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Synopsis
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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About the Authors
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.
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- PublisherCambridge University Press
- Publication date2019
- ISBN 10 1108441025
- ISBN 13 9781108441025
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages272
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Paperback. Condition: new. Paperback. 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 GaussBonnet 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. 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 GaussBonnet Theorem. It is suitable for upper-level undergraduates and contains plentiful examples and exercises, with solutions to selected problems. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781108441025
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