Absolute derivative 625
Absolute differential 625
Absolute space 29 31 702 704ff
Absolute temperature see “Temperature”
Absolute time 31 702
Acceleration 11
Accessory quadratic variational problem 218
action 81 884
Action propagation of 81
Addition theorem for velocities in relativity 708ff
Adiabatic process 380 394
Admissible chart 535
Admissible coordinate system 632
Affine connected manifolds 649
Airy’s stress function 328 337 345
Algebraically simple eigenvalue 1374 853ff
Alternating differential forms 664ff (see also «“Part V”)
Alternating differential forms, basic ideas of the calculus for 665
Alternating differential forms, differentiation of 665 668
Alternating differential forms, integration of 665 669
Amplitude 101
Analytic map 1362
Angular frequency 28 99
Angular momentum in quantum mechanics 115
Angular momentum tensor 725ff
Angular velocity 12
Antisymmetric (skew-symmetric) 622
Approximation methods in elasticity 224ff 252
Approximation methods in general relativity 735
Approximation methods in hydrodynamics 483
Approximation methods in quantum mechanics 129
Approximation models in elasticity 163 240ff
Area preserving maps 644
Asymptotically stable 842
Atlas 534
Atlas abstract 602
Atlas equivalent 536
Atlas maximal 535
Atlas oriented 583
Autonomous differential equations 548 841
B-space (Banach space) 1769ff
Baire category 1802
Baire space 1801
Balance of angular momentum 34
Balance of energy 34
Balance of momentum 34
Banach manifold see “Manifold”
Banach space see “B-space”
Baryon number 416
Basic equations in mathematical physics, list of 953
Basis space of a bundle 544
Beam equation 315ff
Benard problem 505ff 518
Bending of beams and rods 311ff
Bernoulli constant 453
Bernoulli equation 433 438 453
Betti number 688
Bifurcation and loss of stability 221ff 227 841 856ff 860ff
Bifurcation for beams and rods 311ff 320
Bifurcation for dynamical systems 856ff (see also «“Part V”)
Bifurcation for plates 323 333
Bifurcation for variational inequalities 303ff
Bifurcation in elasticity 221 227 303ff 311ff 332 346
Bifurcation in hydrodynamics 448 495 505
Bifurcation point of a variational inequality 304
Bifurcation point of an operator equation 1358
Bifurcation principle 821 837 841
big bang 57ff 742ff
Bilinear form 1141
Bilinear form compact see “Part II”
Bilinear form nondegenerate 561
Bilinear form strictly positive see “Part II”
Bilinear form strongly positive see “Part II”
Bilinear form weakly nondegenerate 561
Black hole 768 771ff 778ff
Black-body radiation 410ff
Black-white dipole hole 768 775ff
Blowing-up lemma 606
Bohr’s atomic model 137
Boltzmann constant 59 366 400 884
Boltzmann statistics 420
Bose statistics 402 408
Bose statistics, basic ideas of 401
Boson 126 751
Boundary layers 518ff
Boundary of stability 222
Boussinesq approximation 506 512
Brouwer’s fixed-point theorem 151
Brouwer’s fixed-point theorem elementary proof of 799
Brouwer’s fixed-point theorem equivalent statements to the 795 810
Brouwer’s principle 797
Buckling force 304 314
Bundle 544
Bundle abstract 544
Bundle cotangent 545
Bundle fiber see “Part V”
Bundle isomorphism 544
Bundle morphism 544
Bundle normal 591
Bundle space 544
Bundle tangent 542
Bundle vector 590
Canonical equation 21 72 83ff
Canonical transformation 83
Carnot’s cycle 394
Catastrophe theory 572ff
Catastrophe theory basic ideas of 572
Causal structure of manifolds 787
Causality 714ff
Cavities 471
Center of mass 33
Center theorem of Ljapunov 868
Center theorem, general see “Part V”
Center, stable, and unstable manifolds see “Part V”
Centrifugal force 30
Chain rule for tangent maps 543
Chandrasekhar mass, critical 412 778
Characteristic classes 690
Chart 533
Chart abstract 536
Chart admissible 535
Chart admissible oriented 584
Chart compatible 534
Chart image 534
Chart map 535
Chart space 534
Chebyshev inequality 115 398
chemical potential 374 398
Chemical potential as a Lagrange multiplier 398
Chemical potential of a photon gas 409
Chemical potential of an ideal gas 377 406
Chemical potential of elementary particles 416
Chemical reactions 373 389ff
Christoffel symbols 623
Christoffel symbols effective calculation of the 734
Christoffel symbols intuitive meaning of the 682
Circulation 438
Closed map 551
Cnoidal waves 466ff
Cobasis 576
Coboundary 671
Cocycle 671
Codimension 1765
Codimension of a map 576
Codimension of a submanifold 557
Coherently oriented 585
Cohomology 671
Cohomology class 671
Cohomology group 671
Compact operator 153
| Compact set 1756 1769
Compact spacelike support 724
Compensated compactness 264ff
Complex flow potential 454
Complex velocity 453
Complexification 1770
Component of a set 1757
Cone 1276
Configuration space 22 48
Conformai maps 645
Conjugate functional 65ff
Connected set 1757
Connection in a principal fiber bundle 690 (see also «“Part V”)
Conservation laws 34 422ff 724
Conservation laws in relativity 724 (see also «Part V)
Conservation laws, basic ideas of 422
Conservation laws, differential forms and 782
Conservation of angular momentum 35
Conservation of energy 34
Conservation of mass 423
Conservation of momentum 35
Conservative force 33
Conserved quantities in mechanics 32
Constitutive laws basic ideas of 147ff
Constitutive laws convex material 237 244ff
Constitutive laws dual 237 246
Constitutive laws elastic energy of the cuboid and 198 230
Constitutive laws elasto-viscoplastic material 151ff 348ft 354
Constitutive laws for homogeneous bodies 205ff
Constitutive laws for homogeneous isotropic bodies 206
Constitutive laws for the friction tensor 436ff
Constitutive laws Fourier’s law 424
Constitutive laws hardening and 148 151ff 348ff 353
Constitutive laws Hencky material 202 256
Constitutive laws Hooke’slaw 8 201 233ff 255
Constitutive laws ideal plastic material 149
Constitutive laws ideal plastic von Mises liquid 157 (see also «“Part V”)
Constitutive laws in heat conduction 424
Constitutive laws in hydrodynamics 434ff
Constitutive laws in hyperelasticity 190
Constitutive laws in linear elasticity 201 208 255
Constitutive laws in nonlinear elasticity 176 185
Constitutive laws in plasticity 148ff 154ff 200ff 257ff 348ff
Constitutive laws inverse (dual) 237 246
Constitutive laws linear material 201 208 255 259
Constitutive laws Mooney — Rivlin material 209
Constitutive laws Navier — Stokes liquid 438
Constitutive laws non-Newtonian liquid 157 (see also «“PartV”)
Constitutive laws Ogden’s material 209
Constitutive laws polyconvex material 209 241 273
Constitutive laws rubberlike material 208 277
Constitutive laws Saint Venant — Kirchhoffmaterial 208
Constitutive laws theory of invariants and 202ff
Constitutive laws viscoplastic Bingham liquid 157 (see also «“Part V”)
Constitutive laws viscoplastic material 149ff 348ff
Constitutive laws viscous material 150
Constitutive laws viscous Williamson liquid 157 (see also «“Part V”)
Constraining force 46ff
Constraining force of a pendulum 93
Continuation method in heat conduction 422ff
Continuation method in nonlinear elasticity 224ff
Continuation method in numerical mathematics 818ff
Continuity equation 434
Continuous operator 1755 1770
Contra variant tensor 619
Contraction of tensors 622
Convex functional III245 III380
Convex set III245
Coriolis force 30
Cosmos early 63 747ff
Cosmos future of the 745ff
Cotangent bundle 545
Cotangent vector 545 595
Couette flow 497
Coulomb (unit of charge) 884
Coulomb’s law 38
Countable basis 1754 536
Covariance 720
Covariant differentiation 623
Covariant differentiation motivation of the 626
Covariant differentiation on surfaces 646
Covariant tensor 618
Covector field on a manifold 546
Critical mass density of the universe 60 744
Critical temperature for elementary particles 62
Cross section for elementary particle processes 106 137 139
Current density vector 422ff 725
Curvature scalar 731
Curvature tensor 642ff 650 653 655 683 731 734 784
Curvature tensor analytic meaning of the 650
Curvature tensor definition of the 642
Curvature tensor geometric meaning of the 654 683
Curvature tensor important properties of the 643 784
Curvature tensor in general relativity 730ff 734
Curvature tensor Riemann’s theorem on local flatness and the 654
Curvature tensor theorema egregium of Gauss and th 642
Curve following algorithm 812ff 822 837
de Broglie matter wave 112
De Rham cohomology 671
Dead water problem 471
Decay of particles 105
Decay probability 106
Deflection of light in general relativity 765
Deformation 177
Deformation of a cuboid 198
Degree of a tensor 619
Derivation 600
Dielectricity constant 38 884
Diffeomorphism 537
Diffeomorphism construction of a 560
Diffeomorphism local 538
Differentiable structure 536
Differential 595
Differential absolute 625
Differential and numerical mathematics 817ff
Differential and the fixed-point index 825
Differential and the mapping degree 825
Differential calculus on manifolds 648 663ff
Differential forms 599
Differential forms and conservation laws 782
Differential forms in mechanics see “Part V”
Differential forms in thermodynamics 383ff
Differential topology 688ff
Differentiation absolute 625 650
Differentiation alternating 664
Differentiation covariant 623 650
Differentiation Lie 673
Differentiation of differential forms 665ff
Differentiation on manifolds 540ff 663ff
Dimension analysis and boundary layers 521
Dimension analysis and turbulence 440 515
Dimension analysis basic ideas of 89
Dimension of a manifold 535
Direct sum 1766
Directional derivative 595 600 673
Dispersion in quantum mechanics 114
Dispersion in statistical physics 398 407
Dispersion in turbulence 515
dispersion relation 100 102 449
Divergence of a tensor 166
Door-in/door-out principle 813 820
Doppler effect 91
Doppler effect and the red shift of galaxies 57
Double splitting maps 531
Dual elastic energy 245
Dualism between waves and particles 107ff
Duality in elasticity 235 237 245ff 289
Duality in plasticity 259 262
Duality in the calculus of variations 284
Duality of Friedrichs 284ff
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