Differential Geometry

3 Credits · Level: Undergraduate

This course discusses the geometry of curves and surfaces. The length and the curvature of a smooth curve in two and three dimensions will be defined and computed. Parametrized surfaces in three-dimensional space are introduced and analyzed. Examples of quadric surfaces and ruled surfaces are presented. Important concepts are the Gauss curvature and Mean curvature of surfaces. Finally the inner geometry of surfaces is discussed and the concept of a geodesic, which is a curve on a surface that minimizes the distance between two points, is introduced. If time permits some theorems of vector calculus that you may have seen in Multivariable Calculus are reviewed. This course will reinforce tools studied in Multivariable Calculus, such as the chain rule, as well as elements of Linear Algebra, in particular the Spectral Theorem.