# Mathematics Formulary, изд. 2

 Автор(ы): Wevers J. C. A. 06.10.2007 Год изд.: 2002 Издание: 2 Описание: This document contains 66 pages with mathematical equations intended for physicists and engineers. It is intended to be a short reference for anyone who often needs to look up mathematical equations. This document can also be obtained from the author, Johan Wevers. The main themes of the book: Probability and statistics; Calculus; Differential equations; Linear algebra; Complex function theory; Tensor calculus; Numerical mathematics. Если вы хотите "левел ап" по математике, y10k.ru настоятельно рекомендует вам эту книгу. Оглавление: Обложка книги. Contents I 1 Basics [1]   1.1 Goniometric functions [1]   1.2 Hyperbolic functions [1]   1.3 Calculus [2]   1.4 Limits [3]   1.5 Complex numbers and quaternions [3]     1.5.1 Complex numbers [3]     1.5.2 Quaternions [3]   1.6 Geometry [4]     1.6.1 Triangles [4]     1.6.2 Curves [4]   1.7 Vectors [4]   1.8 Series [5]     1.8.1 Expansion [5]     1.8.2 Convergence and divergence of series [5]     1.8.3 Convergence and divergence of functions [6]   1.9 Products and quotients [7]   1.10 Logarithms [7]   1.11 Polynomials [7]   1.12 Primes [7] 2 Probability and statistics [9]   2.1 Combinations [9]   2.2 Probability theory [9]   2.3 Statistics [9]     2.3.1 General [9]     2.3.2 Distributions [10]   2.4 Regression analyses [11] 3 Calculus [12]   3.1 Integrals [12]     3.1.1 Arithmetic rules [12]     3.1.2 Arc lengts, surfaces and volumes [12]     3.1.3 Separation of quotients [13]     3.1.4 Special functions [13]     3.1.5 Goniometric integrals [14]   3.2 Functions with more variables [14]     3.2.1 Derivatives [14]     3.2.2 Taylor series [15]     3.2.3 Extrema [15]     3.2.4 The (?)-operator [16]     3.2.5 Integral theorems [17]     3.2.6 Multiple integrals [17]     3.2.7 Coordinate transformations [18]   3.3 Orthogonality of functions [18]   3.4 Fourier series [18] 4 Differential equations [20]   4.1 Linear differential equations [20]     4.1.1 First order linear DE [20]     4.1.2 Second order linear DE [20]     4.1.3 TheWronskian [21]     4.1.4 Power series substitution [21]   4.2 Some special cases [21]     4.2.1 Frobenius' method [21]     4.2.2 Euler [22]     4.2.3 Legendre's DE [22]     4.2.4 The associated Legendre equation [22]     4.2.5 Solutions for Bessel's equation [22]     4.2.6 Properties of Bessel functions [23]     4.2.7 Laguerre's equation [23]     4.2.8 The associated Laguerre equation [24]     4.2.9 Hermite [24]     4.2.10 Chebyshev [24]     4.2.11 Weber [24]   4.3 Non-linear differential equations [24]   4.4 Sturm-Liouville equations [25]   4.5 Linear partial differential equations [25]     4.5.1 General [25]     4.5.2 Special cases [25]     4.5.3 Potential theory and Green's theorem [27] 5 Linear algebra [29]   5.1 Vector spaces [29]   5.2 Basis [29]   5.3 Matrix calculus [29]     5.3.1 Basic operations [29]     5.3.2 Matrix equations [30]   5.4 Linear transformations [31]   5.5 Plane and line [31]   5.6 Coordinate transformations [32]   5.7 Eigenvalues [32]   5.8 Transformation types [32]   5.9 Homogeneous coordinates [35]   5.10 Inner product spaces [36]   5.11 The Laplace transformation [36]   5.12 The convolution [37]   5.13 Systems of linear differential equations [37]   5.14 Quadratic forms [38]     5.14.1 Quadratic forms in IR2 [38]     5.14.2 Quadratic surfaces in IR3 [38] 6 Complex function theory [39]   6.1 Functions of complex variables [39]   6.2 Complex integration [39]     6.2.1 Cauchy's integral formula [39]     6.2.2 Residue [40]   6.3 Analytical functions definied by series [41]   6.4 Laurent series [41]   6.5 Jordan's theorem [42] 7 Tensor calculus [43]   7.1 Vectors andcovectors [43]   7.2 Tensor algebra [44]   7.3 Inner product [44]   7.4 Tensor product [45]   7.5 Symmetric and antisymmetric tensors [45]   7.6 Outer product [45]   7.7 The Hodge star operator [46]   7.8 Differential operations [46]     7.8.1 The directional derivative [46]     7.8.2 The Lie-derivative [46]     7.8.3 Christoffel symbols [46]     7.8.4 The covariant derivative [47]   7.9 Differential operators [47]   7.10 Differential geometry [48]     7.10.1 Space curves [48]     7.10.2 Surfaces in IR3 [48]     7.10.3 The first fundamental tensor [49]     7.10.4 The second fundamental tensor [49]     7.10.5 Geodetic curvature [49]   7.11 Riemannian geometry [50] 8 Numerical mathematics [51]   8.1 Errors [51]   8.2 Floating point representations [51]   8.3 Systems of equations [52]     8.3.1 Triangular matrices [52]     8.3.2 Gauss elimination [52]     8.3.3 Pivot strategy [53]   8.4 Roots of functions [53]     8.4.1 Successive substitution [53]     8.4.2 Local convergence [53]     8.4.3 Aitken extrapolation [54]     8.4.4 Newton iteration [54]     8.4.5 The secant method [55]   8.5 Polynomial interpolation [55]   8.6 Definite integrals [56]   8.7 Derivatives [56]   8.8 Differential equations [57]   8.9 The fast Fourier transform [58] Формат: djvu Размер: 247256 байт Язык: ENG Рейтинг: 30
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