Introduction to Differential Geometry for Engineers

By: Brian F Doolin, Clyde F Martin, Engineering, B F Doolin

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Paperback | 19 June 2012

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176 Pages

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21.59 x 13.34 x 1.27

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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.

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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry Applied Mathematics Engineering & Technology Technology in General Engineering in General Science Science in General

Preface	p. v
List of Figures	p. xi
Introduction	p. 1
Manifolds and their Maps	p. 5
Differentiable Manifolds	p. 5
Examples	p. 13
Manifold Maps	p. 18
Tangent Spaces	p. 23
The Tangent Space of Sphere	p. 24
Equivalence Classes of Curves	p. 30
The Tangent Space in General	p. 33
Tangent Space Maps	p. 36
Vector Fields	p. 45
Vector Fields	p. 46
Derivations	p. 49
A Digression on Notation	p. 53
The Isomorphism	p. 54
The Algebra	p. 60
An Example of a Lie Algebra	p. 63
Exterior Algebra	p. 69
Addition of Forms	p. 70
The Wedge Product	p. 71
Contraction of Forms; Vectors	p. 75
Equation of a Plane	p. 79
Use of Determinants	p. 81
Solution of Linear Equations	p. 84
Linear Transformations	p. 86
Lie Groups and Actions	p. 91
Lie Groups	p. 91
Group Action	p. 93
One-Parameter Subgroups	p. 95
The Symplectic Group	p. 101
Homogeneous Spaces	p. 107
Grassmannian Techniques	p. 115
Linear Optimal Control	p. 116
The Grassmannian	p. 120
An Application	p. 129
Concluding Remarks	p. 141
Appendix: Vector Calculus	p. 143
Real Euclidean Space	p. 143
Topological Spaces	p. 144
Compactness	p. 147
Continuity	p. 148
Derivative	p. 149
Inverse Function Theorems	p. 151
Bibliography	p. 155
Index	p. 159
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Introduction to Differential Geometry for Engineers

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Paperback

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