### Math 317 - Honors Advanced Calculus, II

### Instructor

### Office hours

### Syllabus

#### The implicit function theorem and application

- local properties of
*C*^{1}-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

### Textbooks

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).

### Grading

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.