Elements of Differential Geometry [Paperback]

Richard S. Millman (Author), George D. Parker (Author)

Book Description

Publication Date: April 8, 1977 | ISBN-10: 0132641437 | ISBN-13: 978-0132641432 | Edition: 1st

This text is intended for an advanced undergraduate (having taken linear algebra and multivariable calculus). It provides the necessary background for a more abstract course in differential geometry. The inclusion of diagrams is done without sacrificing the rigor of the material.

 

For all readers interested in differential geometry.

Editorial Reviews

From the Publisher

Makes a strong effort to bring topics up to an undergraduate level, and easily taught by any math prof. Easiest of our books.

Product Details

• Paperback: 265 pages
• Publisher: Prentice Hall; 1st edition (April 8, 1977)
• Language: English
• ISBN-10: 0132641437
• ISBN-13: 978-0132641432
• Product Dimensions: 8.9 x 6 x 0.6 inches
• Shipping Weight: 14.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #210,754 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

15 of 16 people found the following review helpful:

5.0 out of 5 stars A solid introduction, July 20, 2002

By 

Dr. Lee D. Carlson (Baltimore, Maryland USA) - See all my reviews
(VINE VOICE)    (HALL OF FAME REVIEWER)    (REAL NAME)   

This review is from: Elements of Differential Geometry (Paperback)

It is hard to disagree with the idea that one must pursue the learning of mathematics in way that might be at odds with its axiomatic structure. One can pursue the study of differentiable manifolds without ever looking at a book on classical differential geometry, but it is doubtful that one could appreciate the underlying ideas if such a strategy were taken. Some background in linear algebra, topology, and vector calculus would allow one to understand the abstract definition of a differentiable manifold. However, to push forward the frontiers of the subject, or to apply it, one must have a solid understanding of its underlying intuition.

Thus a study of classical differential geometry is warranted for someone who wants to do original research in the area as well as use it in applications, which are very extensive. Differential geometry is pervasive in physics and engineering, and has made its presence known in areas such as computer graphics and robotics. In this regard, the authors of this book have given students a fine book, and they emphasize right at the beginning that an undergraduate introduction to differential geometry is necessary in today's curriculum, and that such a course can be given for students with a background in calculus and linear algebra. They also do not hesitate to use diagrams, without sacrificing mathematical rigour. Too often books in differential geometry omit the use of diagrams, holding to the opinion that to do so would be a detriment to mathematical rigour. Much is to be gained by the reading and studying of this book, and after finishing it one will be on the right track to begin a study of modern differential geometry.

8 of 8 people found the following review helpful:

5.0 out of 5 stars A Perfect Introduction, February 22, 2001

By 

josh kaplan (NU USA) - See all my reviews

This review is from: Elements of Differential Geometry (Paperback)

A Must !!! After reviewing a few dozen books in the subject, this is without any doubt one of the best. It it written with rare clarity, and gives enough motivation and examples to understand the more abstract and difficult aspects of the field. The book is intended for advanced undergraduate (with good understanding of linear algebra and calculus III) and should be read prior to an abstract course in differential geometry (such as is covered in the books of Warner and Hicks).

4 of 4 people found the following review helpful:

4.0 out of 5 stars understandable, clear differential geometry book, September 29, 2005

By 

math monkey "idrinkwhisky" (New York, NY USA) - See all my reviews

This review is from: Elements of Differential Geometry (Paperback)

There are many differential geometry books out there. Some are very rigorous others not. This book walks the road in the middle. Intuition is developed in the first few chapters by discussing familiar surfaces in R^n, and then a discussion on more abstract manifolds follow.

The book requires some very basic knowledge of linear algebra and some multivariate calculus knowledge. So basically every undergrad in the sciences should find this book easy to understand, and a good introduction to differential geometry.