| Description |
1 online resource (xxiv, 410 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
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text file |
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PDF |
| Bibliography |
Includes bibliographical references (pages 397-399) and index. |
| Access |
Use copy Restrictions unspecified star MiAaHDL |
| Reproduction |
Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2011. MiAaHDL |
| System Details |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
| Processing Action |
digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Note |
Print version record. |
| Summary |
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse. |
| Contents |
0 Quick Reference List of Frequently Used Data -- 0.1 Useful Identities 1 -- 0.2 Complex Relationships 2 -- 0.3 Constants 2 -- 0.4 Derivatives of Elementary Functions 3 -- 0.5 Rules of Differentiation and Integration 3 -- 0.6 Standard Integrals 4 -- 0.7 Standard Series 11 -- 0.8 Geometry 13 -- 1 Numerical, Algebraic, and Analytical Results for Series and Calculus -- 1.1 Algebraic Results Involving Real and Complex Numbers 25 -- 1.2 Finite Sums 29 -- 1.3 Bernoulli and Euler Numbers and Polynomials 37 -- 1.4 Determinants 47 -- 1.5 Matrices 55 -- 1.6 Permutations and Combinations 62 -- 1.7 Partial Fraction Decomposition 63 -- 1.8 Convergence of Series 66 -- 1.9 Infinite Products 71 -- 1.10 Functional Series 73 -- 1.11 Power Series 74 -- 1.12 Taylor Series 79 -- 1.13 Fourier Series 81 -- 1.14 Asymptotic Expansions 85 -- 1.15 Basic Results from the Calculus 86 -- 2 Functions and Identities -- 2.1 Complex Numbers and Trigonometric and Hyperbolic Functions 101 -- 2.2 Logarithms and Exponentials 112 -- 2.3 The Exponential Function 114 -- 2.4 Trigonometric Identities 115 -- 2.5 Hyperbolic Identities 121 -- 2.6 The Logarithm 126 -- 2.7 Inverse Trigonometric and Hyperbolic Functions 128 -- 2.8 Series Representations of Trigonometric and Hyperbolic Functions 133 -- 2.9 Useful Limiting Values and Inequalities Involving Elementary Functions 136 -- 3 Derivatives of Elementary Functions -- 3.1 Derivatives of Algebraic, Logarithmic, and Exponential Functions 139 -- 3.2 Derivatives of Trigonometric Functions 140 -- 3.3 Derivatives of Inverse Trigonometric Functions 140 -- 3.4 Derivatives of Hyperbolic Functions 141 -- 3.5 Derivatives of Inverse Hyperbolic Functions 142 -- 4 Indefinite Integrals of Algebraic Functions -- 4.1 Algebraic and Transcendental Functions 145 -- 4.2 Indefinite Integrals of Rational Functions 146 -- 4.3 Nonrational Algebraic Functions 158 -- 5 Indefinite Integrals of Exponential Functions -- 5.1 Basic Results 167 -- 6 Indefinite Integrals of Logarithmic Functions -- 6.1 Combinations of Logarithms and Polynomials 173 -- 7 Indefinite Integrals of Hyperbolic Functions -- 7.1 Basic Results 179 -- 7.2 Integrands Involving Powers of sinh(bx) or cosh(bx) 180 -- 7.3 Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) 181 -- 7.4 Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x 183 -- 7.5 Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x 183 -- 7.6 Integrands Involving (1 [plus or minus] cosh x)[superscript -m] 185 -- 7.7 Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x 185 -- 7.8 Integrands Involving sinh(ax + b) and cosh(cx + d) 186 -- 7.9 Integrands Involving tanh kx and coth kx 188 -- 7.10 Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx 189 -- 8 Indefinite Integrals Involving Inverse Hyperbolic Functions -- 8.1 Basic Results 191 -- 8.2 Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) 193 -- 8.3 Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) 194 -- 8.4 Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) 195 -- 9 Indefinite Integrals of Trigonometric Functions -- 9.1 Basic Results 197 -- 9.2 Integrands Involving Powers of x and Powers of sin x or cos x 197 -- 9.3 Integrands Involving tan x and/or cot x 205 -- 9.4 Integrands Involving sin x and cos x 207 -- 9.5 Integrands Involving Sines and Cosines with Linear Arguments and Powers of x 211 -- 10 Indefinite Integrals of Inverse Trigonometric Functions -- 10.1 Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions 215 -- 11 The Gamma, Beta, Pi, and Psi Functions -- 11.1 The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) 221 -- 12 Elliptic Integrals and Functions -- 12.1 Elliptic Integrals 229 -- 12.2 Jacobian Elliptic Functions 235 -- 12.3 Derivatives and Integrals 237 -- 12.4 Inverse Jacobian Elliptic Functions 237 -- 13 Probability Integrals and the Error Function -- 13.1 Normal Distribution 239 -- 13.2 The Error Function 242 -- 14 Fresnel Integrals, Sine and Cosine Integrals -- 14.1 Definitions, Series Representations, and Values at Intinity 245 -- 14.2 Definitions, Series Representations, and Values at Infinity 247 -- 15 Definite Integrals -- 15.1 Integrands Involving Powers of x 249 -- 15.2 Integrands Involving Trigonometric Functions 251 -- 15.3 Integrands Involving the Exponential Function 254 -- 15.4 Integrands Involving the Hyperbolic Function 256 -- 15.5 Integrands Involving the Logarithmic Function 256 -- 16 Different Forms of Fourier Series -- 16.1 Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] 257 -- 16.2 Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 258 -- 16.3 Fourier Series for f(x) on a [less than or equal] x [less than or equal] b 258 -- 16.4 Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 259 -- 16.5 Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L 259 -- 16.6 Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] 260 -- 16.7 Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L 260 -- 16.8 Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] 260 -- 16.9 Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L 261 -- 16.10 Representative Examples of Fourier Series 261 -- 16.11 Fourier Series and Discontinuous Functions 265 -- 17 Bessel Functions -- 17.1 Bessel's Differential Equation 269 -- 17.2 Series Expansions for J[subscript v](x) and Y[subscript v](x) 270 -- 17.3 Bessel Functions of Fractional Order 272 -- 17.4 Asymptotic Representations for Bessel Functions 273 -- 17.5 Zeros of Bessel Functions 273 -- 17.6 Bessel's Modified Equation 274 -- 17.7 Series Expansions for I[subscript v](x) and K[subscript v](x) 276 -- 17.8 Modified Bessel Functions of Fractional Order 277 -- 17.9 Asymptotic Representations of Modified Bessel Functions 278 -- 17.10 Relationships between Bessel Functions 278 -- 17.11 Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) 281 -- 17.12 Indefinite Integrals of Bessel Functions 281 -- 17.13 Definite Integrals Involving Bessel Functions 282 -- 17.14 Spherical Bessel Functions 283 -- 18 Orthogonal Polynomials -- 18.2 Legendre Polynomials P[subscript n](x) 286 -- 18.3 Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) 290 -- 18.4 Laguerre Polynomials L[subscript n](x) 294 -- 18.5 Hermite Polynomials H[subscript n](x) 296 -- 19 Laplace Transformation -- 20 Fourier Transforms -- 21 Numerical Integration -- 21.1 Classical Methods 315 -- 22 Solutions of Standard Ordinary Differential Equations -- 22.2 Separation of Variables 323 -- 22.3 Linear First-Order Equations 323 -- 22.4 Bernoulli's Equation 324 -- 22.5 Exact Equations 325 -- 22.6 Homogeneous Equations 325 -- 22.7 Linear Differential Equations 326 -- 22.8 Constant Coefficient Linear Differential Equations -- Homogeneous Case 327 -- 22.9 Linear Homogeneous Second-Order Equation 330 -- 22.10 Constant Coefficient Linear Differential Equations -- Inhomogeneous Case 331 -- 22.11 Linear Inhomogeneous Second-Order Equation 333 -- 22.12 Determination of Particular Integrals by the Method of Undetermined Coefficients 334 -- 22.13 The Cauchy-Euler Equation 336 -- 22.14 Legendre's Equation 337 -- 22.15 Bessel's Equations 337 -- 22.16 Power Series and Frobenius Methods 339 -- 22.17 The Hypergeometric Equation 344 -- 22.18 Numerical Methods 345 -- 23 Vector Analysis -- 23.1 Scalars and Vectors 353 -- 23.2 Scalar Products 358 -- 23.3 Vector Products 359 -- 23.4 Triple Products 360 -- 23.5 Products of Four Vectors 361 |
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-- 23.6 Derivatives of Vector Functions of a Scalar t 361 -- 23.7 Derivatives of Vector Functions of Several Scalar Variables 362 -- 23.8 Integrals of Vector Functions of a Scalar Variable t 363 -- 23.9 Line Integrals 364 -- 23.10 Vector Integral Theorems 366 -- 23.11 A Vector Rate of Change Theorem 368 -- 23.12 Useful Vector Identities and Results 368 -- 24 Systems of Orthogonal Coordinates -- 24.1 Curvilinear Coordinates 369 -- 24.2 Vector Operators in Orthogonal Coordinates 371 -- 24.3 Systems of Orthogonal Coordinates 371 -- 25 Partial Differential Equations and Special Functions -- 25.1 Fundamental Ideas 381 -- 25.2 Method of Separation of Variables 385 -- 25.3 The Sturm-Liouville Problem and Special Functions 387 -- 25.4 A First-Order System and the Wave Equation 390 -- 25.5 Conservation Equations (Laws) 391 -- 25.6 The Method of Characteristics 392 -- 25.7 Discontinuous Solutions (Shocks) 396 -- 25.8 Similarity Solutions 398 -- 25.9 Burgers's Equation, the KdV Equation, and the KdVB Equation 400 -- 26 The z-Transform -- 26.1 The z-Transform and Transform Pairs 403 -- 27 Numerical Approximation -- 27.2 Economization of Series 411 -- 27.3 Pade Approximation 413 -- 27.4 Finite Difference Approximations to Ordinary and Partial Derivatives 415. |
| Language |
English. |
| Subject |
Mathematics -- Tables.
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Mathematics -- Formulae.
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Mathématiques -- Tables.
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Mathématiques -- Formules.
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formulas (algorithms)
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Mathematics
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| Indexed Term |
Mathematics |
| Genre/Form |
tables (documents)
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Tables (Data)
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Mathematical formulae
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Tables
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Tables (Data)
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Tables (Données)
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| Added Title |
Mathematical formulas and integrals |
| Other Form: |
Print version: Jeffrey, Alan. Handbook of mathematical formulas and integrals. San Diego : Academic Press, ©1995 (DLC) 95002344 (OCoLC)31969977 |
| ISBN |
0123825806 (electronic bk.) |
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9780123825803 (electronic bk.) |
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0080523013 |
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9780080523019 |
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9781483295145 (e-book) |
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1483295141 |
| Standard No. |
GBVCP 825899648 |
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NZ1 15918648 |
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