Book Review - Buchbesprechung

ROBERT SAVER: IngeniellT Jl,lathematik. Zweiter Band. Differentialgleichungen und Funktionentheorie, Dritte erweiterte Auflage, Springer, 1968. Berlin, Heidelberg, )\ew York This is the second volume of a textbook of introductory Engineering Mathematics covering roughly the basic course program of the third and fourth semesters in German technical colleges. (The first volume containing differential and integral calculus of tunctions of a single and of several real variables covers the first two semesters.) This volume deals with the following topics. Vector analysis including the presentation of the differential invariants in cylindrial and spherical coordinates. Ordinary differential equations, i.e. the standard introductory chapters on classes of differential equations which can be solved directly by elementary methods of integration, the theory of linear differential equations, etc .. with some aspects of graphical and numerical methods of integration, of eigenvalue problems and Fourier series. Classical initial value problems connected with some partial differential equations of mathematical physics. Theory of functions of a complex variable including eonformal mapping, the theory of residues, the Schwarz-Christoffel formula and some potential theory. Emphasis is laid througbout 011 applications; new concepts and theories are introduced via engineering problems where possible. The book contains a paragraph on the theory of oscillations, a paragraph on applications of complex functions in aerodynamics and electricity. Understanding is made easier by several examples worked out in detail. There is equally great emphasis on the presentation of practical, numerical methods, these being unquestionably the most interesting parts for those who consider Mathematics a working tool. Theoretical refinements, possibilities of generalization of the presented ideas are not dealt with. However, basic theorems are clearly stated in the text and mostly proved in the Appendix. There are several clearly drawn figures in the book helping the beginner to understand the text. M. FARKAS