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Rating: 
Summary: A GEM OF A BOOK ON DIFFERENTIAL FORMS
Review: I can't believe that nonone has ever bothered to review this book. This is an outstanding book, filled with valuable insights. The author introduces differential forms right from the beginning. He provides associations with the utility of differential forms in Mathematical Physics through many examples. There is a lot of material in this book that cannot be covered easily, so the prospective reader is advised to be patient and initially skip sections when necessary. This is a book about advanced calculus via differential forms written with great care by someone who has thought things through very thoroughly. The book has all the attributes of a classic:1. Excellent explanations and plenty of examples. 2. Conceptual clarity of key ideas, a rare feature these days. 3. Solutions of all the exercises in the book (truly a lot). 4. Rigorous but not terse mathematics. Having read this book the reader can easily proceed to address more advanced topics without hesitation. I personally would have liked to have seen more applications in mathematical physics but this is by no means a criticism. The author wrote a book that is about the concept of differential forms in advanced calculus and in that he has succeeded admirably. Apparently this book was first published in 1969 and has gone in and out of print over the last three decades. So hurry up, go out and buy this book.
Rating:
Summary: A GEM OF A BOOK ON DIFFERENTIAL FORMS
Review: I can't believe that nonone has ever bothered to review this book. This is an outstanding book, filled with valuable insights. The author introduces differential forms right from the beginning. He provides associations with the utility of differential forms in Mathematical Physics through many examples. There is a lot of material in this book that cannot be covered easily, so the prospective reader is advised to be patient and initially skip sections when necessary. This is a book about advanced calculus via differential forms written with great care by someone who has thought things through very thoroughly. The book has all the attributes of a classic: 1. Excellent explanations and plenty of examples. 2. Conceptual clarity of key ideas, a rare feature these days. 3. Solutions of all the exercises in the book (truly a lot). 4. Rigorous but not terse mathematics. Having read this book the reader can easily proceed to address more advanced topics without hesitation. I personally would have liked to have seen more applications in mathematical physics but this is by no means a criticism. The author wrote a book that is about the concept of differential forms in advanced calculus and in that he has succeeded admirably. Apparently this book was first published in 1969 and has gone in and out of print over the last three decades. So hurry up, go out and buy this book.
Rating:
Summary: Best book on Differential Forms for an Undergraduate.
Review: This book is very well written, and being a reprint of a second edition, has very few misprints. Forms and their calculus are introduced in the 3D Euclidean space familiar to students of Calclulus 3 or University Physics. Later in the book the fundamentals like Stokes' Theorem are generalized to higher dimensions and manifolds. This book is suitable for anyone who has had Calculus 3 and is interested in a better way to do multiple-variable calculus. (Just to whet your appetite: after reading this book, you won't have to remember Green's Theorem, Stokes' Theorem, or the Divergence Theorem separately, they are all one compact and simple theorem {the one on the cover} in the language of Differential Forms.) I, personally, had a lot of trouble with Flanders' and Darling's books on differential forms until I read some outside material on the subject. This book, however, starts off on a more basic level, and does not demand half the mathematical maturity that Flanders or Darling do. For more advanced topics, Flanders and Darling are fine books to go to, after getting the basics right here.
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