A First Course in Differential Geometry: Surfaces in Euclidean Space

ISBN-13: 9781108441025 / Angielski / Miękka / 2019 / 272 str.

John Bolton; L. M. Woodward

Opis

With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.

Recenzje

'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

Spis treści

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.

O autorze

Woodward, Lyndon 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. Bolton, John 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.