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