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Geometry of Surfaces

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 293/5 ( reviews)

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Book Synopsis Geometry of Surfaces by : John Stillwell

Download or read book Geometry of Surfaces written by John Stillwell. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.

Geometry of Surfaces

2013-01-04 Technology & Engineering
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Release : 2013-01-04
Genre : Technology & Engineering
Kind : eBook
Book Rating : 710/5 ( reviews)

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Book Synopsis Geometry of Surfaces by : Stephen P. Radzevich

Download or read book Geometry of Surfaces written by Stephen P. Radzevich. This book was released on 2013-01-04. Available in PDF, EPUB and Kindle. Book excerpt: Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces. Geometry of Surfaces: A Practical Guide for Mechanical Engineers combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering. Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineering Combines differential geometry and gearing theory Highlights new developments in the elementary theory of enveloping surfaces Essential reading for researchers and practitioners in mechanical, automotive and aerospace engineering industries; CAD developers; and graduate students in Mechanical Engineering.

Topological, Differential and Conformal Geometry of Surfaces

2021-10-27 Mathematics
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Release : 2021-10-27
Genre : Mathematics
Kind : eBook
Book Rating : 325/5 ( reviews)

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Book Synopsis Topological, Differential and Conformal Geometry of Surfaces by : Norbert A'Campo

Download or read book Topological, Differential and Conformal Geometry of Surfaces written by Norbert A'Campo. This book was released on 2021-10-27. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.

Geometry and Topology of Surfaces

2021
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Release : 2021
Genre :
Kind : eBook
Book Rating : 006/5 ( reviews)

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Book Synopsis Geometry and Topology of Surfaces by : Sebastian Baader

Download or read book Geometry and Topology of Surfaces written by Sebastian Baader. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt:

Differential Geometry Of Curves And Surfaces

2017-05-12 Mathematics
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Release : 2017-05-12
Genre : Mathematics
Kind : eBook
Book Rating : 268/5 ( reviews)

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Book Synopsis Differential Geometry Of Curves And Surfaces by : Masaaki Umehara

Download or read book Differential Geometry Of Curves And Surfaces written by Masaaki Umehara. This book was released on 2017-05-12. Available in PDF, EPUB and Kindle. Book excerpt: 'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.

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