Bibliography

T. Karman and M. Biot, Mathematical Methods in Engineering. Translated by M. G. Shestopal, edited by A. I. Lur’e, State Publishing House of Technical-Theoretical Literature. Moscow–Leningrad, 1946. 423 pp., price 23 rubles.

The purpose of this book is to raise the mathematical level of the modern engineer and, judging from its program, primarily of the mechanical engineer. In fact, apart from the limits of mechanics, only a few applications of operational calculus to problems of electrical engineering are included. This is perhaps to be regretted: in our view, the modern mechanical engineer is very much in need of a deep knowledge of all kinds of measuring apparatus, which in practice is almost always electrical and radio-technical; a thorough understanding of it is necessary and impossible without mastery of the theories that naturally require mathematical knowledge—both of the apparatus itself and of the close fusion of questions of electrical engineering and mechanics in the work of the modern engineer-researcher.

Now as to the contents. Oscillations play a large role in the book, and Chapters IV, V, VI, and IX are devoted to them. At the same time the authors do not restrict themselves to the usual elementary presentation, but raise questions of nonlinearity and stability. One feels, however, that the development of the theory of nonlinear oscillations that has taken place in the USSR is unknown to the authors, which is why it is not represented to the proper extent, although the mathematical apparatus for this is almost entirely present in the book.

Chapter X contains the foundations of operational calculus and is presented, in our opinion, very successfully.

Chapter XI is a pleasant novelty: it sets forth elements of the theory of finite-difference equations, a very useful method for many engineering calculations, as the authors demonstrate by successful examples.

The first two chapters of the book present the theory of ordinary differential equations and the theory of Bessel functions. The remaining mathematical material is distributed among other chapters and is directly connected with applications.

The book is well thought out and reads without particular difficulty; of course, the reader must arm himself with pencil and paper and actively follow the exposition. It should be noted that there is a large number of problems from the most diverse branches of mechanics. In the text itself many questions are worked out that are usually absent from books of this kind; these include the theory of a string and a beam on an elastic foundation, the “phugoid” motion of an airplane, the calculation of certain second-order equations in matrix form, mechanical and electrical filters, and many interesting problems.

The lively and precise exposition, the large amount and variety of material, and the well-chosen problems make the book useful for the Soviet reader. The translation is generally good. But the publishing house should be reproached not only, in this case, for not ensuring the availability of the book; little time has passed since its publication, yet it can no longer be bought. The need for books in our country is growing as rapidly as all

our culture; there should not be a situation in which even the specialist, who needs the book more than others, has to hunt for it on the book market, and often unsuccessfully.

N. N. Andreev