Winding Around The Winding Number in Topology Geometry and Analysis 1st Edition by John Roe 1470421984 9781470421984

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ISBN-10 :  1470421984 

ISBN-13 :  9781470421984

Author:  John Roe 

Please Read Notes: Brand New, International Softcover Edition, Printed in black and white pages, minor self wear on the cover or pages, Sale restriction may be printed on the book, but Book name, contents, and author are exactly same as Hardcover Edition. Fast delivery through DHL/FedEx express.

 

Winding Around The Winding Number in Topology Geometry and Analysis 1st Table of contents:

Chapter 1. Prelude: Love, Hate, and Exponentials
§1.1. Two sets of travelers
§1.2. Winding around
§1.3. The most important function in mathematics
$1.4. Exercises

Chapter 2. Paths and Homotopies
§2.1. Path connectedness
52.2. Homotopy
§2.3. Homotopies and simple-connectivity
§2.4. Exercises

Chapter 3. The Winding Number
§3.1. Maps to the punctured plane
§3.2. The winding number
53.3. Computing winding numbers
§3.4. Smooth paths and loops

Chapter 4. Topology of the Plane
§4.1. Some classic theorems
§4.2. The Jordan curve theorem I
§4.3. The Jordan curve theorem II
$4.4. Inside the Jordan curve
§4.5. Exercises
Chapter 5. Integrals and the Winding Number
§5.1. Differential forms and integration
§5.2. Closed and exact forms
§5.3. The winding mumber via integration
§5.4. Homology
§5.5. Cauchy’s theorem
55.6. A glimpse at higher dimensions
§5.7. Exercises

Chapter 6. Vector Fields and the Rotation Number
$6.1. The rotation number
§6.2. Curvature and the rotation number
§6.3. Vector fields and singularities
$6.4. Vector fields and surfaces
§6.5. Exercises

Chapter 7. The Winding Number in Functional Analysis
§7.1. The Fredholm index
§7.2. Atkinson’s theorem
§7.3. Toeplitz operators
§7.4. The Toeplitz index there
§7.5. Exercises

 

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