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.
Cuprins
Preface List 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 Calculus Bibliography Index
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