Product Description

This text breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Aimed at physics students, it covers the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The exterior differential calculus is now being recognized by mathematicians and physicists as the best method of formulating the geometrical laws of physics, and the frontiers of physics have already begun to reopen fundamental questions about the geometry of space and time. Covering the basics of differential and integral calculus, the authors then apply the theory to interesting problems in optics, electronics (networks), electrostatics, wave dynamics, and finally to classical thermodynamics. The authors adopt the "spiral method" of teaching (rather than rectilinear), covering the same topic several times at increasing levels of sophistication and range of application.

Product Details

• Amazon Sales Rank: #2043712 in Books
• Published on: 1988-10-28
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 424 pages

Review
"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

"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

"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

"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

Review
"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

Customer Reviews

Good stuff badly written
I'm going to mention the second volume almost exclusively. This is where the action is located. It is hard to find any equivalent treatment of circuit theory using algebraic topology. You should have some mathematics background or some patience and a stack of books on algebra and algebraic topology so you can understand what these authors write so poorly. However, while the text (vol.2) loses a star for being horribly written, it gains four stars for the amazing content. If you are patient you will see a side of circuits you have never dreamt of and then you will be led into the generalized (continuous) version which is electromagnetics.

If you are looking for some really accessible and really interesting mathematics on circuits and EM buy this book (or buy it used, I bought my hardcover for 10$) You might also find it useful to consult the appendix in Frankel's Geometry of Physics for comparison.

Have fun and keep in mind that the book is written by sadists, clever and intelligent, but sadists all the way!

a difficult book with few rewards
I can only say one good thing about this book: it steered me towards a couple of really worthwhile books. I began to read Bamberg/Sternberg about five years ago, when I was looking for a book that could explain the mathematics that physicists use. It was heavy going from the first chapter, although I am not a neophyte in mathematics. I found it slow, obscure, devoid of true proofs and explanations when I needed them most. As another reader said, the books is perfunctory while it seems it wants to aim high. I finally gave up, after the tremendously confusing chapter 5 on scalar products. But I followed a couple of their bibliographic suggestions. In particular, I read the very enjoyable and rewarding Loomis and Sternberg, "Advanced Calculus," a classic textbook, not an easy one, but one that rewards hard work. Loomis/Sternberg is a comprehensive, solid, insightful book that covers a lot of the material of Bamberg/Sternberg's first volume. I took up Bamberg/Stenberg this week again, after a hiatus of several years, having digested several books on linear algebra, topology, and functional analysis, and I still find it very difficult to read Chapter 1. The reason: nothing is fully explained or proven. Rather, the book reads like a collection of hints that barely connect and in places is painfully slow. My advice: don't try to read it unless you are forced to. For a neat, useful, modern introduction to mathematical physics, try Hassani. Or go back to that jewel, Loomis/Sternberg, if you can find it.

Simply fascinating!
In short, I find this kind of a book very rare indeed.

If you are doing physics and electronics at the undergraduate level, this book will open your eyes to a whole new unified approach to several on-the-surface different topics. I wonder why many course designer's haven't looked at this book and realized how accessible it has made some of the relatively modern concepts. The authors laudably attend on each concept with a passion to make the reader confident of grasping at least a few different ways of looking at it, keeping the core well in view all the time. It is also to their credit to have kept the beauty in the ideas intact with a good balance of abstraction and concrete instances.

In particular, the authors treatment of exterior calculus is an eye opener if you are new to the topic. For a student only exposed to traditional methods, it is a revealer to see the laws of linear electrical circuits as well as Maxwell's equations of electromagnetism being expressed in precisely the same language. It is totally to the credit of the authors to have presented the concepts in such a simple to understand progression. For example, they make you see clearly why you have understood the divergence theorem or Stokes theorem of conventional vector calculus if you've grasped the essence of the calculus of functions of a single variable. Its a fantastic voyage folks, and you've got some of the best guides methinks.

All those who find physics and mathematics a drag at college should grab this book and be enlightened. I wish they fix some of the errors in the book in future editions, but the errors don't at all hinder the learning.

Ten thumbs up!