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Lectures on Classical Differential G 2ND Editionby Dirk J Struik
Synopses & ReviewsPublisher Comments:Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thoughtprovoking text — ideal for classroom use, but also perfectly suited for selfstudy. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry. Synopsis:Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, envelopes, more. Many problems and solutions. Bibliography. Synopsis:Excellent brief introduction covers curves, theory of surfaces, fundamental equations, geometry on a surface, conformal mapping, other topics. Problems.
Synopsis:Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Wellillustrated, with abundant pro
Table of ContentsPREFACE
BIBLIOGRAPHY CHAPTER 1. CURVES 11 Analytic representation 12 "Arc length, tangent " 13 Osculating plane 14 Curvature 15 Torsion 16 Formulas of Frenet 17 Contact 18 Natural equations 19 Helices 110 General solution of the natural equations 111 Evolutes and involutes 112 Imaginary curves 113 Ovals 114 Monge CHAPTER 2. ELEMENTARY THEORY OF SURFACES 21 Analytical representation 22 First fundamental form 23 "Normal, tangent plane" 24 Developable surfaces 25 Second fundamental form 26 Euler's theorem 27 Dupin's indicatrix 28 Some surfaces 29 A geometrical interpretation of asymptotic and curvature lines 210 Conjugate directions 211 Triply orthogonal systems of surfaces CHAPTER 3. THE FUNDAMENTAL EQUATIONS 31 Gauss 32 The equations of GaussWeingarten 33 The theorem of Gauss and the equations of Codazzi 34 Curvilinear coordinates in space 35 Some applications of the Gauss and the Codazzi equations 36 The fundamental theorem of surface theory CHAPTER 4. GEOMETRY ON A SURFACE. 41 Geodesic (tangential) curvature 42 Geodesics 43 Geodesic coordinates 44 Geodesics as extremals of a variational problem 45 Surfaces of constant curvature 46 Rotation surfaces of constant curvature 47 NonEuclidean geometry 48 The GaussBonnet theorem CHAPTER 5. SOME SPECIAL SUBJECTS 51 Envelopes 52 Conformal mapping 53 Isometric and geodesic mapping 54 Minimal surfaces 55 Ruled surfaces 56 lmaginaries in surface theory SOME PROBLEMS AND PROPOSITIONS APPENDIX: The method of Pfaffians in the theory of curves and surfaces ANSWERS TO PROBLEMS INDEX What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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