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Details for:
Pressley A. Elementary Differential Geometry 2ed 2010
pressley elementary differential geometry 2ed 2010
Type:
E-books
Files:
1
Size:
25.2 MB
Uploaded On:
March 27, 2023, 6 p.m.
Added By:
andryold1
Seeders:
12
Leechers:
1
Info Hash:
C6748E0AB2F2B47E1EA17F952CCEBA8D719C18FE
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Textbook in PDF format Curves and surfaces are objects that everyone can see, and many of the questions that can be asked about them are natural and easily understood. Differential geometry is concerned with the precise mathematical formulation of some of these questions. It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates. Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout. New features of this revised and expanded second edition include: a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book. Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature. Preface 1. Curves in the plane and in space 2. How much does a curve curve? 3. Global properties of curves 4. Surfaces in three dimensions 5. Examples of surfaces 7. Curvature of surfaces 8. Gaussian, mean and principal curvatures 9. Geodesics 10. Gauss’ Theorema Egregium 11. Hyperbolic geometry 12. Minimal surfaces 13. The Gauss–Bonnet theorem A0. Inner product spaces and self-adjoint linear maps A1. Isometries of Euclidean spaces A2. M¨obius transformations
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Pressley A. Elementary Differential Geometry 2ed 2010.pdf
25.2 MB
