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Differential Geometry (Dover Books on Mathematics), by Erwin Kreyszig
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An introductory textbook on the differential geometry of curves and surfaces in three-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods and results involved. With problems at the end of each section, and solutions listed at the end of the book. Includes 99 illustrations.
- Sales Rank: #354915 in eBooks
- Published on: 2013-04-26
- Released on: 2013-04-26
- Format: Kindle eBook
Most helpful customer reviews
144 of 147 people found the following review helpful.
Agree -- one of the best; elegant; beautiful
By Paul J. Papanek
I had been seeking a book on differential geometry for self-study, as a preface to learning general relativity. A seasoned mathematics friend recommended Kreyszig.
So, I waded in, and patiently made my way through every page of the first six chapters, working the problems along the way, at a pace of a few pages per day. Now that the journey is behind me, I can say that I appreciated this book. It compares favorably to some other texts I had tried reading, with less success.
I realize that the author's approach is an old-style classical one, with a reliance on specific coordinate systems and transformations between coordinate systems. To work the problems requires a fair amount of paper and pencil work. Nonetheless, this approach worked well for me. On those occasions when my reading bogged down, inevitably there was a good reason. If I went back carefully, re-read and pondered, doodled on paper, and tried to visualize what Kreyszig was describing, it always worked! The light would soon go on, usually with a pleasurable sense of discovery.
I went back to re-read certain sections of the book to refresh my memory, and realized how elegant the writing is. Crystal clear, right to the heart, and always trustworthy. Everything follows in a gentle persuasive way; there are no jarring leaps or gaps.
Additionally, I had a nice sense of the different flavor brought to the field by the French geometers who made many of the key advances around the turn of the 19th-20th century.
Finally, the summary of key results and equations at the end is very smart and helpful.
Since finishing Kreysig, I did find it helpful to push on and try to grasp these same ideas from the standpoint of one-forms and the coordinate-free approach to tensors. But I'm not sorry I came at the subject this way first.
I do recommend this book, and think that a beginner needs only a moderate amount of stamina and patience here.
A postscript -- the book is also beautiful. I like that in a math book.
63 of 64 people found the following review helpful.
By far the best intro to classical differential geometry
By Muraari Vasudevan
This is the sort of math book that you pick up, get something to drink, sit on the couch and read through as you would read a novel. I dont know if its possible to write a simpler or clearer treatment on differential geomerty. But be warned that it is still only "classical". Tensros are treated as objects that tranform in a certain way, rather than studied as general multilinear functions. However, after reading this book, any book on tensors is a breeeze to go through. Well worth having, especially considering the price.
23 of 23 people found the following review helpful.
Very nice, useful style
By J. Carlson
I really like this book. I checked out Manfredo P. Do Carmo'sfrom the library and bought this one, and I prefer this one just oncontent. The concepts are explained in a very approachable style and in a nice order to give you an understanding of diff. geometry as well as what you might use it for.. This is not a math text for just math in my opinion. This is geared for you to use differential geometry. I thought most of the concepts are explained nicely but it doesn't hurt to read another book to get another point of view. One advantage this book has over a number of others is that every answer to the exercises is in the back of the book with a very nice solution.. If you're interested in the subject I think this book is a great deal.
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