Tafeln Elementarer Funktionen [antikvár]

Preface to the First Edition Hitherto almost all tables of circular functions have been edited by astronomers and geodesians. Others derived the benefit therefrom. The present compilation of numerical tables is intended to help and facilitate ordinary technical and physical computations. Hence they lay less claim to accuracy, but all the more to comprehensiveness. It was therefore also necessary to make the course of the functions clear by means of many graphic representations, an expedient rarely used by astronomers and geodesians, and consequently missing in the "Logarithmic Tables". For multiplication and division engineers and physicists do not in general use the logarithmic table, but mostly the logarithmic slide-rule; only in those rare cases in which the slide-rule is not sufficiently accurate, do they use a calculating machine, if available. The slide-rule is also the most suitable means for interpolation. These tables are therefore arranged with a view to this. It is taken for granted that the reader is practised in reading numerical values from the slide-rule. Many ofihe tables herein presented, such as the squares, cubes, reciprocals, and roots are not absolutely necessary, but make numerical computation easier. For the sake of convenience with the functions of angles tables are given for three angle units (in decimal subdivision): the degree, the right angle (the quadrant), and the radian. To enable the use of the right angle as a unit without inconvenience in the complex domain, tables for "imaginary right angles" are given, that, is to say, tables of the exponential and hyperbolic functions of ~x. In speaiking of functions the solutions of algebraic equations of a higher degree are not usually considered. In practice, however, it is often important to be able to represent the solution of an equation of the w® degree as an w-valued function of its coefficients, or at least to know if a slight variation of a coefficient would have a comparatively great or only a slight influence on the solution. Such a case might arise in calculating the frequency and damping of natural oscillations. Our book therefore offers assistance for the solution of algebraic equations of the second, third and fourth degree. For some special functions which occur in physics and technics tables or graphical representations will also be found. The table of logarithms given here is of course not intended for logarithmic computations, in which logarithms are only a help in computing, but for those cases in which the logarithms are required. For this purpose they as well as the values of other functions in this book are given with a certain relative accuracy. The interval in the argument is either i or 2 or 5 units of the last figure. The differences printed are calculated throughout for interval I. With these differences one therefore calculates as if the interval were always i. The interval is chosen so great that the maximal error which might arise by linear interpolation does not exceedo -5 • 10-^ of the function value. Further details on this point are to be found in the last chapter. This increase of the interval reduces the tables considerably, so that the values for many functions can be given in a small space. The tables are not overstretched, but adapted to the demand of each function. This book cannot also contain an extensive collection of formulae. Only for circular and hyperbolic functions and for the approximate calculations with polynomials have formulae been compiled. At the end of the book (p. 174) collections of formulae are cited. The first 78 pages of the 1933 Jahnke-Emde, with some alterations, have been included in this book. It was not possible or advantageous to retain the entire material within the Jahnke-Emde, but to divide it into two independent books: impossible, as on account of the differences inserted smaller figures and a larger type area had to be