# Schedule for MAT 319 - Foundations of Analysis - Spring 2021

Week 1
Feb 1-5
MAT 319 and MAT 320 follow the joint schedule through February 25
Tuesday Classes canceled due to weather
Thursday Syllabus
Introduction
Sets and functions
1.1 Homework 1 (Due Feb 10)
1.1 (pages 10-11): 5, 10, 16, 23, 24
Week 2
Feb 8-12
Tuesday Well ordering property and mathematical induction
Finite, countable and uncountable sets, Cantor's theorem
1.2
1.3
Homework 2 (Due Feb 17)
1.2 (page 15): 3, 5, 7, 11
1.3 (page 22): 4, 6, 12
Thursday Field properties and order properties of real numbers 2.1
2.2
Week 3
Feb 15-19
Tuesday The completeness property
Applications of the completeness property
2.3
2.4
Homework 3 (Due Feb 24)
2.4 (pages 44-45): 3, 5, 7, 9, 13, 17
2.5 (pages 52-53): 3, 7, 9, 14
Thursday (Lecture by Prof. Ebin)
Intervals
Limit of a sequence

2.5
3.1
Take-home Quiz (Due Feb 19 at 3pm)
Cumulative, open book,
Week 4
Feb 22-26
Tuesday (Lecture by Prof. Ebin)

3.2
Thursday (Lecture by Prof. Ebin)
Monotone sequences
Subsequences and the Bolzano-Weierstrass theorem

3.3
3.4
Week 5
Mar 1-5
Tuesday Midterm I
During lecture time
Cumulative
(Everything up to Thursday, Feb 26)
Practice exams from previous semesters:
Practice midterm 1 (Solutions)
Practice midterm 2 (with Solutions)
Practice midterm 3 (Solutions)
Practice midterm 4 (Solutions)
Everything from here is for MAT 319 only
Thursday Review of sequences
Properly divergent sequences
3.5
3.6
Homework 4 (Due Mar 10)
3.1 (pages 61-62): 5d, 8, 9
3.2 (pages 69-70): 6b, 6d, 7, 17
3.3 (page 77): 9
Week 6
Mar 8-12
Tuesday Infinite series 3.7 Homework 5 (Due Mar 17)
3.4 (page 84): 1, 5
3.5 (page 91): 1, 2, 4, 5
3.6 (page 93): 3, 6
Thursday Limits of functions 4.1
Week 7
Mar 15-19
Tuesday Limit theorems 4.2
4.3
Homework 6 (Due Mar 24)
3.7 (pages 100-101): 5, 9, 10
4.1 (page 110): 7, 12d, 15
4.2 (page 116): 5, 9
Thursday Continuous functions
Combinations of continuous functions
5.1
5.2
Week 8
Mar 22-26
Tuesday Continuous functions on intervals 5.3 Optional Homework Set
4.3 (page 123): 2, 4, 12
5.1 (page 129): 3, 5, 11
5.2 (pages 133-134): 3, 5, 6
Thursday Continuous functions on intervals 5.3
Week 9
Mar 29-Apr 2
Tuesday Uniform continuity 5.4 Homework 7 (Due Apr 14)
5.3 (page 140): 4, 6, 13
5.4 (page 148): 2, 7, 10
5.6 (page 160): 1, 11
Thursday Monotone and inverse functions
Review
5.6
Week 10
Apr 5-9
Tuesday Midterm II
During lecture time
Cumulative
(with focus on material after Midterm I)
Practice exams from previous semesters:
Practice midterm 1 (with Solutions)
Practice midterm 2 (with Solutions)
Practice midterm 3
Thursday The derivative 6.1
Week 11
Apr 12-16
Tuesday The mean value theorem 6.2 Homework 8 (Due Apr 21)
6.1: 1ac, 4, 8ac
6.2: 1d, 6, 13
Thursday Applications of the mean value theorem 6.2
Week 12
Apr 19-23
Tuesday L'Hospital's rules 6.3 Homework 9 (Due Apr 28)
6.3: 5, 8, 11
6.4: 4, 11, 14c
Thursday Taylor's theorem 6.4
Week 13
Apr 26-30
Tuesday Applications of Taylor's theorem 6.4 Homework 10 (Due May 5)
7.1: 6a, 8, 12
7.2: 8, 9, 12
Thursday Riemann Integral 7.1
Week 14
May 3-7
Tuesday Integrable functions 7.2
Thursday The fundamental theorem of Calculus 7.3
May 18 Tuesday Final Exam
11:15am-1:45pm