Ebook: Dirichlet's principle: A mathematical comedy of errors and its influence on the development of analysis

This books results from lectures given by the author at the Rijks Universiteit at Utrecht. These lectures were part of a series on history of contemporary mathematics in which the author of the present text and his collegues treated several topics in the history of present-day mathematics.
Originally the title of these lectures was: ‘Gauss, Riemann and Dirichlet’s principle’ but writing this text in the form of a book it appeared that this subject leads to a broader domain. The principle of Dirichlet has played an important role in the development of mathematical analysis; there are connections with complex function theory, the calculus of variations, functional analysis. For a good understanding it appeared to be necessary to incorporate some passages in modern mathematical form. They are presented in such a way that the reader is hoped to be able to distinghuish them from the historical de- velopments. There are also passages which are somewhat further away from the central theme — i.e. Dirichlet’s principle — than potential theory and complex function theory but it is believed that they contribute to a better understanding of the development of mathematics in an important period. Attention is given to the physical backgrounds of the subject.
The present book is therefore a mixture of history and mathematics. There seem to be few books written in this style but the author believes that they are useful in a time when the interest in the history of contemporary mathematics is growing. The author hopes that any mathe- matician can profit from this book in view of his mathematical erudition. Profound knowledge of the subject is not required; any student with a certain amount of mathematical erudition will be able to read the book. An extensive bibliography will be helpful for those who want to read themselves in the sources.
I wish to express my thanks to E.M.J.Bertin, H.J.M.Bos and T.A Springer for their most valuable critical remarks. I thank Miss W. Jenner for the accurate way in which she typed the manuscript.
AUGUST 1975 A. F. MONNA