Course Archives Theoretical Statistics and Mathematics Unit

Course: Curves and Surfaces Level: Undergraduate Time: Currently not offered

Syllabus Past Exams Syllabus: Curves in two and three dimensions, Curvature and torsion for space curves, Existence theorem for space curves, Serret-Frenet formula for space curves, Inverse and implicit function theorems, Jacobian theorem, Surfaces in R3 as two dimensional manifolds, Tangent space and derivative of maps between manifolds, First fundamental form, Orientation of a surface, Second fundamental form and the Gauss map, Mean curvature and scalar curvature, Integration on surfaces, Stokes formula, GaussBonnet theorem. Reference Texts: (a) M.P. do Carmo: Differential Geometry of Curves and Surfaces. (b) A. Pressley: Elementary Differential Geometry. (c) J.Thorpe: Elementary Topics in Differential Geometry. Top of the page Past Exams

Midterm 25.pdf Semestral Supplementary and Back Paper Top of the page

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