PDF Ebook Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
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Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
PDF Ebook Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition (Dover Books on Mathematics)
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From the Back Cover
One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.Dover revised and updated republication of the edition originally published by Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1976.www.doverpublications.com
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About the Author
Manfredo P. do Carmo is a Brazilian mathematician and authority in the very active field of differential geometry. He is an emeritus researcher at Rio's National Institute for Pure and Applied Mathematics and the author of Differential Forms and Applications.
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Product details
Series: Dover Books on Mathematics
Paperback: 528 pages
Publisher: Dover Publications; Updated, Revised edition (December 14, 2016)
Language: English
ISBN-10: 0486806995
ISBN-13: 978-0486806990
Product Dimensions:
6 x 1.2 x 9 inches
Shipping Weight: 1.6 pounds (View shipping rates and policies)
Average Customer Review:
4.2 out of 5 stars
16 customer reviews
Amazon Best Sellers Rank:
#95,295 in Books (See Top 100 in Books)
So far, this has been the best book yet on Differential Geometry (DG). It begins with a purpose and then leaves clues for the reader to find out on his own just how DG came about.A resourceful reader will then discover that tracing out the historical path of development from Euclidean to non-Euclidean Geometries is important to understanding DG: specifically that at the intersection of Affine and Metric Geometry, one finds non-Euclidean Geometry arising when either the metric requirement is relaxed, or the parallel postulate is replaced by a suitable alternative. Either case leads directly to the study of curves and surfaces — the proper province of DG.In 1854, Bernard Riemann, following Gauss et. al., picked up on these ideas, and added a few of his own, like “manifolds,†“the Riemannian metric,†and “curvature,†and used them to invent an infinite family of non-Euclidean geometries. By formulating them in terms of the differential calculus of curvature tensors, Riemann allowed non-Euclidean geometry to be applied to curves and surfaces at higher dimensions, and thus allowed DG to take its proper place in the kit of tools for investigating the mechanical sciences.Being able to see how this mid-18th Century “veering away from†the complications of Euclid’s Fifth Postulate led to studying curves and surfaces using differential calculus and curvature tensors, and without having to rely entirely on coordinate geometry, seems to me essential background information for basic understanding of DG itself. Otherwise, one could leave DG as I did 55 years ago, thinking that it was little more than a field of endless theorem-proving headed nowhere.Even though I managed to pass a first course in DG at Washington University 55 years ago, I had no idea how the substance would ever be used? Now, fifty-five years on, while struggling to understand how Einstein’s field equations describe General Relativity, I have finally found the first practical use for DG.From those readings, I had roughly figured out on my own that one of the most important uses of DG was describing the curvature of surfaces in n-space without the need to rely on coordinates or vector components. What remaining doubts I had, became crystal clear with this book and “Modern Classical Physics,†by Thorne and Blandford. In an early discussion of “Tensor Algebra without a Coordinate System,†the utility of DG finally came home.Because, this book too states clearly and early what the goals for DG are — to use differential calculus in the neighborhood of a point to study the local properties of curves and surfaces — I am very pleased with the layout of its content. Later, the local properties whose behavior affect an entire curve or surface, are added and also studied.Thus, in the clearest of expositions, including annotated diagrams, the necessary theorem proofs, and a graduated set of problems, the author then proceeds to show us just how DG is done. Five Stars
Very good intro to differential geometry. The prerequisites are: a basic course in linear algebra, calculus, and an intro course in real analysis. Anything more than this (such as a course on differential equations) would be helpful but isn't necessary. With the said prerequisites, you should be able to follow most, if not all, the proofs.Hard cover books obviously tend to be more durable and longer lasting than paperback ones. However, I'm actually pleased with this book. The paper quality and printing is good and the binding is standard quality for a paperback book. If you treat the book reasonably, then the book should definitely last you long enough to read the book inside and out.There are still typos (ranging from grammatical errors to typos such as h_{uu} instead of h_{vu} or a missing "<") but there aren't a lot of them, so confusion due to typos should be minimal.Overall, the math content of the book is perfect for a first introduction to differential geometry. The quality of the physical paperback book is also pretty good, considering you can buy it for a good price of $20. If you have $20 and are trying to learn differential geometry for the very first time, I'd recommend buying this book.
The book is very modern and surely useful for undertanding the most important facts of this theory. For example the concepts of area of a surface, the Gauss map, the geodesic are into an approach which has great attention for the lector. In fact the proofs and the definitions are introduced with good clearness.
This a great book for a beginning to intermediate student. I wish I had discovered it before I had to struggle thru several confounded arguments to arrive at some understanding of what is going on.
A classic. Read a scanned PDF version (which is low quality) in 2014 summer. It's nice to have a hard copy and read it again. DoCarmo did a really good job to explain things. You won't regret to have this one.
This edition corrects the errors of the book of 1976, thanks to Dover Publications !
I'm not quite happy with this second edition. It got even more stupid errors than the old version.
Especially font and illustration better than 1st Ed of Pearson Prentice-Hall. I love Dover Pub.
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