First Course in Differential Geometry

Surfaces in Euclidean Space

Häftad, Engelska, 2018

Av Lyndon Woodward, John Bolton, Lyndon (University of Durham) Woodward, John (University of Durham) Bolton

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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.

Produktinformation

Utgivningsdatum2018-11-29
Mått188 x 245 x 14 mm
Vikt610 g
FormatHäftad
SpråkEngelska
Antal sidor272
FörlagCambridge University Press
ISBN9781108441025

Tillhör följande kategorier

Matematik inom Naturvetenskap och teknik
Topologi inom Naturvetenskap och teknik

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 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.

'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