- Publisher: Matrix Editions
- Language: English
- ISBN-10: 0971576653
- ISBN-13: 978-0971576650
- Product Dimensions: 10 x 8 x 1.5 inches
- Shipping Weight: 3.2 pounds
- Average Customer Review: 4.2 out of 5 stars See all reviews (25 customer reviews)
- Amazon Best Sellers Rank: #332,404 in Books (See Top 100 in Books)
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Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach Hardcover
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Top Customer Reviews
This is the only text that I have seen that really makes forms clear. It does so by taking the time to carefully, but rigorously, explain them in a "classical" setting. One of the reasons forms are so difficult to grasp is that while some things, such as the exterior derivative and the work form of a function, can be seen as natural objects (when explained well), the connection between these objects and calculating with forms using coordinates is not so easy to make clear. The Hubbards' do make these ideas clear - even when presenting topics as hard as orientation.
Unfortunately, most of us had to wait till graduate school to see forms - usually, in a more abstract setting. By then, we probably didn't have time to sit, calculate, and make clear connections. This text makes that later transition, for those in math, much easier. It also makes physics easier. The Hubbards' make that point by showing that the electric field shouldn't really be a field, but a two form. Any book that lets one explain that - and much more - to high school students, which I do, should be a part of every multivariable calculus course.
Finally, I should note that this book contains much, much more than manifolds, the implicit function theorem and differential forms. But, even if that were all it contained, it would fully be worth the price.
In summary, this book opens the door to new worlds that most students never get to see clearly. What a present to us all.
The author tries hard to retain rigor and present to the readers as many examples and applications as possible. Often he tries to cover a broad range of mathematics and digresses a little. The book more or less touches on most of the areas of undergraduate mathematics curriculum and does not go into depth. It sometimes gives me the impression that the book is almost like a survey of undergradute math. The book is also not error-free. There are many typos and some technical errors. If you buy this book, make sure to get the errata from the author's website.
This book can be studied at several levels. For a first year honours course, one may skip the trickiest proofs, which appear in the appendix. More advanced readers may choose to study constructions and details of selected theorems and proofs. Anyone who buys this book will have a solid companion for many years ahead.
The published version is great. I've looked through most of it over the last few years, admittedly from a more advanced viewpoint (no, I didn't buy it, Hubbard gave us free copies). It's very lucid, and the intros to new concepts provide good motivations. I suspect Barbara Hubbard had a great deal to do with how readable it is; she deserves a good deal of credit. I say this, because John Hubbard himself is incomprehensible. His lectures, while sometimes entertaining, were so dense that no one could follow them.
The unique aspect of the book is the 'unified approach.' This works very well at showing the interconnectedness of mathematics. I also like the fact that it is a useful reference. Of course, most of the theorems are proved in the context of Euclidean space, but it is not hard to see how to generalize it.
This is not an easy book though. I found a reviewer's comment that the book is 'incomprehensible to the average Cornell student' very funny. Any math book would be incomprehensible to the average student, whether at Cornell or not. But one should keep in mind that this book is used for the second year honors calc sequence. It is very 'meaty' and not to be delved into lightly. But compared to other books of the same standards, it holds up well. I give it four stars, or maybe up to four and a half.
Most Recent Customer Reviews
I thought it was about time that I start writing reviews of books that I think are special, unique, or beautiful, and I decided to begin with the Hubbards’ Vector Calculus. Read morePublished 7 months ago by pirhouette
This textbook is accessibly written for those of us that love mathematics but are not as mathematically sophisticated as some of our peers in the classroom. Read morePublished 15 months ago by East Wind Song
The condition of the book was a little lower than I had been led to believe.
Simply not well-written or adequate for the described topic and purpose. I was disappointed as were math students who looked at this work. Read morePublished on September 15, 2013 by Kerri K.
Rather more focused on differential forms than I was seeking but a good book for that. The linear algebra is there but you have to fill in a lot more than in some linear algebra... Read morePublished on June 6, 2013 by Kindle Customer
I was recommended this book and am grateful I brought it, though I never have had to use it in a course. Read morePublished on February 16, 2011 by Luke
Be sure to buy the third edition. But don't pay $100. The web site price at one of the two major book store chains is $63 plus shipping. The other chain does not sell it. Read morePublished on May 31, 2009 by J. Mozdzen
Lots of people know vectors, even today a lots less know forms. This is a real shame because forms are simple and elementary, yet there are very few sources that introduce forms on... Read morePublished on July 11, 2007 by Georg Essl