The second edition of "Formulas, Facts and Constants" has been enlarged without undue increase in volume. The constants have been revised to 1986 values. Prom~ted by comments of many readers a section on error analysis has been added. host impor­ tantly, the new edition now has a subject index in addition to the detailed Table of Contents. The basic format has not been changed and the aim of the book remains to be a handy source of formulas, conversion factors and constants for everyday use. Fundamental tools of mathematics needed in all areas of the physical sciences are given in Section 1. Conversion factors and fundamental constants are 1 isted in Section 2. Section 3 gives information on terms and facts of spectroscopy and atomic structure. Section 4 reviews basic elements of wave mechanics. Section 5 is a resource for work in the laboratory and is intended to be of assistance in the use of frequently encountered equipment such as electronic devices, detectors, vacuum systems, etc. Material constants and other data frequently needed for esti­ mates and problem solving are provided. This new edition is dedicated to the memory of my father, Kurt Fischbeck, who was instrumental that this book was written in the first place. I have benefitted from his experience as an editor and author. He died shortly before the first edition appeared in print. I wish to thank my colleagues Jack Cohn and Stewart Ryan for their useful comments.

1 Basic mathematical facts and figures.- 1.1 Signs and symbols.- 1.1.1 Arithmetic, algebra and analysis of real scalar quantities.- 1.1.2 Arithmetic, algebra and analysis of complex scalar quantities.- 1.1.3 Matrices.- 1.1.4 Algebra and analysis of vectors and other tensors.- 1.1.5 Greek alphabet.- 1.1.6 Roman numerals.- 1.2 Numerical constants.- 1.3 Exponentials and roots.- 1.4 Logarithm.- 1.5 Compi ex numbers.- 1.6 Factorial.- 1.7 Mensuration formulas.- 1.8 Solid angle.- 1.8.1 Solid angle subtended by apertures.- 1.9 Trigonometric functions.- 1.9.1 Range and sign of trigonometric functions.- 1.9.2 Values of trigonometric functions for multiples of 30° (?/6) and 45° (?/4).- 1.9.2.1 Values of sine and cosine for multiples of ?.- 1.9.3 Relations between trigonometric functions.- 1.9.3.1 Relations involving one angle.- 1.9.3.2 Sums and differences of angles.- 1.9.3.3 Multiples of one angle.- 1.9.3.4 Functions of half angles.- 1.9.3.5 Sums and differences of trigonometric functions.- 1.9.3.6 Products and powers of trigonometric functions.- 1.9.4 Exponential definition of trigonometric functions.- 1.9.5 Inverse trigonometric functions.- 1.9.5.1 Fundamental relations for principal values of inverse trigonometric functions.- 1.9.6 Series expansion of trigonometric functions.- 1.9.6.1 Series expansion of inverse trigonometric functions.- 1.9.7 Small angle approximations.- 1.9.8 Values of trigonometric functions.- 1.10 Relations between sides and angles of a triangle.- 1.11 Hyperbolic functions.- 1.11.1 Relations between hyperbolic functions.- 1.11.1.1 Relations involving one angle.- 1.11.1.2 Sums and differences of two angles.- 1.11.1.3 Multiples of one angle.- 1.11.1.4 Functions of half angles.- 1.11.1.5 Sums and differences of hyperbolic functions.- 1.11.1.6 Products and powers of hyperbolic functions.- 1.11.2 Relations between hyperbolic and trigonometric functions.- 1.11.3 Hyperbolic functions of complex argument.- 1.11.4 The inverse hyperbolic functions.- 1.11.4.1 Fundamental relations for inverse hyperbolic functions.- 1.11.4.2 Relations between inverse hyperbolic and inverse trigonometric functions.- 1.11.5 Series expansion of hyperbolic functions.- 1.11.5.1 Series expansion of inverse hyperbolic functions.- 1.11.6 Values of hyperbolic functions.- 1.12 Algebraic equations and solutions.- 1.12.1 Linear: ax + b = 0.- 1.12.2 Quadratic: ax2 + bx + c = 0.- 1.12.3 Cubic: ax3 + bx2 + cx + d = 0.- 1.12.4 System of linear equations.- 1.12.4.1 Homogeneous system of linear equations.- 1.12.4.2 Inhomogeneous system of linear equations.- 1.13 Calculus.- 1.13.1 Derivatives.- 1.13.1.1 Derivatives of elementary functions.- 1.13.1.2 Higher derivatives of elementary functions.- 1.13.2 Elementary rules of integration.- 1.13.3 Integrals.- 1.13.3.1 Definite integrals.- 1.13.3.2 Elliptic integrals.- 1.13.3.3 Complete elliptical integrals.- 1.14 Series.- 1.14.1 Finite series.- 1.14.2 Infinite series.- 1.14.2.1 Sums of reciprocal powers.- 1.14.3 Binomial series.- 1.14.3.1 Binomial coefficients.- 1.14.4 Fourier series.- 1.14.5 Taylor series.- 1.14.6 MacLaurin series.- 1.15 Polynomials.- 1.15.1 Bernoulli's polynomials and Bernoulli's numbers.- 1.15.2 Legendre's polynomials (First kind).- 1.15.2.1 Associated Legendre's polynomials (First kind).- 1.15.3 Hermite polynomials.- 1.16 Special functions.- 1.16.1 Error function.- 1.16.1.1 Error function for complex argument.- 1.16.2 Bessel functions.- 1.16.3 Gamma and Beta function.- 1.17 Fourier transformation.- 1.17.1 Fourier cosine transforms.- 1.17.2 Fourier sine transforms.- 1.17.3 Exponential Fourier transforms.- 1.18 Vectors and vector analysis.- 1.18.1 Unit vectors defining right handed orthogonal systems.- 1.18.1.1 Rectangular coordinates (x,y,z).- 1.18.1.2 Cylindrical coordinates (r,?,z).- 1.18.1.3 Spherical coordinates (R,?,?).- 1.18.1.4 Transformation between unit vector systems.- 1.18.1.5 Derivatives of unit vectors in polar coordinates.- 1.18.1.6 Time derivatives of unit vectors in polar coordinates.- 1.18.2 Line elements.- 1.18.3 Area el ements.- 1.18.4 Position vector.- 1.18.5 Vector algebra.- 1.18.5.1 Vector sum.- 1.18.5.2 Scalar or "dot" product.- 1.18.5.3 Vector or "cross" product.- 1.18.6 Derivatives of vectors.- 1.18.6.1 Time derivative of vectors.- 1.18.7 Vector differential operator $$\nabla$$ (del).- 1.18.7.1 Gradient.- 1.18.7.2 Divergence.- 1.18.7.3 Rotation or curl.- 1.18.7.4 Identities involving the vector operator $$\nabla$$.- 1.18.7.5 Laplacian operator $$\overrightarrow {{{\overrightarrow \nabla }^2}}$$.- 1.18.7.6 Identities involving line and surface integrals.- 1.18.7.7 Identities involving surface and volume integrals.- 1.19 Solution of important differential equations.- 1.19.1 Harmonic oscillator.- 1.19.1.1 Oscillator with damping.- 1.19.2 Laplace equation.- 1.19.2.1 Laplace equation in rectangular coordinates.- 1.19.2.2 Laplace equation in polar coordinates.- 1.19.2.3 Example for the solution of the Laplace equation.- 1.19.3 The wave equation.- 1.19.3.1 Telegraph equation (Wave equation in a conducting medium).- 1.19.4 Heat conduction or diffusion equation (linear).- 2 Units, conversion factors and constants.- 2.1 The international system of units (SI).- 2.1.1 The basic SI units.- 2.1.2 Supplementary SI units.- 2.1.3 Derived SI units with special names.- 2.1.4 Commonly used derived SI units without special names.- 2.1.5 Prefixes for multiples and fractions of SI units.- 2.1.6 Multiples and fractions of SI units with special names but not part of the system.- 2.1.7 Other units exactly defined in terms of SI units.- 2.1.8 Units used in the international system whose values are obtained experimentally.- 2.1.9 Symbols for SI units in alphabetical order.- 2.1.10 Derived SI units admitted in connection with human health.- 2.2 Conversion factors listed by physical quantity.- 2.2.1 Length - macroscopic.- 2.2.1.1 Length - microscopic.- 2.2.2 Area.- 2.2.3 Volume.- 2.2.4 Mass.- 2.2.5 Speed.- 2.2.6 Force.- 2.2.7 Pressure.- 2.2.8 Power.- 2.2.9 Energy.- 2.2.9.1 Energy - atomic units.- 2.2.9.2 Energy equivalents.- 2.2.9.3 Energy equivalents in terms of the Rydberg constant.- 2.2.9.4 Energy or voltage to wavelength conversion.- 2.2.10 Temperature.- 2.2.11 Electromagnetic quantities.- 2.2.11.1 Fundamental electromagnetic relations in Gaussian and SI units.- 2.2.12 Factors for converting from half-life to decay constant.- 2.2.13 Time unit conversion.- 2.3 Conversion factors in alphabetical order.- 2.4 Atomic units.- 2.4.1 Values of frequently occurring q…