Differential Forms with Applications to the Physical Sciences

By Harley Flanders

Book Overview

"To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." -- T. J. Willmore, London Mathematical Society Journal.
This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics.
Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory.
"The book is very readable, indeed, enjoyable -- and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." -- F. E. J. Linton, Wesleyan University, American Mathematical Monthly.

• Format: Paperback
• Language: English
• ISBN: 0486661695
• ISBN13: 9780486661698
• Release Date: December 1989
• Publisher: Dover Publications
• Length: 240 Pages
• Weight: 0.58 lbs.
• Dimensions: 0.4" x 5.4" x 8.5"

Customer Reviews

Good But not the best

I was searching for a good source discussing the differential forms "from the ground up",while passing a course on GR. My motivation in studying this book was Weinberg's mentioning af it as "An extremely readable book" on the topic,in his book on GR.I belive that this is a good book if you have enough time and motivation to study differential forms from basic and without much hurry to use them operationally , but (at least in my opinion) it lacks that degree of clarity that one requires from a book on mathematical physics.To truly understand some parts (even at the early definitions)you may need to spend much more time that you could imagine at the first sight.Some basic ideas are expressed too concise.If you want to learn about differential forms in physics, this book would be some good, but not(I think) during a semester on something else (like GR), beacuse the way of presenting the material is not so stright , nor is operational enough.You may find the books by Lovelock & Rund or by Goldberg & Bishop more useful.

Generalize vector calculus for general relativity

This book covers the basic math behind the "geometric approach" to tensor calculus. The math required is not heavy, but it requires some considerable mathematical maturity. If talk of "the boundary of a boundary is zero" or "exterior derivative" confuses you, this is a good book. An intuitive approach, not a sea of indices. If you want really heavy stuff then Bishop & Goldberg is good.Most Dover math books are first rate. This one is.

An intro to differential forms for physicists

This book introduces differential forms to physicists. It is suitable for those with no advanced training in math other than multivarible calculus and linear algebra. No prior knowledge of topology is needed, although it doesn't hurt. The book starts with a good intro explaining the motivation for forms and when they might be useful over tensors and vectors. The exterior algebra is then presented in chapter 2, followed by a chapter on the exterior derivative. The rest of the book prestents a good deal of applications of forms including the statement and proof of the Newton-Leibniz-Ostrogradksy-Gauss-Green-Stokes Theorem, usually just called Stoke's Theorem. I'd recommend this book to any grad student in Theoretical physics that plans on doing research on physics in the 21st century.