Bergman¿s Linear Integral Operator Method in the Theory of Compressible Fluid Flow

The reader who is somewhat acquainted with the field of compressible fluid flow hears much about Stefan Bergman's method of integral operators. It took many years for him to develop this method which is based primarily on the theory of analytic functions and particularly on the theory of)functions of two complex variables. The method, as a whole, is scattered throughout many papers in mathematical journals, and as a matter of fact, in its present state, is accessible only to those who are fully acquainted with mathematical literature. In one of their papers, Professors R. von Mises and M. Schiffer greatly simplified the method in the subsonic casco The purpose of the present work is to represent the method in all its variations in such a way that a theoretical engineer or an applied aerodynamicist can use it in practical applications. A professional mathematician will find the discussion too elementary for him. The parts of Bergman's presentation which are most interesting mathe­ matically-the proofs-are mostly omitted in the present work. The emphasis was put upon the simplified representation of the final results and formulas, rather than upon the derivation of those formulas. In the preliminary remarks the author discusses various types of singularities in a very elementary way. The first two parts of the work deal with the subsonic case. In these sections the author followed mostly the paper of von Mises and Schiffer.

0. Preliminary remarks. Singularities.- I. General theory of subsonic flow.- II. Simplified pressure-density relation.- III. Supersonic flow.- IV. Transonic flow.- V. Axially symmetric flow.- VI. Singularities.- VII. Review of other methods.- VIII. Review of tables and particular formulas.- IX. General remarks.- X. List of tables.- XI. Examples.- XII. Errata in previous papers.- XIII. Generalization of Bergman's method to diabatic flow.- XIV. Integral operators in the case of certain differential equations in three variables.- XV. Some SEAC computations of subsonic fluid flows by Drs. P. Davis and P. Rabinowitz.- Final remarks.- Additional bibliography.- Index of authors.