Title
Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218),Used
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This book is an introductory graduatelevel textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A fewnew topics have been added, notably Sard?s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of firstorder partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
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- Q: How many pages does this book have? A: This book has seven hundred twenty four pages. It provides an in-depth exploration of smooth manifolds suitable for graduate-level study.
- Q: What is the binding type of this book? A: The book is bound in hardcover. This ensures durability and makes it suitable for frequent use in academic settings.
- Q: What are the dimensions of this book? A: The book measures six point fourteen inches in length, one point five inches in width, and nine point twenty one inches in height. These dimensions make it a manageable size for reading and transport.
- Q: What topics does this book cover? A: This book covers smooth structures, tangent vectors, vector bundles, and more. It is designed to familiarize students with essential tools for mathematical and scientific research.
- Q: Who is the author of this book? A: The author of this book is John Lee. He is known for his contributions to the field of mathematics, specifically in differential geometry.
- Q: Is this book suitable for beginners? A: No, this book is not suitable for beginners. It is intended for graduate-level students with prior knowledge of general topology and linear algebra.
- Q: What prerequisites are needed for this book? A: A solid understanding of general topology, the fundamental group, and basic linear algebra is required. Familiarity with real analysis is also beneficial.
- Q: How can I use this book effectively? A: You can use this book as a textbook for graduate courses or as a reference for research. It provides clear explanations and examples to aid understanding of complex topics.
- Q: Is there a specific audience for this book? A: Yes, this book is tailored for graduate students and researchers in mathematics and related fields. It may not be suitable for casual readers.
- Q: How should I care for this book? A: To care for this book, keep it in a dry and clean environment. Avoid exposing it to direct sunlight to prevent fading and damage.
- Q: Can I return this book if I am unsatisfied? A: Yes, you can typically return this book if you are unsatisfied. Check the retailer's return policy for specific details.
- Q: What should I do if my book arrives damaged? A: If your book arrives damaged, contact the seller immediately to report the issue. They will provide instructions for returning or exchanging the item.
- Q: Is this book available in other formats? A: No, this book is currently only available in hardcover format. There is no indication of an ebook or paperback version.
- Q: Does this book include exercises or problems? A: Yes, this book includes exercises to test understanding and application of the concepts discussed. This is helpful for students in mastering the material.
- Q: Is this book updated from previous editions? A: Yes, this is the second edition, which has been extensively revised and clarified from the first edition. New topics have also been added.