Math 317 - Honors Advanced Calculus, II
The implicit function theorem and application
- local properties of C1-functions
- the implicit function theorem
- local extrema with constraints
Change of variables and the integral theorems by Green, Gauß, and Stokes
- the change of variables formula
- integration on curves and surfaces
- the classical integral theorems by Green, Gauß, and Stokes
- Stoke's theorem for differential forms
Infinite series and improper integrals
- infinite series
- improper integrals
Sequences and series of functions
- pointwise convergence
- uniform convergence
- power series
- Fourier series
All recommended texts for Math 217 are also recommended for Math 317. Besides,
James S. Muldowney, Advanced Calculus Lecture Notes for Mathematics 217-317, II, Third Edition.
is also recommended. I will also continue revising my TeXed lectures notes from Math 217 (click here for the old version).
The grade will be based on weekly homework assignments (30%), an in-class-midterm on February 18 (20%), and a final (50%).
Last update: 9/21/05.