MATH 317 - Honors Advanced Calculus, II

Instructor

Volker Runde

Office hours

by appointment

Syllabus

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

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 continue following my own TeXed lectures notes from MATH 217.

Grading

The grade will be based on weekly homework assignments (30%), an in-class-midterm on February 26 (20%), and a final (50%).