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Harley Flanders. Elementary Differential Geometry, Revised 2nd Edition. Barrett O'Neill. Customer reviews.
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There was a problem filtering reviews right now. Please try again later. Format: Paperback Verified Purchase. I ordered for differential geometry text by Thorpe but i got some geometry text. Format: Hardcover. See all 2 customer reviews. Most helpful customer reviews on Amazon. Verified Purchase. The only warning I will give is that this is a very dense and formal presentation of the subject, which is typical of several other advanced undergraduate and graduate level math textbooks I've come across.
As a math undergrad at Kent State University some twenty-odd years ago, I took a course in differential geometry.
 Some topics in differential geometry of normed spaces
This was the text; I still have my copy. Autographed by the author, in fact; I met him on a visit to his university, where I subsequently attended grad school. This is one of those 'transition' books that introduces students familiar with Subject A to a more-or-less-systematic smattering of elementary topics in Subject B. Here, Subject A is multivariate calculus and Subject B is, of course, differential geometry. Since that's what this book is for, there are way more numbers and pictures in it than you'll ever see in a modern graduate-level differential geometry text.
In short, much of the motivation here is geometric. I liked it a lot and I am still grateful for its highly accessible introduction to a fascinating field. However, I must also add that its approach is not representative of any graduate-level math course I ever took. Of course this is an undergraduate text and isn't supposed to represent graduate-level coursework.
Is there some personal history lurking behind that remark?
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You guess. An excellent 'transitional' book, then, and highly recommended to readers who want to connect their knowledge of multivariate calculus to the geometry of Euclidean space. It's also a fine example of an expository work on mathematics that remembers its target audience. However, as other reviewers have commented, it needs some answers to the exercises in order to be really useful for self-study.
This book could be considered as the second semester of an advanced calculus course and serves as an excellent introduction to differential geometry. The approach is rigorous, but the author does employ a great deal of illustrations to explain the relevant concepts. The first five chapters cover vector fields on curves and surfaces. The many concrete examples given by the author illustrate effectively the normal and tangent vector fields. This is followed by a discussion of geodesics and parallel transport in the next two chapters.
The important concept of holonomy is introduced in the exercises along with the Fermi derivative. We are always looking for ways to improve customer experience on Elsevier. We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit. If you decide to participate, a new browser tab will open so you can complete the survey after you have completed your visit to this website.
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Institutional Subscription. Free Shipping Free global shipping No minimum order. Davies 1. Projective Differential Geometry 2. Introduction 2. Students bunk classes as they do not understand the complex concepts in differential geometry and hence they end up scoring less in the subject. The assignments and projects are time consuming and there are various methods of solving the same problem which makes it difficult for students to understand which concept should be applied in which problem.
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