Mathematics Formulary

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:
Mathematics Formulary — 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]
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Язык:ENG
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