Lyndon Woodward, John Bolton

A First Course in Differential Geometry

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 274
• Erscheinungstermin: 30. November 2018
• Englisch
• Abmessung: 246mm x 189mm x 15mm
• Gewicht: 610g
• ISBN-13: 9781108441025
• ISBN-10: 1108441025
• Artikelnr.: 53166824

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