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Laplace Transformation:Definition of the Laplace Transform, Laplace Transform Pairs

<< Orthogonal Polynomials:Legendre Polynomials Pn(x), Hermite Polynomials Hn(x)
Fourier Transforms:Fourier Exponential Transform, Fourier Cosine and Sine Transform Pairs >>



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Table of Contents:
  1. Numerical, Algebraic, and Analytical Results for Series and Calculus:Finite Sums, Determinants
  2. Functions and Identities:Logorithms and Exponentials, Trigonometric Identities
  3. Derivatives of Elementary Functions:Derivatives of Inverse Hyperbolic Functions
  4. Indefinite Integrals of Algebraic Functions:Algebraic and Transcendental Functions
  5. Indefinite Integrals of Exponential Functions:Basic Results, Indefinite Integrals Involving eax
  6. Indefinite Integrals of Logarithmic Functions:Combinations of Logarithms and Polynomials, The Logarithm
  7. Indefinite Integrals of Hyperbolic Functions:Basic Results, Integrands Involving tanh kx and coth kx
  8. Indefinite Integrals Involving Inverse Hyperbolic Functions:Basic Results
  9. Indefinite Integrals of Trigonometric Functions:Integrands Involving tan x and/or cot x
  10. Indefinite Integrals of Inverse Trigonometric Functions:Integrands Involving xn arcsinm(x/a)
  11. The Gamma, Beta, Pi, and Psi Functions, and the Incomplete Gamma Functions:Definitions and Notation
  12. Elliptic Integrals and Functions:Elliptic Integrals, Legendre Normal Forms, Jacobian Elliptic Functions
  13. Probability Distributions and Integrals, and the Error Function:Distributions, The Error Function
  14. Fresnel Integrals, Sine and Cosine Integrals:The Fresnel Integrals, Sine and Cosine Integrals
  15. Definite Integrals:Integrands Involving Trigonometric Functions
  16. Different Forms of Fourier Series:Fourier Series and Discontinuous Functions
  17. Bessel Functions:Bessel’s Differential Equation, Zeros of Bessel Functions
  18. Orthogonal Polynomials:Legendre Polynomials Pn(x), Hermite Polynomials Hn(x)
  19. Laplace Transformation:Definition of the Laplace Transform, Laplace Transform Pairs
  20. Fourier Transforms:Fourier Exponential Transform, Fourier Cosine and Sine Transform Pairs
  21. Numerical Integration:Classical Methods, Open- and Closed-Type Formulas
  22. Solutions of Standard Ordinary Differential Equations:Basic Definitions, Exact Equations
  23. Vector Analysis:Scalars and Vectors, Triple Products, Products of Four Vectors
  24. Systems of Orthogonal Coordinates:Curvilinear Coordinates, Systems of Orthogonal Coordinates
  25. Partial Differential Equations and Special Functions:Fundamental Ideas, The Method of Characteristics
  26. Qualitative Properties of the Heat and Laplace Equation
  27. Solutions of Elliptic, Parabolic, and Hyperbolic Equations:Hyperbolic Equations
  28. The z-Transform:The z-Transform and Transform Pairs
  29. Numerical Approximation:Linear Interpolation, Lagrange Polynomial Interpolation
  30. Conformal Mapping and Boundary Value Problems:Boundary Value Problems
  31. Short Classified Reference List:General Tables of Integrals, General Reading
  32. Index