Mathematics Formulary, изд. 2
| Автор(ы): | Wevers J. C. A.
06.10.2007
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| 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.
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 |
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