Week | Day | Topic | Reading | Assignments |
---|---|---|---|---|
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 | 2.12.2 | ||
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, administered through Blackboard |
|
Week 4 Feb 22-26 | Tuesday | (Lecture by Prof. Ebin) Theorems about limits |
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 (administered through Blackboard) |
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 (administered through Blackboard) |
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 (administered through Blackboard) |
Cumulative | Practice exams from previous semesters: Practice final 1 (with Solutions) Practice final 2 (with Solutions) Practice final 3 |
Back to the main page of the course