# Math 5302, Elementary Analysis II

# Spring 2019

## John Zweck

## Course Materials

Syllabus

Conceptual Learning: Senses, Emotions and Math

Mathematics Professors and Mathematics Majors'
Expectations of Lectures in Advanced Mathematics
[Keith Weber, AMS Blog]

## Lecture Notes

1A. Course Overview (Part A)

1B. Course Overview (Part B)

2. The Riemann Integral and Conditions for Integrability

3A. Lower and Upper Darboux Integrals (Part A)

3A. Lower and Upper Darboux Integrals (Part B)

4. Integrability Results

5. Properties of the Riemann Integral

6. Main Integration Theorems

7. Improper Integrals

8A. The Gamma Function

8B. Integration of Radially Symmetric Functions

9A. Functions of Bounded Variation (Part A)

9B. Functions of Bounded Variation (Part B)

9C. Functions of Bounded Variation (Part C)

10A. Riemann Stieltjes Integration (Part A)

10B. Riemann Stieltjes Integration (Part B)

10C. Riemann Stieltjes Integration (Part C)

10D. Riemann Stieltjes Integration (Part D)

11. Summary of Results on BV and RSI

12. Topology of Euclidean Space

13A. Lebesgue Measure on Euclidean Space (Part A)

13B. Lebesgue Measure on Euclidean Space (Part B)

14. Lebesgue Measure on Euclidean Space (Cont'd)

15. Inner and Outer Measure; Measurable Sets

16. Sigma-Algebras and Measurable Functions

17. Introduction to the Lebesgue Integral

## Homework Assignments

Homework 1 [Due Th Jan 31]

Homework 2 [Due Tu Feb 12]

Homework 3 [Due Tu Feb 19]

Homework 4 [Due Tu Mar 5]

Homework 5 [Due Tu Mar 28]

## Exam Preparation Resources

Practice Exam I