Rating: 
Summary: 2nd edition much improved
Review: 'I personally own a first printing of this book. There are many errors both large and small in scope. A friend of mine owns a copy of the second printing which I read from (sporadically) when I took Math 223/224 at Cornell. The second edition is much better than the first but not quite adaquate. I have no first-hand experience with the third printing although I hear that it is very good. ...Know that there is an errata page which can be easily found by searching the internet... With that aside, my personal opinion of both the material and presentation that Prof. Hubbard offers is very high. When I compared this text to other texts that friends of mine have used in similar classes at various other universities, I found one of two things to be true. Either my friends owned a copy of Hubbard's text or they owned an rather dull, uninspired, possibly outdated text. In the latter case, I was then able to understand why I often hear complaints that math is a "cold," "esoteric," "dry," or "soulless" subject. Finally, what is the verdict. If you enjoy reading math books or if you consider yourself a competent math student who needs to understand the material than I highly reccomend either the THIRD printing of this book or the second edition which is rumored to appear in the fall of 2001. If you like the color yellow than I would also recommend looking at "Differential Equations, A Dynamical Systems Approach Part I" and "Differential Equations, A Dynamical Systems Approach: Higher-Dimensional Systems" which are both authored by John H. Hubbard. I plan to buy a second edition when it prints!
Rating: 
Summary: VERY IMPORTANT to know before buying
Review: ' I personally own a first printing of this book. There are many errors both large and small in scope. A friend of mine owns a copy of the second printing which I read from (sporadically) when I took Math 223/224 at Cornell. The second edition is much better than the first but not quite adaquate. I have no first-hand experience with the third printing although I hear that it is very good. ...Know that there is an errata page which can be easily found by searching the internet... With that aside, my personal opinion of both the material and presentation that Prof. Hubbard offers is very high. When I compared this text to other texts that friends of mine have used in similar classes at various other universities, I found one of two things to be true. Either my friends owned a copy of Hubbard's text or they owned an rather dull, uninspired, possibly outdated text. In the latter case, I was then able to understand why I often hear complaints that math is a "cold," "esoteric," "dry," or "soulless" subject. Finally, what is the verdict. If you enjoy reading math books or if you consider yourself a competent math student who needs to understand the material than I highly reccomend either the THIRD printing of this book or the second edition which is rumored to appear in the fall of 2001. If you like the color yellow than I would also recommend looking at "Differential Equations, A Dynamical Systems Approach Part I" and "Differential Equations, A Dynamical Systems Approach: Higher-Dimensional Systems" which are both authored by John H. Hubbard. I plan to buy a second edition when it prints!
Rating:
Summary: A beautiful book for undergrads and grads alike
Review: Although I am a graduate student in Mathematics, I found
Hubbard's "undergraduate" text to be extremely helpful.
Hubbard combines an intuitive heuristic approach appropriate
for undergraduates with a thoroughly rigorous set of proofs
appropriate for graduate students. I found his discussion of
differential forms particularly helpful. He provides an
excellent intuitive motivation for the definitions, and then
he follows this with a mathematically sound treatment of the
topic. This is a much nicer approach than one will find in
texts such as Rudin's Principals of Mathematical Analysis.
I highly recommend Hubbard's book to anyone wishing to learn
differential forms.
Rating:
Summary: Excellent text for beginners and more advanced students
Review: As the title suggests, this "unified approach" is is a very unique and effective teaching method of presenting three subject areas (that are normally taught as two or three individual classes) in a single text! The authors do a magnificent job of showing and stressing the interconnectedness among vector calculus, linear algebra, and differential forms; so for those readers expecting a bland and disjoint presentation, you'll be in for a very pleasant surprise! This text is suitable for beginning and more advanced students alike. Exercises are clearly marked as basic, intermediate, or more difficult problems. Also, the more difficult proofs are placed in an appendix for the more advanced readers, so that beginners can focus on learning fundamentals without having to bog down in the details of the proof in question. The authors' clear and concise presentation of topics coupled with penetrating insights offered at key moments (in the form of side-notes, footnotes, remarks, inserts, margin notes, etc.) make reading (and LEARNING) the subject matter a most enjoyable experience! The comments and insights are there for those who need them; those who don't can simply skip them (i.e. no loss of continuity). This reader wishes that this textbook was available when he was taking vector calculus and linear algebra! For those who have this book, be on the lookout for the sequel (that's right, part II).
Rating:
Summary: Excellent text for beginners and more advanced students
Review: As the title suggests, this "unified approach" is is a very unique and effective teaching method of presenting three subject areas (that are normally taught as two or three individual classes) in a single text! The authors do a magnificent job of showing and stressing the interconnectedness among vector calculus, linear algebra, and differential forms; so for those readers expecting a bland and disjoint presentation, you'll be in for a very pleasant surprise! This text is suitable for beginning and more advanced students alike. Exercises are clearly marked as basic, intermediate, or more difficult problems. Also, the more difficult proofs are placed in an appendix for the more advanced readers, so that beginners can focus on learning fundamentals without having to bog down in the details of the proof in question. The authors' clear and concise presentation of topics coupled with penetrating insights offered at key moments (in the form of side-notes, footnotes, remarks, inserts, margin notes, etc.) make reading (and LEARNING) the subject matter a most enjoyable experience! The comments and insights are there for those who need them; those who don't can simply skip them (i.e. no loss of continuity). This reader wishes that this textbook was available when he was taking vector calculus and linear algebra! For those who have this book, be on the lookout for the sequel (that's right, part II).
Rating:
Summary: A Must Text
Review: I have used this book to teach gifted high school students about the following topics: the implicit function theorem, manifolds, and differential forms. With the Hubbards' approach, even students without a course in linear algebra actually get it! Not only do they understand the material, but they also become amazingly enthusiastic when they begin to see the unifying effect of understanding differential forms.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.
Rating:
Summary: A Must Text
Review: I have used this book to teach gifted high school students about the following topics: the implicit function theorem, manifolds, and differential forms. With the Hubbards' approach, even students without a course in linear algebra actually get it! Not only do they understand the material, but they also become amazingly enthusiastic when they begin to see the unifying effect of understanding differential forms. 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.
Rating:
Summary: 2nd edition much improved
Review: I've read sections of both the first & second editions and the second has numerous minor changes that make it a much better book. The changes are not major--the content and order are almost identical. However, places where the explanations were unclear or difficult frequently have new diagrams or helpful comments in the margins. A few topics that were too difficult or digressions have been moved to appendices or omitted. It remains a challenging book, intended for honors students, but is now a reasonable alternative to Apostol or a sequel to Spivak.
Rating:
Summary: Confusing book
Review: Math and Physics major
This is a good book if you are solid in set theory. The prerequisites do not emphasized set theory enough. It gives a brief overview in the begining but not extensive enough.
Also, although I can accept theorems written in set theory, even the examples are in set theory. In fact, alot of examples are really just corollaries. I take math to apply to physics. There are very few practical examples that apply to the real world.
Also, notation is horrendous. Hubbard tends to make up the notation as he goes along. This is going to make it very confusing in later classes.
Needless to say, there are careless typos.
This is not a well written pratical textbook.
Rating:
Summary: I wish I had such a book when I was student.. A must have !
Review: The authors condensate in less than 600 pages an incredible amount of classical material. Most of it is presented in a very original way, many times very different from classical presentations (e.g. Stokes formula, Lebesgue dominated convergence for Riemann integrals,...) The book compiles material scattered over the mathematical litterature and is an excellent reference book. It is the best book that I know for freshmen with a taste for mathematics. The presentation, pictures, anecdotes and historical comments make it extremely enjoyable, not only for the student but also for the professor. A must have that will become a classic. Prof. Ricardo Perez-Marco, UCLA Dept. Mathematics Disclaimer : The authors did not offer to the reviewer an old bottle of wine from their cellar (but the turkey was excellent :-))
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