A Course in Mathematics for Students of Physics: Volume 1

by Paul Bamberg, Shlomo Sternberg

Overview

This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in the widest sense, with an interest in physics and mathematics, will gain from its study.

Product Details

ISBN-13:	9781107384637
Publisher:	Cambridge University Press
Publication date:	08/30/1991
Sold by:	Barnes & Noble
Format:	eBook
File size:	23 MB
Note:	This product may take a few minutes to download.

Table of Contents

1. Linear transformations of the plane; 2. Eigenvectors and eigenvalues; 3. Linear differential equations in the plane; 4. Scalar products; 5. Calculus in the plane; 6. Applications of differential calculus; 7. Differential forms and line integrals; 8. Double integrals; 9. Gaussian optics; 10. Vector spaces and linear transformations; 11. Determinants; Index.

Editorial Reviews

Part I of a remarkable two-volume text, derived from a course taught in recent years at Harvard by the distinguished authors, and intended to serve the mathematical needs of intermediate/advanced undergraduate students of physics and related fields. Distinguished from other such texts by the sophistication of the approach and the clarity of the writing, as well as by the principles which have motivated the inclusion/exclusion of material. The present volume (eleven chapters, each with summary and exercises) treats linear mathematics, multivariable calculus and some applications (mainly to Gaussian optics). Very cleanly designed and produced, with a useful brief bibliography. Outstandingly fine, likely to influence the thinking of a generation of physicists, and to inspire the authors of some future textbooks. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"A Course in Mathematics by Bamberg and Sternberg is in a class by itself....The authors have drawn on their wide teaching experience to produce a book whose tone is authoritative, whose vision is fresh, and whose whole feel is original....there is to my knowledge no comparable book, and it is hard to imagine a more inspiring one." Times Literary Supplement

"You can find about a dozen books on exterior calculus, that is, the calculus of differential forms, written for physicists. The one reviewed here is the most elementary. It is excellent, and provides a solid foundation....Not only is the mathematics clean, elegant, and modern, but the presentation is humane, especially for a mathematics text." American Journal of Physics

"This textbook (Vol. 1 & 2) is a well-written and well illustrated introduction to the mathematics of modern physics. The combination of mathematics and physical applications provides an excellent learning environment for students of physics and for scientists wishing to upgrade their education. This textbook emphasizes the geometric visualization of mathematical equations, and tries to develop in the student an intuitive feel for the mathematics. Overall, this book is a welcomed introduction to the mathematics required in modern physics." Physics in Canada

"I consider Sternberg's book a fine addition to the existing literature and strongly recommend it to anyone with an interest in learning how to use group-theoretical methods to understand concrete physical problems." Siam Review

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