A First Course in Differential Geometry

Lyndon Woodward

ISBN 10: 1108424937 / ISBN 13: 9781108424936

Published by Cambridge University Press, 2019

About this Item

Druck auf Anfrage Neuware - Printed after ordering - With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space. Seller Inventory # 9781108424936

Bibliographic Details

Title: A First Course in Differential Geometry

Publisher: Cambridge University Press

Publication Date: 2019

Binding: Buch

Condition: Neu

About this title

Synopsis:

Differential geometry is the study of curved spaces using the techniques of calculus. It is a mainstay of undergraduate mathematics education and a cornerstone of modern geometry. It is also the language used by Einstein to express general relativity, and so is an essential tool for astronomers and theoretical physicists. This introductory textbook originates from a popular course given to third year students at Durham University for over twenty years, first by the late L. M. Woodward and later by John Bolton (and others). It provides a thorough introduction by focusing on the beginnings of the subject as studied by Gauss: curves and surfaces in Euclidean space. While the main topics are the classics of differential geometry - the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss-Bonnet Theorem - the treatment is modern and student-friendly, taking direct routes to explain, prove and apply the main results. It includes many exercises to test students' understanding of the material, and ends with a supplementary chapter on minimal surfaces that could be used as an extension towards advanced courses or as a source of student projects.

Book Description:

This textbook covers the classical topics of differential geometry of surfaces as studied by Gauss: the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss-Bonnet Theorem. It is suitable for upper-level undergraduates and contains plentiful examples and exercises, with solutions to selected problems.