Math 5302, Elementary Analysis II
Spring 2020
John Zweck
Course Materials
Syllabus
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 Wed Jan 29]
Homework 2 [Due Wed Feb 12]
Homework 3 [Due Wed Feb 26]
Homework 4 [Due Mon Mar 9]
Homework 5 [Due Wed Apr 1]
Homework 6A [Due Fri Apr 10]
Homework 6B [Due Mon Apr 20]
Homework 7 [Due Mon Apr 27]
Homework 8 [Due Fri May 1]
Homework 9 [Not Due]
Exam Preparation Resources
Practice Exam Midterm Questions
Spring 2019 Midterm Exam
Practice Final Exam
Theory Summary [provided on Final Exam]