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

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Предметный указатель

Addition formulas, for Bessel functions      145
Addition formulas, for elliptic functions      180
Addition formulas, for Hermite polynomials      152
Addition formulas, for hyperbolic functions      27
Addition formulas, for trigonometric functions      15
Agnesi, witch of      43
Algebraic equations, solutions of      32 33
Amplitude, of complex number      22
Amplitude, of elliptic integral      179
Analytic geometry, plane      see “Plane analytic geometry”
Analytic geometry, solid      see “Solid analytic geometry”
Angle between lines, in a plane      35
Angle between lines, in space      47
Annuity, amount of      201 242
Annuity, present value of      243
Anti-derivative      57
Antilogarithms, common      23 195 204 205
Antilogarithms, natural or Napierian      24 226 227
Archimedes, spiral of      45
Area integrals      122
Argand diagram      22
Arithmetic mean      185
Arithmetic series      107
Arithmetic-geometric series      107
Associated Laguerre polynomials      see also “Laguerre polynomials” 155 156
Associated Laguerre polynomials, generating function for      155
Associated Laguerre polynomials, orthogonal series for      156
Associated Laguerre polynomials, orthogonality of      156
Associated Laguerre polynomials, recurrence formulas for      156
Associated Laguerre polynomials, special      155
Associated Laguerre polynomials, special results involving      156
Associated Legendre functions      see also “Legendre functions” 149 150
Associated Legendre functions, generating function for      149
Associated Legendre functions, of the first kind      149
Associated Legendre functions, of the second kind      150
Associated Legendre functions, orthogonal series for      150
Associated Legendre functions, orthogonality of      150
Associated Legendre functions, recurrence formulas for      149
Associated Legendre functions, special      149
Associative law      117
Asymptotes of hyperbola      39
Asymptotic expansions or formulas, for Bernoulli numbers      115
Asymptotic expansions or formulas, for Bessel functions      143
Asymptotic expansions or formulas, for gamma function      102
Base of logarithms      23
Base of logarithms, change of      24
Ber and Bei functions      140 141
Ber and Bei functions, definition of      140
Ber and Bei functions, differential equation for      141
Ber and Bei functions, graphs of      141
Bernoulli numbers      98 107 114 115
Bernoulli numbers, asymptotic formula for      115
Bernoulli numbers, definition of      114
Bernoulli numbers, relationship to Euler numbers      115
Bernoulli numbers, series involving      115
Bernoulli numbers, table of first few      114
Bernoulli's differential equation      104
Bessel functions      136—145
Bessel functions addition formulas for      145
Bessel functions asymptotic expansions of      143
Bessel functions definite integrals involving      142 143
Bessel functions generating functions for      137 139
Bessel functions graphs of      141
Bessel functions indefinite integrals involving      142
Bessel functions infinite products for      188
Bessel functions integral representations for      143
Bessel functions modified      see “Modified Bessel functions”
Bessel functions of first kind of order n      136 137
Bessel functions of order half an odd integer      138
Bessel functions of second kind of order n      136 137
Bessel functions orthogonal series for      144 145
Bessel functions recurrence formulas for      137
Bessel functions tables of      244—249
Bessel functions zeros of      250
Bessel's differential equation      106 136
Bessel's differential equation general solution of      106 137
Bessel's differential equation transformed      106
Bessel's modified differential equation      138
Bessel's modified differential equation general solution of      139
beta function      103
Beta function relationship of to gamma function      103
Biharmonic operator      120
Biharmonic operator in curvilinear coordinates      125
Binomial coefficients      3
Binomial coefficients properties of      4
Binomial coefficients table of values for      236 237
Binomial distribution      189
Binomial formula      2
Binomial series      2 110
Bipolar coordinates      128 129
Bipolar coordinates Laplacian in      128
Branch, principal      17
Briggsian logarithms      23
Cardioid      41 42 44
Cassini, ovals of      44
Catalan's constant      181
Catenary      41
Cauchy or Euler differential equation      105
Cauchy — Schwarz inequality      185
Cauchy — Schwarz inequality for integrals      186
Cauchy's form of remainder in Taylor series      110
Chain rule for derivatives      53
Characteristic      194
Chebyshev polynomials      157—159
Chebyshev polynomials generating functions for      157 158
Chebyshev polynomials of first kind      157
Chebyshev polynomials of second kind      158
Chebyshev polynomials orthogonal series for      158 159
Chebyshev polynomials orthogonality of      158 159
Chebyshev polynomials recursion formulas for      158 159
Chebyshev polynomials relationships involving      159
Chebyshev polynomials special      157 158
Chebyshev polynomials special values of      157 159
Chebyshev's differential equation      157
Chebyshev's differential equation general solution of      159
Chebyshev's inequality      186
Chi square distribution      189
Chi square distribution percentile values for      259
Circle, area of      6
Circle, equation of      37
Circle, involute of      43
Circle, perimeter of      6
Circle, sector of      see “Sector of circle”
Circle, segment of      see “Segment of circle”
Cissoid of Diodes      45
Common antilogarithms      23 195 204 205
Common antilogarithms sample problems involving      195
Common antilogarithms table of      204 205
Common logarithms      23 194 202 203
Common logarithms computations using      196
Common logarithms sample problems involving      194
Common logarithms table of      202 203
Commutative law, for dot products      118
Commutative law, for vector addition      117
Complement      20
Complementary error function      183
Complex conjugate      21
Complex inversion formula      161
complex numbers      21 22 25
Complex numbers addition of      21
Complex numbers amplitude of      22
Complex numbers conjugate      21
Complex numbers definitions involving      21
Complex numbers division of      21 25
Complex numbers graphs of      22
Complex numbers imaginary part of      21
Complex numbers logarithms of      25
Complex numbers modulus of      22
Complex numbers multiplication of      21 25
Complex numbers polar form of      22 25

Complex numbers real part of      21
Complex numbers roots of      22 25
Complex numbers subtraction of      21
Complex numbers vector representation of      22
Component vectors      117
Components of a vector      117
Compound amount, table of      240
Cone right circular      see “Right circular cone”
Cone, elliptic      51
Confocal ellipses      127
Confocal ellipses ellipsoidal coordinates      130
Confocal ellipses hyperbolas      127
Confocal ellipses parabolas      126
Confocal ellipses paraboloidal coordinates      130
Conical coordinates      129
Conical coordinates Laplacian in      129
Conies      see also “Ellipse Parabola Hyperbola” 37
Conjugate, complex      21
Constant of integration      57
Convergence factors, table of      192
Convergence of Fourier series      131
Convergence, interval of      110
Coordinate curves      124
Coordinate curves system      11
Coordinates curvilinear, cylindrical      49 126
Coordinates curvilinear, polar      22 36
Coordinates curvilinear, rectangular      36 117
Coordinates curvilinear, rotation of      36 49
Coordinates curvilinear, special orthogonal      126—130
Coordinates curvilinear, spherical      50 126
Coordinates curvilinear, transformation of      36 48 49
Coordinates curvilinear, translation of      36 49
Coordinates, curvilinear      124—130
Cosine integral      184
Cosine integral Fresnel      184
Cosine integral table of values for      251
Cosines, law of for plane triangles      19
Cosines, law of for spherical triangles      19
Counterclockwise      11
Cross or vector product      118
Cube roots, table of      238 239
Cube, duplication of      45
Cubes, table of      238 239
Cubic equation, solution of      32
Curl      120
Curl in curvilinear coordinates      125
Curtate cycloid      42
Curves, coordinate      124
Curves, coordinate special plane      40—45
Curvilinear coordinates      124 125
Curvilinear coordinates orthogonal      124—130
Cycloid      40 42
Cycloid curtate      42
Cycloid prolate      42
Cylinder, elliptic      51
Cylinder, elliptic lateral surface area of      8 9
Cylinder, elliptic volume of      8 9
Cylindrical coordinates      49 126
Cylindrical coordinates Laplacian in      126
Definite integrals      94—100
Definite integrals approximate formulas for      95
Definite integrals definition of      94
Definite integrals general formulas involving      94 95
Definite integrals table of      95—100
DEGREES      1 199 200
Degrees conversion of to radians      199 200 223
Degrees relationship of to radians      12 199 200
Del operator      119
Del operator miscellaneous formulas involving      120
Delta function      170
DeMoivre's theorem      22 25
derivatives      see also “Differentiation” 53—56
Derivatives anti-      57
Derivatives chain rule for      53
Derivatives definition of      53
Derivatives higher      55
Derivatives of elliptic functions      181
Derivatives of exponential and logarithmic functions      54
Derivatives of hyperbolic and inverse hyperbolic functions      54 55
Derivatives of trigonometric and inverse trigonometric functions      54
Derivatives of vectors      119
Derivatives partial      56
Descartes, folium of      43
Differential equations, solutions of basic      104—106
Differentials      55
Differentials rules for      56
Differentiation      see also “Derivatives” 53
Differentiation general rules for      53
Differentiation of integrals      95
Diocles, cissoid of      45
Direction cosines      46 47
Direction cosines numbers      46 48
Directrix      37
Discriminant      32
Distance, between two points in a plane      34
Distance, between two points in space      46
Distance, from a point to a line      35
Distance, from a point to a plane      48
Distributions, probability      189
Distributive law      117
Distributive law for dot products      118
Divergence      119
Divergence in curvilinear coordinates      125
Divergence theorem      123
Dot or scalar product      117 118
Double angle formulas, for hyperbolic functions      27
Double angle formulas, for trigonometric functions      16
Double integrals      122
Duplication formula for gamma functions      102
Duplication of cube      45
Eccentricity, definition of      37
Eccentricity, of ellipse      38
Eccentricity, of hyperbola      39
Eccentricity, of parabola      37
ellipse      7 37 38
Ellipse area of      7
Ellipse eccentricity of      38
Ellipse equation of      37 38
Ellipse evolute of      44
Ellipse focus of      38
Ellipse perimeter of      7
Ellipse semi-major and-minor axes of      7 38
Ellipses, confocal      127
Ellipsoid, equation of      51
Ellipsoid, volume of      10
Elliptic cone      51
Elliptic cone cylinder      51
Elliptic cone paraboloid      52
Elliptic cylindrical coordinates      127
Elliptic cylindrical coordinates Laplacian in      127
Elliptic functions      see also “Elliptic integrals” 179—182
Elliptic functions addition formulas for      180
Elliptic functions derivatives of      181
Elliptic functions identities involving      181
Elliptic functions integrals of      182
Elliptic functions Jacobi's      180
Elliptic functions periods of      181
Elliptic functions series expansions for      181
Elliptic functions special values of      182
Elliptic integrals      see also “Elliptic functions” 179 180
Elliptic integrals amplitude of      179
Elliptic integrals Landen's transformation for      180
Elliptic integrals Legendre's relation for      182
Elliptic integrals of the first kind      179
Elliptic integrals of the second kind      179
Elliptic integrals of the third kind      179 180
Elliptic integrals table of values for      254 255
Envelope      44
Epicycloid      42
Equation of line      34

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