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Spiegel M.R. — Mathematical Handbook of Formulas and Tables
Spiegel M.R. — Mathematical Handbook of Formulas and Tables

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Название: Mathematical Handbook of Formulas and Tables

Автор: Spiegel M.R.

Аннотация:

Book Description
This handbook is unusual in that it combines in a single volume formulas and tables from both elementary and advanced mathematics. For example, topics treated range from those in algebra, geometry, trigonometry, analytic geometry and calculus to Fourier series, Laplace and Fourier transforms, Bessel and Legendre functions and many other advanced special functions. Such topics are needed by both students and research workers in the fields of engineering, physics, mathematics and other sciences.

From the Back Cover

Students love Schaum's Outlines! Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use Schaum's!

If you don't have a lot of time but want to excel in class, this book helps you:

* Brush up before tests
* Find answers fast
* Learn key formulas and tables
* Study quickly and more effectively

Schaum's Outlines give you the information teachers expect you to know in a handy and succinct format­­without overwhelming you with unnecessary detail. You get a complete overview of the subject, plus plenty of practice exercises to test your skill. Compatible with any classroom text, Schaum's let you study at your own pace and reminds you of all the important facts you need to remember­­fast! And Schaum's are so complete, they're perfect for preparing for graduate or professionalexams!

Inside, you will find:

* More than 2400 formulas and tables
* Clear and concise explanations of all results
* Formulas and tables for elementary to advanced topics
* Complete index to all topics

If you want top grades and easy-to-use information for your math and science courses, this powerful study tool and reference is the best guide you can have!


Язык: en

Рубрика: Математика/Справочники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1968

Количество страниц: 271

Добавлена в каталог: 21.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
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      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      149 150
Associated Legendre functions of the first kind      149
Associated Legendre functions of the second kind      150
Associated Legendre functions, generating function for      149
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
Base of logarithms, definition of      140
Base of logarithms, differential equation for      141
Base of logarithms, graphs of      141
Ber and Bei functions      140 141
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 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, 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, 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 of first kind      157
Chebyshev polynomials of second kind      158
Chebyshev polynomials, generating functions for      157 158
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
Cissoid of Diocles      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, 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      37 (see also “Ellipse” “Parabola” “Hyperbola”)
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 system      11
Coordinates spherical      50 126
Coordinates, curvilinear      124—130
Coordinates, cylindrical      49 126
Coordinates, polar      22 36
Coordinates, rectangular      36 117
Coordinates, rotation of      36 49
Coordinates, special orthogonal      126—130
Coordinates, transformation of      36 48 49
Coordinates, translation of      36 49
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, 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, lateral surface area of      8 9
Cylinder, 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      53—56 (see also “Differentiation”)
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, anti-      57
Derivatives, chain rule for      53
Derivatives, definition of      53
Derivatives, higher      55
Derivatives, partial      56
Descartes, folium of      43
Differential equations, solutions of basic      104-106
Differentials      55
Differentials of integrals      95
Differentials, rules for      56
Differentiation      53 (see also “Derivatives”)
Differentiation, general rules for      53
Diocles cissoid of      45
Direction cosines      46 47
Direction 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 of ellipse      38
Eccentricity of hyperbola      39
Eccentricity of parabola      37
Eccentricity, definition of      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 cylinder      51
Elliptic cylindrical coordinates      127
Elliptic cylindrical coordinates, Laplacian in      127
Elliptic functions      179—182 (see also “Elliptic integrals”)
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      179 180
Elliptic integrals of the first kind      179
Elliptic integrals of the second kind      179
Elliptic integrals of the third kind      179 180
Elliptic integrals, amplitude of      179
Elliptic integrals, Landen's transformation for      180
Elliptic integrals, Legendre's relation for      182
Elliptic integrals, table of values for      254 255
Elliptic paraboloid      52
Envelope      44
Epicycloid      42
Equation of line      34
Equation of line in parametric form      47
Equation of line in standard form      47
Equation of line perpendicular to plane      48
Equation of line, general      35
Equation of line, intercept form for      34
Equation of line, normal form for      35
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