Skip to content
Register Sign in Wishlist

A First Course in Differential Geometry
Surfaces in Euclidean Space

textbook
  • Date Published: November 2018
  • availability: In stock
  • format: Paperback
  • isbn: 9781108441025

Paperback

Add to wishlist

Other available formats:
Hardback, eBook


Request inspection copy

Lecturers may request a copy of this title for inspection

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • 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.

    • Explains some of the main classical highlights of the geometry of surfaces (Theorema Egregium, geodesics, Gauss–Bonnet Theorem) using a minimal amount of theory, while presenting some advanced material suitable for self-study at the end
    • Builds up geometric intuition by providing many examples to illustrate definitions and concepts, and drawing analogies with real-life experiences
    • Includes many exercises at the end of each chapter. Students can challenge their understanding of the contents through problem solving, and brief solutions are given to about a third of the exercises
    Read more

    Reviews & endorsements

    '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

    'How to present a coherent and stimulating introduction to a mathematical subject without getting carried away into bloating it by our love for the subject? This book not only expresses the authors' enthusiasm for differential geometry but also condenses decades of teaching experience: it focuses on few milestones, covering the required theory in an efficient and stimulating way. It will be a pleasure to teach/learn alongside this text.' Udo Hertrich-Jeromin, Technische Universität Wien, Austria

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: November 2018
    • format: Paperback
    • isbn: 9781108441025
    • length: 272 pages
    • dimensions: 245 x 188 x 14 mm
    • weight: 0.61kg
    • contains: 135 b/w illus.
    • availability: In stock
  • Table of Contents

    Preface
    1. Curves in Rn
    2. Surfaces in Rn
    3. Smooth maps
    4. Measuring how surfaces curve
    5. The Theorema Egregium
    6. Geodesic curvature and geodesics
    7. The Gauss–Bonnet theorem
    8. Minimal and CMC surfaces
    9. Hints or answers to some exercises
    Index.

  • Resources for

    A First Course in Differential Geometry

    Lyndon Woodward, John Bolton

    Lecturer Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    *This title has one or more locked files and access is given only to lecturers adopting the textbook for their class. We need to enforce this strictly so that solutions are not made available to students. To gain access to locked resources you either need first to sign in or register for an account.


    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email lecturers@cambridge.org

  • Authors

    Lyndon Woodward, University of Durham
    Lyndon Woodward obtained his D.Phil. from the University of Oxford. They embarked on a long and fruitful collaboration, co-authoring over thirty research papers in differential geometry, particularly on generalisations of 'soap film' surfaces. Between them they have over seventy years teaching experience, being well-regarded as enthusiastic, clear, and popular lecturers. Lyndon Woodward passed away in 2000.

    John Bolton, University of Durham
    John Bolton earned his Ph.D. at the University of Liverpool and joined the University of Durham in 1970, where he was joined in 1971 by Lyndon Woodward.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×