Spiegel M.R. — Schaum's mathematical handbook of formulas and tables :: Электронная библиотека попечительского совета мехмата МГУ

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Spiegel M.R. — Schaum's mathematical handbook of formulas and tables

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Название: Schaum's mathematical handbook of formulas and tables

Автор: Spiegel M.R.

Аннотация:

Students and research workers in mathematics, physics, engineering and other sciences will find this compilation of more than 2000 mathematical formulas and tables [__include exact number?_____] invaluable. They will see quickly why half a million copies were sold of the first edition! All the information included is practical — rarely used results are excluded. Topics range from elementary to advanced-from algebra, trigonometry and calculus to vector analysis, Bessel functions, Legendre polynomials and elliptic integrals. Great care has been taken to present all results concisely and clearly. Excellent to keep as a handy reference!

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Рубрика: Математика/Справочники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 278

Добавлена в каталог: 03.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Equation of line general      35
Equation of line in parametric form      47
Equation of line in standard form      47
Equation of line intercept form for      34
Equation of line normal form for      35
Equation of line perpendicular to plane      48
Equation of plane, general      47
Equation of plane, intercept form for      47
Equation of plane, normal form for      48
Equation of plane, passing through three points      47
Error function      183
Error function complementary      183
Error function table of values of      257
Euler numbers      114 115
Euler numbers definition of      114
Euler numbers relationship of, to Bernoulli numbers      115
Euler numbers series involving      115
Euler numbers table of first few      114
Euler or Cauchy differential equation      105
Euler — Maclaurin summation formula      109
Euler's constant      1
Euler's identities      24
Evolute of an ellipse      44
Exact differential equation      104
Exponential functions      23—25 200
Exponential functions, periodicity of      24
Exponential functions, relationship of to trigonometric functions      24
Exponential functions, sample problems involving calculation of      200
Exponential functions, series for      111
Exponential functions, table of      226 227
Exponential integral      183
Exponential integral table of values for      251
Exponents      23
F distribution      1899
F distribution 95th and 99th percentile values for      260 261
Factorial n      3
Factorial n, table of values for      234
Factors      2
Focus, of conic      37
Focus, of ellipse      38
Focus, of hyperbola      39
Focus, of parabola      38
Folium of Descartes      43
Fourier series      131—135
Fourier series, complex form of      131
Fourier series, convergence of      131
Fourier series, definition of      131
Fourier series, Parseval's identity for      131
Fourier series, special      132—135
Fourier transforms      174—178
Fourier transforms sine      175
Fourier transforms table of      176—178
Fourier transforms, convolution theorem for      175
Fourier transforms, cosine      176
Fourier transforms, definition of      175
Fourier transforms, Parseval's identity for      175
Fourier's integral theorem      174
Fresnel sine and cosine integrals      184
Frullani's integral      100
Frustrum of right circular cone, lateral surface area of      9
Frustrum of right circular cone, volume of      9
Gamma function      1 101 102
Gamma function asymptotic expansions for      102
Gamma function definition of      101 102
Gamma function derivatives of      102
Gamma function duplication formula for      102
Gamma function for negative values      101
Gamma function graph of      101
Gamma function infinite product for      102 188
Gamma function recursion formula for      101
Gamma function relationship of to beta function      103
Gamma function relationships involving      102
Gamma function special values for      101
Gamma function table of values for      235
Gauss' theorem      123
Gaussian plane      22
Generalized integration by parts      59
Generating functions      137 139 146 149 151 153 155 157 158
Geometric formulas      5—10
Geometric mean      185
Geometric series      107
Geometric series arithmetic-      107
Gradient      119
Gradient in curvilinear coordinates      125
Green's first and second identities      124
Green's theorem      123
Half angle formulas, for hyperbolic functions      27
Half angle formulas, for trigonometric functions      16
Half rectified sine wave function      172
Hankel functions      138
Harmonic mean      185
Heaviside's unit function      173
Hermite polynomials      151 152
Hermite polynomials addition formulas for      152
Hermite polynomials generating function for      151
Hermite polynomials orthogonal series for      152
Hermite polynomials orthogonality of      152
Hermite polynomials recurrence'formulas for      151
Hermite polynomials Rodrigue's formula for      151
Hermite polynomials special      151
Hermite polynomials special results involving      152
Hermite's differential equation      151
Higher derivatives      55
Higher derivatives Leibnitz rule for      55
Holder's inequality      185
Holder's inequality for integrals      186
Homogeneous differential equation      104
Homogeneous differential equation linear second order      105
Hyperbola      37 39
Hyperbola asymptotes of      39
Hyperbola eccentricity of      39
Hyperbola equation of      37
Hyperbola focus of      39
Hyperbola length of major and minor axes of      39
Hyperbolas, confocal      127
Hyperbolic functions      26—31
Hyperbolic functions addition formulas for      27
Hyperbolic functions definition of      26
Hyperbolic functions double angle formulas for      27
Hyperbolic functions graphs of      29
Hyperbolic functions half angle formulas for      27
Hyperbolic functions inverse      see “Inverse hyperbolic functions”
Hyperbolic functions multiple angle formulas for      27
Hyperbolic functions of negative arguments      26
Hyperbolic functions periodicity of      31
Hyperbolic functions powers of      28
Hyperbolic functions relationship of to trigonometric functions      31
Hyperbolic functions relationships among      26 28
Hyperbolic functions sample problems for calculation of      200 201
Hyperbolic functions series for      112
Hyperbolic functions sum, difference and product of      28
Hyperbolic functions table of values for      228—233
Hyperbolic paraboloid      52
Hyperboloid, of one sheet      51
Hyperboloid, of two sheets      52
Hypergeometric differential equation      160
Hypergeometric differential equation distribution      189
Hypergeometric functions      160
Hypergeometric functions miscellaneous properties of      160
Hypergeometric functions special cases of      160
Hypocycloid, general      42
Hypocycloid, general with four cusps      40
Imaginary part of a complex number      21
Imaginary unit      21
Improper integrals      94
Indefinite integrals      57—93
Indefinite integrals definition of      57
Indefinite integrals table of      60—93
Indefinite integrals transformation of      59 60
Inequalities      185 186

Infinite products      102 188
Infinite products series      see “Series”
Initial point of a vector      116
Integral calculus, fundamental theorem of      94
Integrals, definite      see “Definite integrals”
Integrals, double      122
Integrals, improper      94
Integrals, indefinite      see “Indefinite integrals”
Integrals, involving vectors      121
Integrals, line      see “Line integrals”
Integrals, multiple      122 125
Integration      see also “Integrals” 57
Integration by parts      57
Integration by parts generalized      59
Integration constants of      57
Integration general rules of      57—59
Intercepts      34 47
Interest      201 240—243
Interpolation      195
Interval of convergence      110
Inverse hyperbolic functions      29—31
Inverse hyperbolic functions definition of      29
Inverse hyperbolic functions expressed in terms of logarithmic functions      29
Inverse hyperbolic functions graphs of      30
Inverse hyperbolic functions principal values for      29
Inverse hyperbolic functions relationship of to inverse trigonometric functions      31
Inverse hyperbolic functions relationships between      30
Inverse Laplace transforms      161
Inverse trigonometric functions      17—19
Inverse trigonometric functions definition of      17
Inverse trigonometric functions graphs of      18 19
Inverse trigonometric functions principal values for      17
Inverse trigonometric functions relations between      18
Inverse trigonometric functions relationship of to inverse hyperbolic functions      31
Involute of a circle      43
Jacobi's elliptic functions      180
Jacobian      125
Ker and Kei functions      140 141
Ker and Kei functions definition of      140
Ker and Kei functions differential equation for      141
Ker and Kei functions graphs of      141
Lagrange form of remainder in Taylor series      110
Laguerre polynomials      153 154
Laguerre polynomials associated      see “Associated Laguerre polynomials”
Laguerre polynomials generating function for      153
Laguerre polynomials orthogonal series for      154
Laguerre polynomials orthogonality of      154
Laguerre polynomials recurrence formulas for      153
Laguerre polynomials Rodrigue's formula for      153
Laguerre polynomials special      153
Laguerre's associated differential equation      155
Laguerre's differential equation      153
Landen's transformation      180
Laplace transforms      161—173
Laplace transforms complex inversion formula for      161
Laplace transforms definition of      161
Laplace transforms inverse      161
Laplace transforms table of      162—173
Laplacian      120
Laplacian in curvilinear coordinates      125
Legendre functions      see also “Legendre polynomials” 146—148
Legendre functions associated      see “Associated Legendre functions”
Legendre functions of the second kind      148
Legendre polynomials      see also “Legendre functions” 146 147
Legendre polynomials generating function for      146
Legendre polynomials orthogonal series of      147
Legendre polynomials orthogonality of      147
Legendre polynomials recurrence formulas for      147
Legendre polynomials Rodrigue's formula for      146
Legendre polynomials special      146
Legendre polynomials special results involving      147
Legendre polynomials table of values for      252 253
Legendre's associated differential equation      149
Legendre's associated differential equation general solution of      150
Legendre's differential equation      106 146
Legendre's differential equation general solution of      148
Legendre's relation for elliptic integrals      182
Leibnitz's rule, for differentiation of integrals      95
Leibnitz's rule, for higher derivatives of products      55
Lemniscate      40 44
Limacon of Pascal      41 44
Line integrals      121 122
Line integrals definition of      121
Line integrals independence of path of      121 122
Line integrals properties of      121
Line, equation of      see “Equation of line”
Line, equation of integrals      see “Line integrals”
Line, slope of      34
Linear first order differential equation      104
Linear second order differential equation      105
Logarithmic functions      see also “Logarithms” 23—25
Logarithmic functions, series for      111
Logarithms      see also “Logarithmic functions” 23
Logarithms base of      23
Logarithms Briggsian      23
Logarithms change of base of      24
Logarithms characteristic of      194
Logarithms common      see “Common logarithms”
Logarithms mantissa of      194
Logarithms natural      24
Logarithms of trigonometric functions      216—221
Logarithms, antilogarithms and      see “Antilogarithms”
Logarithms, of complex numbers      25
Maclaurin series      110
Mantissa      194
Mean value theorem, for definite integrals      94
Mean value theorem, generalized      95
Minkowski's inequality      186
Minkowski's inequality for integrals      186
Modified Bessel functions      138 139
Modified Bessel functions of order half an odd integer      140
Modified Bessel functions, differential equation for      138
Modified Bessel functions, generating function for      139
Modified Bessel functions, graphs of      141
Modified Bessel functions, recurrence formulas for      139
Modulus, of a complex number      22
Moments of inertia, special      190 191
Multinomial formula      4
Multiple angle formulas, for hyperbolic functions      27
Multiple angle formulas, for trigonometric functions      16
Multiple integrals      122
Multiple integrals, transformation of      125
Napier's rules      20
Napierian logarithms      24 196
Napierian logarithms, tables of      224 225
Natural logarithms and antilogarithms      24 196
Natural logarithms and antilogarithms, tables of      224—227
Neumann's function      136
Nonhomogeneous equation, linear second order      105
Normal curve, areas under      257
Normal curve, ordinates of      256
Normal distribution      189
Normal form, equation of line in      35
Normal form, equation of plane in      48
Normal, outward drawn or positive      123
Normal, outward drawn or positive unit      122
Null function      170
Null vector      116
Numbers, complex      see “Complex numbers”
Oblate spheroidal coordinates      128
Oblate spheroidal coordinates, Laplacian in      128
Orthogonal curvilinear coordinates      124—130
Orthogonal curvilinear coordinates formulas involving      125
Orthogonality and orthogonal series      144 145 147 150 152 154 156 158 159
Ovals of Cassini      44
parabola      37 38
Parabola eccentricity of      37
Parabola equation of      37 38
Parabola focus of      38
Parabola segment of      see “Segment of parabola”

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