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Preface | |

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Preface to the Second Edition | |

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Index of Special Functions and Notations | |

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Quick Reference List of Frequently Used Data | |

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Useful Identities | |

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Complex Relationships | |

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Constants | |

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Derivatives of Elementary Functions | |

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Rules of Differentiation and Integration | |

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Standard Integrals | |

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Standard Series | |

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Geometry | |

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Numerical, Algebraic, and Analytical Results for Series and Calculus | |

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Algebraic Results Involving Real and Complex Numbers | |

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Finite Sums | |

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Bernoulli and Euler Numbers and Polynomials | |

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Determinants | |

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Matrices | |

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Permutations and Combinations | |

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Partial Fraction Decomposition | |

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Convergence of Series | |

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Infinite Products | |

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Functional Series | |

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Power Series | |

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Taylor Series | |

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Fourier Series | |

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Asymptotic Expansions | |

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Basic Results from the Calculus | |

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Functions and Identities | |

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Complex Numbers and Trigonometric and Hyperbolic Functions | |

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Logarithms and Exponentials | |

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The Exponential Function | |

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Trigonometric Identities | |

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Hyperbolic Identities | |

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The Logarithm | |

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Inverse Trigonometric and Hyperbolic Functions | |

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Series Representations of Trigonometric and Hyperbolic Functions | |

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Useful Limiting Values and Inequalities Involving Elementary Functions | |

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Derivatives of Elementary Functions | |

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Derivatives of Algebraic, Logarithmic, and Exponential Functions | |

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Derivatives of Trigonometric Functions | |

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Derivatives of Inverse Trigonometric Functions | |

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Derivatives of Hyperbolic Functions | |

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Derivatives of Inverse Hyperbolic Functions | |

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Indefinite Integrals of Algebraic Functions | |

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Algebraic and Transcendental Functions | |

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Indefinite Integrals of Rational Functions | |

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Nonrational Algebraic Functions | |

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Indefinite Integrals of Exponential Functions | |

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Basic Results | |

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Indefinite Integrals of Logarithmic Functions | |

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Combinations of Logarithms and Polynomials | |

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Indefinite Integrals of Hyperbolic Functions | |

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Basic Results | |

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Integrands Involving Powers of sinh(bx) or cosh(bx) | |

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Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) | |

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Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x | |

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Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x | |

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Integrands Involving (1 [plus or minus] cosh x)[superscript -m] | |

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Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x | |

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Integrands Involving sinh(ax + b) and cosh(cx + d) | |

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Integrands Involving tanh kx and coth kx | |

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Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx | |

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Indefinite Integrals Involving Inverse Hyperbolic Functions | |

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Basic Results | |

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Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) | |

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Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) | |

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Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) | |

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Indefinite Integrals of Trigonometric Functions | |

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Basic Results | |

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Integrands Involving Powers of x and Powers of sin x or cos x | |

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Integrands Involving tan x and/or cot x | |

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Integrands Involving sin x and cos x | |

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Integrands Involving Sines and Cosines with Linear Arguments and Powers of x | |

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Indefinite Integrals of Inverse Trigonometric Functions | |

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Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions | |

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The Gamma, Beta, Pi, and Psi Functions | |

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The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) | |

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Elliptic Integrals and Functions | |

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Elliptic Integrals | |

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Jacobian Elliptic Functions | |

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Derivatives and Integrals | |

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Inverse Jacobian Elliptic Functions | |

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Probability Integrals and the Error Function | |

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Normal Distribution | |

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The Error Function | |

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Fresnel Integrals, Sine and Cosine Integrals | |

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Definitions, Series Representations, and Values at Intinity | |

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Definitions, Series Representations, and Values at Infinity | |

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Definite Integrals | |

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Integrands Involving Powers of x | |

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Integrands Involving Trigonometric Functions | |

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Integrands Involving the Exponential Function | |

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Integrands Involving the Hyperbolic Function | |

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Integrands Involving the Logarithmic Function | |

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Different Forms of Fourier Series | |

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Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] | |

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Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L | |

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Fourier Series for f(x) on a [less than or equal] x [less than or equal] b | |

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Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] | |

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Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L | |

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Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] | |

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Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L | |

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Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] | |

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Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L | |

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Representative Examples of Fourier Series | |

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Fourier Series and Discontinuous Functions | |

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Bessel Functions | |

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Bessel's Differential Equation | |

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Series Expansions for J[subscript v](x) and Y[subscript v](x) | |

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Bessel Functions of Fractional Order | |

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Asymptotic Representations for Bessel Functions | |

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Zeros of Bessel Functions | |

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Bessel's Modified Equation | |

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Series Expansions for I[subscript v](x) and K[subscript v](x) | |

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Modified Bessel Functions of Fractional Order | |

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Asymptotic Representations of Modified Bessel Functions | |

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Relationships between Bessel Functions | |

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Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) | |

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Indefinite Integrals of Bessel Functions | |

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Definite Integrals Involving Bessel Functions | |

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Spherical Bessel Functions | |

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Orthogonal Polynomials | |

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Introduction | |

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Legendre Polynomials P[subscript n](x) | |

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Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) | |

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Laguerre Polynomials L[subscript n](x) | |

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Hermite Polynomials H[subscript n](x) | |

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Laplace Transformation | |

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Introduction | |

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Fourier Transforms | |

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Introduction | |

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Numerical Integration | |

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Classical Methods | |

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Solutions of Standard Ordinary Differential Equations | |

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Introduction | |

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Separation of Variables | |

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Linear First-Order Equations | |

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Bernoulli's Equation | |

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Exact Equations | |

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Homogeneous Equations | |

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Linear Differential Equations | |

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Constant Coefficient Linear Differential Equations--Homogeneous Case | |

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Linear Homogeneous Second-Order Equation | |

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Constant Coefficient Linear Differential Equations--Inhomogeneous Case | |

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Linear Inhomogeneous Second-Order Equation | |

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Determination of Particular Integrals by the Method of Undetermined Coefficients | |

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The Cauchy-Euler Equation | |

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Legendre's Equation | |

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Bessel's Equations | |

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Power Series and Frobenius Methods | |

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The Hypergeometric Equation | |

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Numerical Methods | |

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Vector Analysis | |

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Scalars and Vectors | |

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Scalar Products | |

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Vector Products | |

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Triple Products | |

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Products of Four Vectors | |

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Derivatives of Vector Functions of a Scalar t | |

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Derivatives of Vector Functions of Several Scalar Variables | |

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Integrals of Vector Functions of a Scalar Variable t | |

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Line Integrals | |

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Vector Integral Theorems | |

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A Vector Rate of Change Theorem | |

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Useful Vector Identities and Results | |

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Systems of Orthogonal Coordinates | |

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Curvilinear Coordinates | |

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Vector Operators in Orthogonal Coordinates | |

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Systems of Orthogonal Coordinates | |

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Partial Differential Equations and Special Functions | |

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Fundamental Ideas | |

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Method of Separation of Variables | |

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The Sturm-Liouville Problem and Special Functions | |

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A First-Order System and the Wave Equation | |

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Conservation Equations (Laws) | |

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The Method of Characteristics | |

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Discontinuous Solutions (Shocks) | |

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Similarity Solutions | |

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Burgers's Equation, the KdV Equation, and the KdVB Equation | |

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The z-Transform | |

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The z-Transform and Transform Pairs | |

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Numerical Approximation | |

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Introduction | |

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Economization of Series | |

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Pade Approximation | |

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Finite Difference Approximations to Ordinary and Partial Derivatives | |

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Short Classified Reference List | |

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Index | |