David B. Gauld

Differential Topology (eBook, ePUB)

An Introduction

• Format: ePub

Produktbeschreibung

Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.
This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curves, surgery, classification of orientable surfaces, and Whitney's embedding theorem. Suitable for advanced undergraduate courses in introductory or differential topology, this volume also serves as a supplementary text in advanced calculus and physics courses, as well as a key source of information for students of mechanics.

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Produktdetails

• Verlag: Apa Publications
• Seitenzahl: 256
• Erscheinungstermin: 26. Juni 2013
• Englisch
• ISBN-13: 9780486319070
• Artikelnr.: 39074021

Autorenporträt

David B. Gauld is a Professor of Mathematics at New Zealand's University of Auckland.

Inhaltsangabe

1. What Is Topology? 2. Topological Spaces 3. Some Topological Properties
4. Some Advanced Calculus 5. Differentiable Manifolds 6. Orientability 7.
Submanifolds and an Embedding Theorem 8. Tangent Spaces 9. Critical Points
Again 10. Vector Fields and Integral Curves 11. Surgery 12. The Trace of a
Surgery 13. Surgery on a Surface 14. Classification of Orientable Surfaces
15. Whitney's Embedding Theorem Appendix A. The Unproved Theorems Appendix
B. Further Topics Notation Bibliography Index

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