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Zeidler E. — Oxford User's Guide to Mathematics
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Название: Oxford User's Guide to MathematicsАвтор: Zeidler E. Аннотация: The Oxford User's Guide to Mathematics in Science and Engineering represents a comprehensive handbook on mathematics. It covers a broad spectrum of mathematics including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimization, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. This is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics. The book offers a broad modern picture of mathematics starting from basic material up to more advanced topics. It emphasizes the relations between the different branches of mathematics and the applications of mathematics in engineering and the natural sciences. The book addresses students in engineering, mathematics, computer science, natural sciences, high-school teachers, as well as a broad spectrum of practitioners in industry and professional researchers. A comprehensive table at the end of the handbook embeds the history of mathematics into the history of human culture. The bibliography represents a comprehensive collection of the contemporary standard literature in the main fields of mathematics.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 1308Добавлена в каталог: 15.09.2014Операции: Положить на полку |
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Предметный указатель
Space, linear, symplectic 869 Space, linear, with indefinite scalar product 850 Space, locally convex 638 Space, metric 254 352 596 716 Space, metric, neighborhood 257 Space, Minkowski 850 Space, Minkowski, multilinear algebra on 852 Space, Minkowski, orientation 852 Space, phase 922 Space, polar 529 Space, probability 989 Space, pseudo-unitary 847 Space, ringed 835 Space, Schwartz 401 Space, Sobolev 511 1129 Space, tangent 638 Space, topological 558 Space, unitary 840 Space, vector see "Space linear" Space-like vector 851 span 647 Spec R 836 Special theory of relativity 306 854 Specific heat 372 493 Spectral analysis 392 Spectral density 1036 Spectral radius 626 Spectrum 626 635 Speed of sound 519 Speiser, Andreas 909 Spherical angle 737 Spherical coordinates 346 507 Spherical cylinder 349 Spherical excess 738 Spherical function 510 Spherical geometry 736 Spherical pendulum 591 Spherical triangle 737 Spherical triangle, area of 739 Spin 838 Spinor 862 Spinor, algebra 661 Spiral 793 SPLINE 1082 Spring 411 Square 7 Square-free number 719 Stability 292 410 417 457 Stability, CFL-conditions 1145 Stability, of difference operator 1145 Stability, theorem of Liapunov 458 Stable, equilibrium 428 Stable, optimally 1146 Standard deviation 981 1000 Standard deviation (empirical) 76 Standard model 694 769 838 860 864 1198 state, condition 493 State, ground 927 State, recurrent 1041 State, stable equilibrium 1096 State, transient 1041 Statement 873 896 Stationary phase 126 Stationary process 427 502 514 Statistical comparison of sequences of trials 80 Statistical hypothesis 1017 Statistical physics 306 694 986 Statistical physics, basic problem of 950 Statistical system 687 Statistics, golden rule 1015 Statistics, main theorem 1022 Statistics, mathematical 75 Steiner, Jakob 768 Steinitz' theorem (change of basis) 639 Steinitz' theorem (on algebraic closure) 679 Step width 1109 Stereographic projection 558 Stevin, Simon 59 Stieltjes integral 998 Stifel, Michael 28 1184 Stirling formula 3 573 Stirling interpolation formula 1080 STIRLING, JAMES 1010 Stochastic matrix 1039 Stochastic process 500 976 1046 Stokes equation 1134 Stokes theorem 143 336 372 542 Strassmann, Fritz 1196 streamline 366 Strictly hyperbolic differential equation 514 String, equation of vibrating 939 String, theory 543 582 662 808 Strophoid 810 819 Sturm, Jacques Charles 459 622 Subdeterminant 614 Subdeterminant, major 630 Subdifferential 951 Subfield 672 Subgradient 951 Subgroup 665 Subgroup, normal 665 Subgroup, trivial 665 Subharmonic function 597 Subring 670 Subsequence 247 Subsequence, convergent 257 Subset 885 subspace 640 Substitution, Euler 148 Substitution, rule 140 Substitution, rule, for integrals 314 Subtangent 951 Sudan, Madhu 1202 Sum, direct 647 Sum, double 381 Sum, Gauss 715 Sum, of angles in an n-gon 6 Sum, of powers 33 Sum, of squares 33 Sum, ordinal 903 Sum, outer direct 659 Sum, rule 135 Sumeria 5 Summation formula of Leibniz 710 Summation formula of Newton 710 Summation symbol 28 377 Sun 354 491 Sun, death of 45 Superalgebra 662 Supercommutativity 305 Superposition principle 426 Supersymmetry (SUSY) 864 Supremum 241 surface 638 778 Surface integral 343 Surface, canonical coordinate system 783 Surface, capillary 919 Surface, constant Gaussian curvature 783 Surface, first fundamental form of 780 Surface, frame 778 Surface, map 781 Surface, minimal 784 919 936 Surface, orientation 782 Surface, principal curvature directions of 783 Surface, quadratic 631 755 Surface, Riemann 686 804 807 819 1191 Surface, Riemann, genus of 807 819 Surface, ruled 785 Surface, second fundamental form of 782 Surface, singularity 779 Surface, tangent plane 779 Surjective 642 889 Sylvester's law of inertia 631 Symbol 512 514 Symmetric bilinear form 651 Symmetry 306 432 1191 Symmetry, duality of Maxwell equations 858 Symmetry, infinitesimal 839 Symmetry, supersymmetry (SUSY) 864 Symplectic basis 869 Symplectic form 474 481 633 869 Symplectic geometry 306 633 Symplectic geometry, canonical differential form 474 Symplectic geometry, of 542 Symplectic geometry, of the plane 542 Symplectic map 869 Symplectic space, isotropic subspace 870 Symplectic space, Lagrangian subspace 870 Symplectic structure 489 542 Symplectic transformation 480 486 Symplectic volume form 870 System of sets 895 System, oscillating 705 t-test 81 Table, cost 967 Table, of mathematical statistics 83 Table, of values 46 Table, transport 967 Tangent 59 262 269 770 817 Tangent Law 727 Tangent plane 638 Tangent space 638 Tangent to a circle 18 Tangent to a curve 638 Tangent to a hyperbola 21 Tangent to an ellipse 20 Tangent to parabola 22 Tangent, equation of 262 Tangent, hyperbolic 64 Tarjan, Robert 1202 Tautology 876 897 Taylor's theorem 271 293 Taylor, Brook 1187 Taylor, expansion 404 638 769 Taylor, series 269 359 384 408 Taylor, series, integral remainder term 272 Taylor, series, remainder term 271 Temperature 284 694 Temperature, absolute 519 950 Temperature, distribution 498 Tensor 655 Tensor, algebra 658 Tensor, contraction 656 Tensor, covariant 779 Tensor, electromagnetic field 858 Tensor, Levi-Civita 782 Tensor, metric 781 Tensor, product 301 519 655 657 Tensor, product, universal property of 657 Test function 472 Test, 1024 Test, correlation 1020 Test, F 1020 Test, for normal distribution 1021 Test, Kolmogorov — Smirnov 1022 Test, minimal 957 Test, significance (t-test) 1019 Test, Wilcoxon 1026 Testing hypothesis 1013 tetrahedron 14 Thales of Milet 733 1181 Theophrast of Eresos 877 Theorem, Abel's 383 Theorem, addition 54 Theorem, addition, algebraic 577 Theorem, addition, for 579 Theorem, addition, for elliptic functions 581 Theorem, addition, for the 805 Theorem, addition, of Fagnano 574 Theorem, alternate 1107 Theorem, approximation, of Liouville 706 Theorem, approximation, of Roth 707 Theorem, Atiyah — Singer Index 643 831 868 1197 Theorem, Banach fixed-point 434 1095 Theorem, basis 848 Theorem, basis (for exterior algebra) 658 Theorem, basis (Hilbert space) 842 Theorem, Bayes' 994 Theorem, binomial 31 Theorem, Bolzano's theorem on zeros 262 Theorem, Bonnet 788 Theorem, Cantor's 892 Theorem, Cartan — Kaehler 306 424 Theorem, central limit 982 1006 Theorem, Darboux 869 Theorem, de Rham 341 542 Theorem, Desargues 762 Theorem, Dirichlet — Jordan 401 Theorem, equivalence (difference operators) 1145 Theorem, ergodic (Markov) 1040 Theorem, Euler (on convergence of binomial series) 32 Theorem, Euler's 693 695 698 Theorem, Faltings 826 Theorem, Fejer 389 Theorem, Fermat's 697 Theorem, Fermat's last 723 808 827 1198 Theorem, finite generation of ideals 833 Theorem, Fubini 143 Theorem, Fundamental theorem of Algebra 1189 Theorem, fundamental, decomposition theorem of Dedekind 720 Theorem, Fundamental, of Algebra 532 546 552 618 Theorem, fundamental, of arithmetic 688 Theorem, fundamental, of calculus 143 307 312 321 539 Theorem, fundamental, of logic 877 Theorem, gap 691 Theorem, Gauss 143 Theorem, Gauss (on constuctions) 684 Theorem, Gauss — Stokes 143 Theorem, generalized vortex theorem of Helmholtz 484 Theorem, global limit 1010 Theorem, Godel's completeness 900 Theorem, Godel's incompleteness 906 Theorem, Hardy's 694 Theorem, Herglotz' spectral 1037 Theorem, Hilbert (on real numbers) 745 Theorem, Hilbert Basis 719 Theorem, Hironaka 834 Theorem, implicit function 288 290 Theorem, integrality (transport problems) 968 Theorem, Jacobi 697 Theorem, Kolmogorov — Smirnov 1022 Theorem, Lebesgue 266 Theorem, Lindemann 712 Theorem, Liouville (phase flow) 922 Theorem, Liouville's 489 578 Theorem, local limit theorem of de Moivre and Laplace 1010 Theorem, main, of Galois theory 681 Theorem, main, of linear optimization 953 Theorem, main, of mathematical statistics 1022 Theorem, mean value 252 262 266 Theorem, mean, for integrals 312 332 Theorem, Minkowski lattice point 715 Theorem, monodromy 571 Theorem, Mordell 826 Theorem, Noether's 432 913 Theorem, Nullstellensatz 833 Theorem, of Abel and Galois 681 Theorem, of Bezout 815 Theorem, of Bolzano 252 Theorem, of Bolzano — Weierstrass 248 257
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