Handbook of Mathematical Formulas and Integrals

ISBN-10: 0123825806
ISBN-13: 9780123825803
Edition: 2nd 2000
Authors: Alan Jeffrey
List price: $30.00
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Description: 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  More...

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Book details

List price: $30.00
Edition: 2nd
Copyright year: 2000
Publisher: Elsevier Science & Technology Books
Publication date: 9/13/1995
Binding: Paperback
Pages: 410
Size: 7.50" wide x 9.25" long x 1.00" tall
Weight: 1.738
Language: English

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. Special thumb-tab index throughout the book for ease of use Answers are keyed to the type of problem they solve Formulas are provided for problems across the entire spectrum of Mathematics All equations are sent from a computer-checked source code Companion to Gradshteyn: Table of Integrals, Series, and Products, Fifth Edition The following features make the Handbook a Better Value than its Competition: Less expensive More comprehensive Equations are computer-validated with Scientific WorkPlace(tm) and Mathematica(r) Superior quality from one of the most respected names in scientific and technical publishing Offers unique thumb-tab indexing throughout the book which makes finding answers quick and easy

Preface
Preface to the Second Edition
Index of Special Functions and Notations
Quick Reference List of Frequently Used Data
Useful Identities
Complex Relationships
Constants
Derivatives of Elementary Functions
Rules of Differentiation and Integration
Standard Integrals
Standard Series
Geometry
Numerical, Algebraic, and Analytical Results for Series and Calculus
Algebraic Results Involving Real and Complex Numbers
Finite Sums
Bernoulli and Euler Numbers and Polynomials
Determinants
Matrices
Permutations and Combinations
Partial Fraction Decomposition
Convergence of Series
Infinite Products
Functional Series
Power Series
Taylor Series
Fourier Series
Asymptotic Expansions
Basic Results from the Calculus
Functions and Identities
Complex Numbers and Trigonometric and Hyperbolic Functions
Logarithms and Exponentials
The Exponential Function
Trigonometric Identities
Hyperbolic Identities
The Logarithm
Inverse Trigonometric and Hyperbolic Functions
Series Representations of Trigonometric and Hyperbolic Functions
Useful Limiting Values and Inequalities Involving Elementary Functions
Derivatives of Elementary Functions
Derivatives of Algebraic, Logarithmic, and Exponential Functions
Derivatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Hyperbolic Functions
Derivatives of Inverse Hyperbolic Functions
Indefinite Integrals of Algebraic Functions
Algebraic and Transcendental Functions
Indefinite Integrals of Rational Functions
Nonrational Algebraic Functions
Indefinite Integrals of Exponential Functions
Basic Results
Indefinite Integrals of Logarithmic Functions
Combinations of Logarithms and Polynomials
Indefinite Integrals of Hyperbolic Functions
Basic Results
Integrands Involving Powers of sinh(bx) or cosh(bx)
Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx)
Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x
Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x
Integrands Involving (1 [plus or minus] cosh x)[superscript -m]
Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x
Integrands Involving sinh(ax + b) and cosh(cx + d)
Integrands Involving tanh kx and coth kx
Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx
Indefinite Integrals Involving Inverse Hyperbolic Functions
Basic Results
Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a)
Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a)
Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a)
Indefinite Integrals of Trigonometric Functions
Basic Results
Integrands Involving Powers of x and Powers of sin x or cos x
Integrands Involving tan x and/or cot x
Integrands Involving sin x and cos x
Integrands Involving Sines and Cosines with Linear Arguments and Powers of x
Indefinite Integrals of Inverse Trigonometric Functions
Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions
The Gamma, Beta, Pi, and Psi Functions
The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x)
Elliptic Integrals and Functions
Elliptic Integrals
Jacobian Elliptic Functions
Derivatives and Integrals
Inverse Jacobian Elliptic Functions
Probability Integrals and the Error Function
Normal Distribution
The Error Function
Fresnel Integrals, Sine and Cosine Integrals
Definitions, Series Representations, and Values at Intinity
Definitions, Series Representations, and Values at Infinity
Definite Integrals
Integrands Involving Powers of x
Integrands Involving Trigonometric Functions
Integrands Involving the Exponential Function
Integrands Involving the Hyperbolic Function
Integrands Involving the Logarithmic Function
Different Forms of Fourier Series
Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi]
Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L
Fourier Series for f(x) on a [less than or equal] x [less than or equal] b
Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi]
Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L
Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi]
Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L
Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi]
Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L
Representative Examples of Fourier Series
Fourier Series and Discontinuous Functions
Bessel Functions
Bessel's Differential Equation
Series Expansions for J[subscript v](x) and Y[subscript v](x)
Bessel Functions of Fractional Order
Asymptotic Representations for Bessel Functions
Zeros of Bessel Functions
Bessel's Modified Equation
Series Expansions for I[subscript v](x) and K[subscript v](x)
Modified Bessel Functions of Fractional Order
Asymptotic Representations of Modified Bessel Functions
Relationships between Bessel Functions
Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x)
Indefinite Integrals of Bessel Functions
Definite Integrals Involving Bessel Functions
Spherical Bessel Functions
Orthogonal Polynomials
Introduction
Legendre Polynomials P[subscript n](x)
Chebyshev Polynomials T[subscript n](x) and U[subscript n](x)
Laguerre Polynomials L[subscript n](x)
Hermite Polynomials H[subscript n](x)
Laplace Transformation
Introduction
Fourier Transforms
Introduction
Numerical Integration
Classical Methods
Solutions of Standard Ordinary Differential Equations
Introduction
Separation of Variables
Linear First-Order Equations
Bernoulli's Equation
Exact Equations
Homogeneous Equations
Linear Differential Equations
Constant Coefficient Linear Differential Equations--Homogeneous Case
Linear Homogeneous Second-Order Equation
Constant Coefficient Linear Differential Equations--Inhomogeneous Case
Linear Inhomogeneous Second-Order Equation
Determination of Particular Integrals by the Method of Undetermined Coefficients
The Cauchy-Euler Equation
Legendre's Equation
Bessel's Equations
Power Series and Frobenius Methods
The Hypergeometric Equation
Numerical Methods
Vector Analysis
Scalars and Vectors
Scalar Products
Vector Products
Triple Products
Products of Four Vectors
Derivatives of Vector Functions of a Scalar t
Derivatives of Vector Functions of Several Scalar Variables
Integrals of Vector Functions of a Scalar Variable t
Line Integrals
Vector Integral Theorems
A Vector Rate of Change Theorem
Useful Vector Identities and Results
Systems of Orthogonal Coordinates
Curvilinear Coordinates
Vector Operators in Orthogonal Coordinates
Systems of Orthogonal Coordinates
Partial Differential Equations and Special Functions
Fundamental Ideas
Method of Separation of Variables
The Sturm-Liouville Problem and Special Functions
A First-Order System and the Wave Equation
Conservation Equations (Laws)
The Method of Characteristics
Discontinuous Solutions (Shocks)
Similarity Solutions
Burgers's Equation, the KdV Equation, and the KdVB Equation
The z-Transform
The z-Transform and Transform Pairs
Numerical Approximation
Introduction
Economization of Series
Pade Approximation
Finite Difference Approximations to Ordinary and Partial Derivatives
Short Classified Reference List
Index

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