A Course in Mathematics for Students of Physics: 2

by Paul Bamberg and Shlomo Sternberg

Book 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...

• Format: Paperback
• Language: English
• ISBN: 0521406501
• ISBN13: 9780521406505
• Release Date: August 1991
• Publisher: Cambridge University Press
• Length: 464 Pages
• Weight: 1.80 lbs.
• Dimensions: 1.0" x 6.9" x 9.7"

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!

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!

An interested amateur physicist

I don't understand why some of the reviews here are mediocre. Although I haven't read the book to any depth, I have a knack of knowing whether a book exudes quaity by browsing briefly through it to get a general feel; the breadth of the material presented is breathtaking and at least eye-opening. Here are some reviews from the back cover...American Journal Of Physics:- Not only is the mathematics clean, elegant, and modern blah, blah, blah... This is first rate!Times Higher Education Supplement:-...There is to my knowledge no comparable book, and it is hard to imagine a more inspiring one.Remember also that there are two volumes.

GREAT BOOK, EXCEPT...

The presentation and despriptions are every good. The progression sequence of the material is right on. I am both a mathematician and a physicist in that I develop "real-world" algorithms for computer models for atmospheric, marine and alluvial environments. I use the Series (both Vol. 1 & 2) to tutor physics students, most of which are good at plugging into established formulas but need work at developing a formula from scratch. There is an occasional error which can usually be figured out by reading-on if you know anything about math and physics; THIS BOOK is not written for a freshman year math/physics student. My only complaint with the book is that there is no solutions for any of the exercises at the ends of the chapters. Trivial as it may sound; when a student is trying to work through the problems, sometimes they need to know if they are right to move-on. Which means they have to call me, which after a while get's to be a pain.....my suggestion for the next edition is give the solutions for at least the odds or evens to help out the teachers...In spite of this discrepancy I still use the book and recommend it.....

Mathematics for 21st century

This book gives a glimpse of the style the mathematics will be taught in schools say 30 years from now (despite the fact that actual results presented in it are all at least 70 years old - such is the inertia of the education). Despite the title, it should be strongly recommended to the students and teachers of pure mathematics. Reader that rated this book with one star obviously does not understand what mathematics is all about. The first chapter alone is worth more.