The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. The Third Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation. - Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results - Contents selected and organized to suit the needs of students, scientists, and engineers - Contains tables of Laplace and Fourier transform pairs - New section on numerical approximation - New section on the z-transform - Easy reference system

Preface
Index of Special Functions and Notations
Quick Reference List of Frequently Used Data
Numerical, Algebraic, and Analytical Results for Series and Calculus
Functions and Identities
Derivatives of Elementary Functions
Indefinite Integrals of Algebraic Functions
Indefinite Integrals of Exponential Functions
Indefinite Integrals of Logarithmic Functions
Indefinite Integrals of Hyperbolic Functions
Indefinite Integrals Involving Inverse Hyperbolic Functions
Indefinite Integrals of Trigonometric Functions
Indefinite Integrals of Inverse Trigonometric Functions
The Gamma, Beta, Pi, and Psi Functions
Elliptic Integrals and Functions
Probability Integrals and the Error Function
Fresnel Integrals, Sine and Cosine Integrals
Definite Integrals
Different Forms of Fourier Series
Bessel Functions
Orthogonal Polynomials
Laplace Transformation
Fourier Transforms
Numerical Integration
Solutions of Standard Ordinary Differential Equations
Vector Analysis
Systems of Orthogonal Coordinates
Partial Differential Equations and Special Functions
The z-Transform
Numerical Approximation
Short Classified Reference List
Solutions of Elliptic, Parabolic and Hyperbolic Equations
Qualitative Properties of the Heat and Laplace Equation