Elementary Differential Geometry - Christian BÃ¤r

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Elementary Differential Geometry

By: Christian BÃ¤r

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Paperback | 6 May 2010

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334 Pages

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24.41 x 16.99 x 1.78

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The link between the physical world and its visualisation is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science.

The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss-Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The only prerequisites are one year of undergraduate calculus and linear algebra.

'A terrific new book on differential geometry: a preliminary chapter eases the way from the familiar axiomatic treatment into the differential perspective. There are also very good discussions of discrete approximations to curves and surfaces, a complete proof of the existence of triangulations on Surfaces, and a beautiful discussion of cartography and constant curvature geometries. BSr provides plenty of intuition and many examples, while not stinting on the rigour.'-Rafe Mazzeo, Stanford University

Industry Reviews

'The book under review presents a detailed and pedagogically excellent study about differential geometry of curves and surfaces by introducing modern concepts and techniques so that it can serve as a transition book between classical differential geometry and contemporary theory of manifolds. the concepts are discussed through historical problems as well as motivating examples and applications. Moreover, constructive examples are given in such a way that the reader can easily develop some understanding for extensions, generalizations and adaptations of classical differential geometry to global differential geometry.' Zentralblatt MATH

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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Topology

Preface
Notation
Euclidean geometry
Curve theory
Classical surface theory
The inner geometry of surfaces
Geometry and analysis
Geometry and topology
Hints for solutions to (most) exercises
Formulary
List of symbols
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Elementary Differential Geometry

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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