## Analysis II

Department:
MATH
Course Number:
4318
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every spring and fall semesters

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

Prerequisites:
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