Analysis II

Department: 
MATH
Course Number: 
4318
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Spring only starting Spring 2020

Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n

Prerequisites: 

MATH 4317

Course Text: 

Bartle, Elements of Real Analysis

Topic Outline: 
  • The derivative: mean value theorem, L'Hôpital's rule, Taylor's theorem
  • The Riemann Stieltjes integral, integration by parts, change of variables. Sets of measure zero, Cantor functions
  • Improper integrals
  • The derivative in Rn: Jacobians, chain rule, implicit and inverse function theorems. Extrema, second derivative tests, Lagrange multipliers
  • Integration in Rn: Mean value theorem, iterated integrals, and change of variables. Sets of measure zero and Sard's theorem