Introduction to Differential Geometry for Engineers

Name: Introduction to Differential Geometry for Engineers
Price: 12.61 USD
Availability: InStock
ISBN: 9780486488165

ISBN-10: 0486488160

ISBN-13: 9780486488165

Edition: 2012

Authors: Brian F. Doolin, Clyde F. Martin, Engineering

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Description:

This book acquaints engineers with the basic concepts and terminology of modern global differential geometry. It introduces the Lie theory of differential equations and examines the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, and vector fields. 1990 edition.

Book details

List price: $20.25
Copyright year: 2012
Publisher: Dover Publications, Incorporated
Publication date: 7/17/2012
Binding: Paperback
Pages: 176
Size: 5.25" wide x 8.50" long x 0.50" tall
Weight: 0.396
Language: English



Preface


List of Figures



Introduction



Manifolds and their Maps



Differentiable Manifolds



Examples



Manifold Maps



Tangent Spaces



The Tangent Space of Sphere



Equivalence Classes of Curves



The Tangent Space in General



Tangent Space Maps



Vector Fields



Vector Fields



Derivations



A Digression on Notation



The Isomorphism



The Algebra



An Example of a Lie Algebra



Exterior Algebra



Addition of Forms



The Wedge Product



Contraction of Forms; Vectors



Equation of a Plane



Use of Determinants



Solution of Linear Equations



Linear Transformations



Lie Groups and Actions



Lie Groups



Group Action



One-Parameter Subgroups



The Symplectic Group



Homogeneous Spaces



Grassmannian Techniques



Linear Optimal Control



The Grassmannian



An Application



Concluding Remarks



Appendix: Vector Calculus



Real Euclidean Space



Topological Spaces



Compactness



Continuity



Derivative



Inverse Function Theorems


Bibliography


Index