Margenau/Murphy (1943)


The Mathematics of Physics and Chemistry by H. Margenau and G.M. Murphy, published by D. Van Nostrand Company, Inc, 250 Fourth Avenue, New York and printed in the USA. This finely preserved copy is a seventh printing from February 1947.


Only the first three chapters are specifically relevant to classical thermodynamics, but that needn’t stop the reader from delving into the calculus of variations, vector analysis, statistical mechanics and much more besides.

The 15 chapters of this book add up to a fascinating compendium of college mathematics as it was in WW2 and the immediately post-war years.


A page from Chapter 1 of the book, featuring the implicit function theorem.

The preface, written at the height of the Second World War, gives a concise picture of the authors’ intentions with this book and is reproduced here in full.


The authors’ aim has been to present, between the covers of a single book, those parts of mathematics which form the tools of the modem worker in theoretical physics and chemistry. They have endeavored to do this by steering a middle course between the mere recording of facts and formulas which is typical of handbook treatments, and the ponderous development which characterizes treatises in special fields. Therefore, as far as space permitted, all results have been embedded in the logical texture of proofs. Occasionally, when full demonstrations are lengthy or not particularly illuminating with respect to the subject at hand, they have been omitted in favor of references to the literature. Except for the first chapter, which is primarily a survey, proofs have always been given where omission would destroy the continuity of treatment.

Arbitrary selection of topics has been necessary for lack of space. This was based partly on the authors’ opinions as to the relevance of various subjects, partly on the results of consultations with colleagues. The degree of difficulty of the treatment is such that a Senior majoring in physics or chemistry would be able to read most parts of the book with understanding.

While inclusion of large collections of routine problems did not seem conformable to the purpose of the book, the authors have felt that its usefulness might be augmented by two minor pedagogical devices: the insertion here and there of fully worked examples illustrative of the theory under discussion, and the dispersal, throughout the book, of special problems confirming, and in some cases supplementing, the ideas of the text. Answers to the problems are usually given.

The degree of rigor to which we have aspired is that customary in careful scientific demonstrations, not the lofty heights accessible to the pure mathematician. For this we make no apology; if the history of the exact sciences teaches anything it is that emphasis on extreme rigor often engenders sterility, and that the successful pioneer depends more on brilliant hunches than on the results of existence theorems. We trust, of course, that our effort to avoid rigor mortis has not brought us dangerously close to the opposite extreme of sloppy reasoning.

A careful attempt has been made to insure continuity of presentation within each chapter, and as far as possible throughout the book. The diversity of the subjects has made it necessary to refer occasionally to chapters ahead. Whenever this occurs it is done reluctantly and in order to avoid repetition.

As to form, considerations of literacy have often been given secondary rank in favor of conciseness and brevity, and no great attempt has been made to disguise individual authorship by artificially uniformising the style.

The authors have used the material of several of the chapters in a number of special courses and have found its collection into a single volume convenient. To venture a few specific suggestions, the book, if it were judged favorably by mathematicians, would serve as a foundation for courses in applied mathematics on the senior and first year graduate level. A thorough introductory course in quantum mechanics could be based on chapter 2, parts of 3, 8 and 10, and chapter 11. Chapters 1, 10 and parts of 11 may be used in a short course which reviews thermodynamics and then treats statistical mechanics. Reading of chapters 4, 9, and 15 would prepare for an understanding of special treatments dealing with polyatomic molecules, and the liquid and solid state. Since ability to handle numerical computations is very important in all branches of physics and chemistry, a chapter designed to familiarize the reader with all tools likely to be needed in such work has been included.

The index has been made sufficiently complete so that the book can serve as a ready reference to definitions, theorems and proofs. Graduate students and scientists whose memory of specific mathematical details is dimmed may find it useful in review. Last, but not least, the authors have had in mind the adventurous student of physics and chemistry who wishes to improve his mathematical knowledge through self-study.


March, 1943

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