Please the see policy on problem sets for more about these.
- Some Linear Algebra Review
- Vectors and Vector Operations
- Linear Independence
- Basis Vectors
- Linear Maps
- Curves in the Plane and Space
- Definitions
- Arc length
- Reparametrization
- Curvature and Torsion
- Tangent, Normal, Binormal vectors
- Osculating Pane and Circle
- Involute and Evolute
- Quick Introduction to Topology
- Open and Closed sets
- Continuity
- Connectivity
- Homomorphism, Diffeomorphism
- Surfaces in Space
- Regular Surfaces
- Curves on Surfaces
- Surfaces of Revolution
- Inverse Function Theorem
- Tangent Planes
- First and Second Fundamental Forms
- Curvatures (Principal, Mean, etc)
- Gauss Map
- Geodesics
- Orientability
- Theorema Egregium
- Gauss-Bonnet Theorem
See the course calendar for the timing of exams and quizzes. The final exam will be scheduled by the registrar; see the official exam schedule when it is available.
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