Math 4351.001 Advanced Calculus II
TEXTBOOKS: Introduction to Real Analysis, 4th Ed. by Bartle and Sherbert; Methods of Real Analysis by Goldberg.
Chapters 6,7,8,9,11 (Bartle and Sherbert), Chapter 11 (Goldberg)
Exams (65%), Written Assignments (35%)
Syllabus Syllabus
Review Topics from Advanced Calculus I topics
All Written Assignments must be written neatly and clearly with correct mathematical arguments to justify your steps.
- Written Assignment #1, 6.1 #4,7,9; 6.2 #4,5,6,11,14; Friday, September 7
- Graphs of sin(1/x), xsin(1/x), x^2sin(1/x) Graphs
- Written Assignment #2, Friday, September 14 Assignment #2
- Characteristic Function, Friday, September 21 In-Class #1
- Riemann Integral In-Class #2
- Written Assignment #3, Monday, September 24 Assignment #3
- Selected Proofs Assign #1-#3 Proofs
- Review Topics for Exam #1 Review #1
- Practice Problems 1 Answers
- Exam #1, Chapters 6.1-6.4, 7.2-7.4, Friday, September 28 Answers
- Sequences and Series of Functions 8.1,8.2,9.4
- In Class Presentations, Wednesday, October 10, 8.1 #5,14,15; 8.2#6,
- Written Assignment #4, Friday, October 12, 8.1 #4,5,14,15,21; 8.2 #3,6,9,12
- Written Assignment #5, Friday, October 19, 9.1 #1,7,8; 9.2#1b,2b,3b,4b,7b,8;9.3#1b
- In Class Presentations, Monday, October 22, 9.3 #9; 9.4 # 1bd,2
- In Class Assignment Series of Functions
- Review Topics for Exam #2 Review #2
- Exam #2, Friday, October 26, Chapters 8.1-8.2,9.1-9.4 Answers
- Written Assignment #6, Friday, November 9, 2018 Assignment #6
- In Class Assignments, Chapter 11 Goldberg, 11.1-11.4 November 12-19
Exercises
- Review Topics for Exam #3 Review #3
- Exam #3, Chapter 11 Bartle and Sherbert (Glimpse into Topology) and Chapter 11.1-11.4, Goldberg (Lebesgue Integral), Wednesday, November 28
- Exam #3 Answers Answers
- Lebesgue Integral Defined Lebesgue Integral
- Goldberg 11.6 # 1, Monday, December 3 (Optional)
- Comprehensive Final Exam #4, Tuesday, December 11 (7:30-10 am)