Table of Contents

Section I: Elementary Constants, Products, Formulas. Greek Alphabet and Special Constants. Special Products and Factors. The Binomial Formula and Binomial Coefficients. Complex Numbers. Solutions of Algebraic Equations. Conversion Factors. Section II: Geometry. Geometric Formulas. Formulas from Plane Analytic Geometry. Special Plane Curves. Formulas from Solid Analytical Geometry. Special Moments of Inertia. Section III: Elementary Transcendental Functions. Trigonometric Functions. Exponential and Logarithmic Functions. Hyperbolic Functions. Section IV: Calculus. Derivatives. Indefinite Integrals. Tables of Special Indefinite Integrals. Definite Integrals. Section V: Differential Equations and Vector Analysis. Basic Differential Equations and Solutions. Formulas from Vector Analysis. Section VI: Series. Series of Constants. Taylor Series. Bernoulli and Euler Numbers. Fourier Series. Section VII: Special Functions and Polynomials. The Gamma Function. The Beta Function. Bessel Functions. Legendre and Associated Legendre Functions. Hermite Polynomials. Laguerre and Associated Laguerre Polynomials. Chebyshev Polynomials. Hypergeometric Functions. Section VIII: Laplace and Fourier Transforms. Laplace Transforms. Fourier Transforms. Section IX: Elliptic and Miscellaneous Special Functions. Elliptic Functions. Miscellaneous and Riemann Zeta Functions. Section X: Inequalities and Infinite Products. Inequalities. Infinite Products. Section XI: Probability and Statistics. Descriptive Statistics. Random Variables. Probability Distributions. Section XII: Numerical Methods. Interpolation. Quadrature. Solution of Nonlinear Equations. Numerical Methods for Ordinary Differential Equations. Numerical Methods for Partial Differential Equations. Iteration Methods for Linear Systems.

About the Author

The Late MURRAY R. SPIEGEl received the M.S degree in Physics and the Ph.D. in Mathematics from Cornell University. He had positions at Harvard University, Columbia University, Oak Ridge and Rensselaer Polytechnic Insitute, and served as a mathematical consultant at several large Companies. His last Position was professor and Chairman of mathematics at the Rensselaer Polytechnic Institute Hartford Graduate Center. He was interested in most branches of mathematics at the Rensselaer polytechnic Institute, Hartford Graduate Center. He was interested in most branches of mathematics, especially those which involve applications to physics and engineering problems. He was the author of numerous journal articles and 14 books on various topics in mathematics.