A Differential Approach to Geometry

Geometric Trilogy III

Authors: Borceux, Francis

  • Pays particular attention to historical development and preliminary approaches that support the contemporary geometrical notions
  • Links classical surface theory in the three dimensional real space to modern Riemannian geometry
  • Can be used to teach classical differential geometry up to an advanced level ​
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About this book

This book presents the classical theory of curves in the plane and three-dimensional space, and the classical theory of surfaces in three-dimensional space. It pays particular attention to the historical development of the theory and the preliminary approaches that support contemporary geometrical notions. It includes a chapter that lists a very wide scope of plane curves and their properties. The book approaches the threshold of algebraic topology, providing an integrated presentation fully accessible to undergraduate-level students.

At the end of the 17th century, Newton and Leibniz developed differential calculus, thus making available the very wide range of differentiable functions, not just those constructed from polynomials. During the 18th century, Euler applied these ideas to establish what is still today the classical theory of most general curves and surfaces, largely used in engineering. Enter this fascinating world through amazing theorems and a wide supply of surprising examples. Reach the doors of algebraic topology by discovering just how an integer (= the Euler-Poincaré characteristics) associated with a surface gives you a lot of interesting information on the shape of the surface. And penetrate the intriguing world of Riemannian geometry, the geometry that underlies the theory of relativity.

The book is of interest to all those who teach classical differential geometry up to quite an advanced level. The chapter on Riemannian geometry is of great interest to those who have to “intuitively” introduce students to the highly technical nature of this branch of mathematics, in particular when preparing students for courses on relativity.

About the authors

Francis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.

Reviews

“The book has a very logical structure and is written in a lively fashion. Ultimately it will serve as a very useful material for undergraduate students learning differential geometry, but it is also recommended basically to all master or PhD students in physics and mathematics.” (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 81 (3-4), 2015)

“This is the third volume of the geometric trilogy which is an introductory three-volume book in geometry. … The book contains interesting exercises which allow the reader to practice the techniques and notions treated in it as well as problems which have more theoretical interest and give the reader the possibility to explore deeper issues of geometry. … it is written with love and care. It generates interest and enthusiasm to the reader and inspires for further study of geometry.” (Charalampos Charitos, zbMATH, Vol. 1290, 2014)

Table of contents (7 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-01736-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-01735-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-319-37747-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Differential Approach to Geometry
Book Subtitle
Geometric Trilogy III
Authors
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-319-01736-5
DOI
10.1007/978-3-319-01736-5
Hardcover ISBN
978-3-319-01735-8
Softcover ISBN
978-3-319-37747-6
Edition Number
1
Number of Pages
XVI, 452
Number of Illustrations and Tables
159 b/w illustrations
Topics