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Elements of Differential Geometry 1st Edition
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Top Customer Reviews
In short, here is a book which takes the key aspects of classical and modern differential geometry, and teaches them in the concrete setting of R^3. This has several advantages:
(1) The student isn't lost in the abstraction immediately. When I took my first diff. geometry course, we spent the entire time taking derivatives in n-dimensional projective space and other equally abstract spaces. This book keeps it concrete, and supplements each idea with several worked out examples to help ground the student's intuition.
(2) The book uses modern techniques when applicable. Just because this book teaches the material in a concrete/classical setting does not mean that its methods are outdated. The student will become very used to modern techniques, but applied here in easier settings than what you would find in a standard graduate leveled book. Hence, when the student eventually takes graduate leveled courses, he or she will come to see the definitions and techniques as natural extensions of those learned previously.
(3) The student learns the classical theory first, which entirely motivates the modern theory.Read more ›
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.
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.
Most Recent Customer Reviews
I had the class from Prof. Parker ~20 years ago. (BS Mathematics 83 from SIU) It was a wonderful class and this is a wonderful book. I still have my signed! copy. Read morePublished on March 23, 2004 by M. Goeckner