A First Course in Differential Geometry

Surfaces in Euclidean Space

by Lyndon Woodward,

Subject categories
ISBNs
  • 9781108424936
  • 9781108582049
  • 9781108600910
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.
  • Cambridge University Press; November 2018
  • ISBN: 9781108582049
  • Read online, or download in secure PDF or secure ePub format
  • Title: A First Course in Differential Geometry
  • Author: Lyndon Woodward; John Bolton
  • Imprint: Cambridge University Press
Subject categories
ISBNs
  • 9781108424936
  • 9781108582049
  • 9781108600910

In The Press

'An excellent introduction to the subject, suitable for learners and lecturers alike. The authors strike a perfect balance between clear prose and clean mathematical style and provide plenty of examples, exercises and intuitive diagrams. The choice of material stands out as well: covering the essentials and including interesting further topics without cluttering. This wonderful book again reminded me of the beauty of this topic!' Karsten Fritzsch, Gottfried Wilhelm Leibniz Universität Hannover, Germany

Subject categories
ISBNs
  • 9781108424936
  • 9781108582049
  • 9781108600910