Abstract
THE aim of the author of this book is to give a connected and fairly comprehensive account of the most important mathematical methods of approximate calculations. Strictly speaking, all scientific calculations are approximate; but by suitable processes the approximation may be carried to a degree of accuracy sufficient to satisfy the most exacting requirements. How best to effect the approximation in any given case must ever be a most important problem. The necessity for it begins with ordinary arithmetical operations, to which, accordingly, Dr. Biermann devotes a large part of the first chapter. A good deal of detail might have been spared here if only to make room for a complete account of Horner's method of solving numerical equations and extracting roots. The algebraical theory only of Horner's method is given in a later chapter, but not the expeditious arithmetical process. To give an idea of the scope of the book, we find systematic discussions of the calculations of logarithms, graphical solution of equations, methods of interpolation and differences, determination of Fourier coefficients, methods of quadrature and cubature, and a chapter containing, among other things, a description of the sliding scale and Amsler's planimeter. There are some interesting novelties in the sections on graphical solution of equations which might well find a place in our English text-books of algebra, such, for example, as Mehmke's method. The book does not cover all the ground indicated by the term Näherungsmethoden, but it certainly covers more ground than any other book. Indeed, it fills what has been until now a distinct blank in mathematical literature; and the author is to be congratulated on the production of a work which cannot fail to be of service to the student of mathematical methods.
Vorlesungen über mathematische Näherungsmethoden.
By Dr. Otto Biermann. Pp. ix + 226. (Brunswick: Vieweg und Sohn, 1905.) Price 8 marks.
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Vorlesungen über mathematische Näherungsmethoden . Nature 73, 245 (1906). https://doi.org/10.1038/073245c0
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DOI: https://doi.org/10.1038/073245c0