000			a
999			_c31241 _d31241
008			221104b xxu||||| |||| 00| 0 eng d
020			_a9781108441025
082			_a516.36 _bWOO
100			_aWoodward, L. M.
245			_aFirst course in differential geometry : surfaces in Euclidean space
260			_bCambridge University Press, _c2019 _aCambridge :
300			_ax, 263 p.; _bill., _c25 cm
365			_b30.99 _cGBP _d95.20
504			_aIncludes index.
520			_aDifferential 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 project.
650			_aSmooth maps
650			_aTheorema Egregium
650			_aHints or answers to some exercises
700			_aBolton, J.
942			_2ddc _cBK