statistical physics, Boltzmann statistics in 420
Statistical physics, Bose statistics in 402 408
Statistical physics, classification of states and 401
Statistical physics, Fermi statistics in 403 408
Statistical physics, ideal gas in 403ff
Statistical physics, photon gas in 408ff
Statistical physics, pure energy statistics in 402
Statistical physics, quasi-classical 417
Statistical potential 387 400
Statistical solution of the Navier — Stokes equations 522
Stefan — Boltzmann law 409ff 781
Stored energy function 165 190
Stored energy function dual 246 256 294
Stored energy function general structure of the 207
Strain tensor 165 770
Strain tensor linearized 170
Strain tensor, geometrical meaning of the 171ff
Strange Attractor 522 (see also “Part V”)
Stream line 454
Stress force 165 777 181
Stress tensor 165 177 181ff
Stress tensor basic formulas for the 189
Stress tensor for the inner friction 434 436ff
Stress tensor in hyperelasticity 190
Strict local minimum III 193
Strictly stable 193
strings 753ff
Strongly continuous operator 1498
Strongly elliptic systems 213
Strongly k-determined map 574
Strongly stable solution 193 218 244
Structural stability 579
Subgradient III385
Subimmersion 551
Submanifold 556
Submanifold with boundary 556
Submersion 551
Sun, history of the 777
Super-Lie groups 752
Supergravity 751
Supermanifolds 752
Superstring theory 752
Supersymmetry 751
Surface maps 644
Surface theory curvature properties in 636ff
Surface theory metric properties in 63Iff
Symplectic geometry and mechanics 22 (see also “Part V”)
Tangent bundle 542
Tangent map 543
Tangent map at a point 541
Tangent vector 538
Tangent vector abstract 539
Tangent vector concrete 538
Tangent vector, local coordinates of a 539
Tangent vector, transformation rule for a 539
Taylor problem 495ff
Taylor vortices 495
Tconstant in the sense of Lie 675
Tcurl of a 630
Tdivergence of a 166 626 629
Temperature as a Lagrange multiplier 398
Temperature basic ideas for 363ff
Temperature compensation 388
Temperature Gibbs’ fundamental equation and 374
Temperature in statistical physics 398
Temperature of radiation 58 408
Temperature regular states and 380
Temperature zero-th law of thermodynamics and 380
Tensor 618ff
Tensor antisymmetric (skew-symmetric) 622
Tensor calculus 615ff
Tensor calculus basic ideas of the 615
Tensor calculus on manifolds 648ff
Tensor construction of a 681
Tensor contraction of a 622
Tensor contravariant 619
Tensor covariant 618ff
Tensor curvature see “Curvature tensor”
Tensor degree of a 619
Tensor density 630
Tensor field constant in the sense of Levi-Civita 627
Tensor in three-dimensional space 13 166
Tensor parallel transport of a see “Parallel transport”
Tensor symmetric 622
Tensor trace of a 166
Tensor type of a 679
Theorem of (see also “Lemma of”)
Theorem of Adams 692
Theorem of Birkhoff 786
Theorem of Bolzano — Poincare — Miranda 808
Theorem of Bonnet (main theorem of surface theory) 640
Theorem of Brouwer 799
Theorem of Chern 689
Theorem of Crandall and Rabinowitz 858 862 879
Theorem of de Rham 688
Theorem of Euler (polyeder theorem) 687
Theorem of Fan and Glicksberg 805
Theorem of Gale, Nikaido, and Debreu 807
Theorem of Gauss (angular sum theorem) 686
Theorem of Gauss (integral theorem) 665
Theorem of Gauss (theorema egregium) 643
Theorem of Gauss — Bonnet — Chern 685ff
Theorem of Hartman — Stampacchia 803
Theorem of Hodge 672
Theorem of Hopf 862 876
Theorem of Kakutani 804
Theorem of Ljapunov (center theorem) 868
Theorem of Ljapunov (stability theorem) 843
Theorem of Morse 691
Theorem of Murat 267
Theorem of Nash 661
Theorem of Poincare (differential forms) 669
Theorem of Poincare (duality theorem) 688
Theorem of Poincare — Hopf 691
Theorem of Riemann 654
Theorem of Rivlin — Ericksen 207
Theorem of Sard 587
Theorem of Sard (parametrized) 823
Theorem of Sard — Smale 829ff
Theorem of Sard — Smale (parametrized) 832
Theorem of Stokes (integral theorem) 660 670
Theorem of Thorn (transversality theorem) 570
Theorem of Whitney 588
Theorema egregium of Gauss 643
Theory of relativity general 730ff
Theory of relativity special 694ff
Thermodynamical equilibrium states 373 387ff
Thermodynamical potential 385 387
Thermodynamical process 371ff 379
Thermodynamical process adiabatic 380
Thermodynamical process closed 380
Thermodynamical process irreversible 365 381
Thermodynamical process isothermal 387
Thermodynamical process reversible 365 381
Thermodynamical quasi-equilibrium states 372ff 374 379ff
Thermodynamical states 371ff 379ff
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