Differential Geometry

by Erwin Kreyszig

This book is intended to meet the need for a text introducing advanced students in mathematics, physics, and engineering to the field of differential geometry. It is self-contained, requiring only a knowledge of the calculus. The material is presented in a simple and understandable but rigorous manner, accompanied by many examples which illustrate the ideas, methods, and results. The use of tensors is explained in detail, not omitting little formal tricks which are useful in their applications. Though never formalistic, it provides an introduction to Riemannian geometry. The theory of curves and surfaces in three-dimensional Euclidean space is presented in a modern way, and applied to various classes of curves and surfaces which are of practical interest in mathematics and its applications to physical, cartographical, and engineering problems. Considerable space is given to explaining and illustrating basic concepts such as curve, arc length, surface, fundamental forms; covariant and contravariant vectors; covariant, contravariant and mixed tensors, etc. Interesting problems are included and complete solutions are given at the end of the book, together with a list of the more important formulae. No pains have been spared in constructing suitable figures.

Genres: Mathematics, Reference, Science, Textbooks, Physics

394 pages, Paperback

First published June 1, 1991

Reviews

[Kyle · Rating 4 out of 5]

This is a good book to go through to get an understanding of differential geometry. It has all the things you need to study. I had hoped that it would be a bit more general, but the book heavily focuses on 2-dimensional surfaces. I like that it has problems with solutions at the back of the book. This makes it much better suited for self-study. I also thought it had fairly clear explanations overall. There were a couple of times I thought the presentation could have been clearer, however, and some of the problems are less enlightening than I would have hoped. That is, a few problems seemed purely for calculation without really giving any deeper insight into anything, but the majority of problems were good and helped cement understanding.