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Formal Sciences
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Mathematics
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Handbook of Mathematical Formulas and Integrals |
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Quick Reference List of Frequently Used Data:Useful Identities
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Numerical, Algebraic, and Analytical Results for Series and Calculus:Finite Sums, Determinants
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Functions and Identities:Logorithms and Exponentials, Trigonometric Identities
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Derivatives of Elementary Functions:Derivatives of Inverse Hyperbolic Functions
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Indefinite Integrals of Algebraic Functions:Algebraic and Transcendental Functions
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Indefinite Integrals of Exponential Functions:Basic Results, Indefinite Integrals Involving eax
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Indefinite Integrals of Logarithmic Functions:Combinations of Logarithms and Polynomials, The Logarithm
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Indefinite Integrals of Hyperbolic Functions:Basic Results, Integrands Involving tanh kx and coth kx
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Indefinite Integrals Involving Inverse Hyperbolic Functions:Basic Results
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Indefinite Integrals of Trigonometric Functions:Integrands Involving tan x and/or cot x
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Indefinite Integrals of Inverse Trigonometric Functions:Integrands Involving xn arcsinm(x/a)
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The Gamma, Beta, Pi, and Psi Functions, and the Incomplete Gamma Functions:Definitions and Notation
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Elliptic Integrals and Functions:Elliptic Integrals, Legendre Normal Forms, Jacobian Elliptic Functions
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Probability Distributions and Integrals, and the Error Function:Distributions, The Error Function
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Fresnel Integrals, Sine and Cosine Integrals:The Fresnel Integrals, Sine and Cosine Integrals
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Definite Integrals:Integrands Involving Trigonometric Functions
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Different Forms of Fourier Series:Fourier Series and Discontinuous Functions
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Bessel Functions:Bessel’s Differential Equation, Zeros of Bessel Functions
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Orthogonal Polynomials:Legendre Polynomials Pn(x), Hermite Polynomials Hn(x)
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Laplace Transformation:Definition of the Laplace Transform, Laplace Transform Pairs
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Fourier Transforms:Fourier Exponential Transform, Fourier Cosine and Sine Transform Pairs
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Numerical Integration:Classical Methods, Open- and Closed-Type Formulas
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Solutions of Standard Ordinary Differential Equations:Basic Definitions, Exact Equations
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Vector Analysis:Scalars and Vectors, Triple Products, Products of Four Vectors
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Systems of Orthogonal Coordinates:Curvilinear Coordinates, Systems of Orthogonal Coordinates
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Partial Differential Equations and Special Functions:Fundamental Ideas, The Method of Characteristics
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Qualitative Properties of the Heat and Laplace Equation
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Solutions of Elliptic, Parabolic, and Hyperbolic Equations:Hyperbolic Equations
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The z-Transform:The z-Transform and Transform Pairs
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Numerical Approximation:Linear Interpolation, Lagrange Polynomial Interpolation
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Conformal Mapping and Boundary Value Problems:Boundary Value Problems
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Short Classified Reference List:General Tables of Integrals, General Reading
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Index
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