Second Year Calculus: From Celestial Mechanics to Special Relativity

I do not know another book that presents Differential Forms and their usage in the framework of Calculus better than this one. (I've looked at several.) A lot of the other books present this material at a high level that loses the reader in ten pages or less. Professor Bressoud's book, by contrast, is a model of the clarity that I would love to see more Math Book writers adopt. The subject is potentially confusing because the notation of first-year calculus -- dx, dy, dz -- is here used in a way, and with a revised meaning, that you may not have seen before. Bressoud takes the time to EXPLAIN Forms to the reader carefully, and in sufficient detail, to be understood. He even explicitly warns the reader about situations in which the new notation may cause confusion, given the new usage. ( in multiple vs iterated integrals, for example ). It's clear enough to be used for self-study. Strongly recommended. After you finish the book, you will be in a position to tackle a more extended treatment, such as H. Edward's Advanced Calculus: A Differential Forms Approach. But do start with this book.

I agree with the review of "gsibbery" (Baton Rouge, LA) Chapters: 1 F=ma 2 Vector Algebra 3 Celestial Mechanics 4 Differential Forms 5 Line Integrals, Multiple Integrals 6 Linear Transformations 7 Differential Calculus 8 Integration by Pullback 9 Techniques of Differential Calculus 10 The Fundamental Theorem of Calculus 11 E=mc^2 Plus a great collection of problems!

Ok, for all those of you out there who always wanted to learn the math that you need to know to be able to do some really fun physics, THIS IS IT! Most introductions to "higher mathematics" tend to be rather impractical and largely useless and uninteresting topics (to the physical scientist) such as set theory or abelian group theory, but this book really delivers. The emphasis is on working out problems . . . there is some theory, but this is really meant for engineers and physicists rather than for mathematicians who are interested in theory alone. You need a very solid grounding in first year calculus before you even think of beginning this course. But once you get going, the topics that are introduced include: multiple integrals, vectors, differential forms (including tensors), and continues in this fashion until the last chapters on electromagnetics, celestial mechanics and special relativity. Now, this is not an easy book, but unlike many math texts that I have seen, it is by no means impossible to learn all own your own. Thus, if something that really interest you in the classroom is not covered, then this book would make a great supplement. It is superb for self-study and contains most of what you need to know to begin studying real physics and more advanced paractical mathematics. I can't thank Dr. Bressoud enough for writing this much-needed book! I only wish that I could give in ten stars instead of only five!