Course overview
Using methods from calculus and linear algebra, this course develops essential ideas in the study of curves and surfaces in three dimensions. The central focus are the various concepts of curvature that can be assigned to a surface, and how these concepts determine most of the fundamental properties of curves and surfaces. Geometric intuition will be a point of departure from where students will produce rigorous proofs, building on concepts learned in Multivariable Calculus, and preparing the way for the study of Riemannian Geometry.
Course learning outcomes
- Obtain information about curves in space through the use of vectors and derivatives
- Derive the main properties of surface curvature through the use of curves and of the Gaussian map
- Obtain equations for geodesics, and explicit descriptions for geodesics on special surfaces
- Demonstrate ability in applying the results of the Theorema Egregium, and the Gauss-Bonnet Theorem
- Build rigorous arguments and proofs
- Communicate results in writing in a clear manner, through text, equations, and suitable figures
Degree list
The following degrees include this course