Lyndon Woodward

First Course in Differential Geometry (eBook, PDF)

Surfaces in Euclidean Space

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 29. November 2018
• Englisch
• ISBN-13: 9781108582049
• Artikelnr.: 56704422

Autorenporträt

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.

Inhaltsangabe

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.

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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.

Rezensionen

'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