MATH 3002--Advanced Calculus

OFFICE HOURS

Monday, December 18, 1:30-4:30 PM

Tuesday, December 19, 1:30-4:30 PM

Assignments

Course Notes (by Dr. C.K. Fong)

- Basic rules
- Equations involving differentials: Pfaffian quations
- Scalar fields,
vector fields, covector fields

- Formation of differential forms: wedge products
- Integrating 2-forms and vector-valued functions
- The theorems of Green and Stokes

- Complex 1-forms, the delbar-operator and the winding number
- Complex 2-forms: Cauchy-Pompeiu's formula
- The residue and the index

- Vector differentials and moving frames, Darboux frames in particular
- Metrics as symmetric tensors
- Cartan's structural equations and the curvature form
- The second fundamental form
- The Gauss curvature
- Geodesics and
the Gauss-Bonnet Theorem