Introduction to Differential Geometry for Engineers

by Brian F. Doolin, Clyde F. Martin

Overview

This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.

Product Details

ISBN-13:	9780486281940
Publisher:	Dover Publications
Publication date:	05/13/2013
Series:	Dover Civil and Mechanical Engineering
Sold by:	Barnes & Noble
Format:	eBook
Pages:	176
File size:	7 MB

About the Author

Brian F. Doolin (1925–2009) was an engineer with NASA as well as Lockheed. At NASA he was a leader of the Control Theory and Applications Group.
Clyde F. Martin is Paul Whitfield Horn Professor of Mathematics at Texas Tech University.

Table of Contents

PrefaceList of Figures1. Introduction2. Manifolds and Their Maps3. Tangent Spaces4. Vector Fields5. Exterior Algebra6. Lie Groups and Actions7. Homogeneous Spaces8. Grassmannian Techniques9. Concluding Remarks10. Appendix: Vector CalculusBibliographyIndex

Editorial Reviews

Treats "the basic concepts and terminology of modern global differential geometry" for the benefit of engineers--particularly control engineers. And unlike many books (written by authors who seem anxious to vanish as soon as possible over the nearest abstract horizon) which pretend to be "useful", this one shows every sign of having been actually and extensively field-tested. The authors adhere to the absolute essentials of their topic, and have been at pains to write with exquisite clarity. Index and brief bibliography, but no exercises. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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