| Date |
Material covered |
Book section |
Assignment |
| January 25 |
Introduction/sets/functions
|
0.1 and 0.2
|
Assignment Zero tex and pdf
|
| January 27 |
Natural numbers/induction
|
0.3
|
Assignment 1 - Due February 3rd, tex and pdf |
| January 29 |
Countable sets
|
0.4
|
|
| February 1 |
Real numbers
|
0.5
|
|
| February 3 |
Sequences
|
1.1
|
Assignment 2 - Due February 10th, tex and pdf |
| February 5 |
Cauchy sequences
|
1.2
|
|
| February 8 |
Operations with sequences
|
1.3
|
|
| February 10 |
Subsequences I
|
1.4
|
Assignment 3 - Due February 17th, tex and pdf |
| February 12 |
Subsequences II
|
2.1
|
|
| February 15 |
Limits of functions
|
2.2
|
|
| February 17 |
Operations with limits
|
2.3
|
|
| February 19 |
Continuity
|
3.1
|
|
| February 22 |
Algebra of continuous functions
|
3.2
|
|
| February 24 |
Uniform continuity
|
3.3
|
Assignment 4 - Due March 3rd, tex and pdf |
| February 26 |
Special topic I
|
|
Exam 1 - Due February 26th by 6pm Central time, tex and pdf (Solutions) |
| March 1 |
Compact sets
|
3.3
|
|
| March 3 |
Properties of continuous functions
|
3.4
|
|
| March 5 |
Properties of continuous functions II
|
3.4
|
Assignment 5 - Due March 12th, tex and pdf |
| March 8 |
The derivative of a function
|
4.1
|
|
| March 10 |
Operations with derivatives
|
4.2
|
|
| March 12 |
Mean value theorem
|
4.3
|
Assignment 6 - Due March 17th, tex and pdf |
| March 15 |
Mean value theorem II
|
4.3
|
|
| March 17 |
L'Hospital's rule
|
4.4
|
|
| March 19 |
The Riemann Integral
|
5.1
|
|
| March 22 |
Integrable functions
|
5.2
|
|
| March 24 |
Riemann sums
|
5.3
|
|
| March 26 |
Special topic II
|
|
Exam 2 due March 26th by 6pm Central time, tex and pdf (Solutions) |
| March 29 |
The Fundamental Theorem of Integral Calculus
|
5.4
|
|
| March 31 |
The algebra of integrable functions
|
5.5
|
|
| April 2 |
Derivatives of integrals
|
5.6
|
Assignment 7 - Due April 9th, tex and pdf |
| April 5 |
Change of variables
|
5.6
|
|
| April 7 |
Change of variables II
|
5.7
|
|
| April 9 |
Convergence of series
|
6.1
|
|
| April 12 |
Absolute convergence
|
6.2
|
|
| April 14 |
Ratio and root test
|
6.3
|
|
| April 16 |
Conditional convergence
|
6.4
|
|
| April 19 |
Power series
|
6.5
|
|
| April 21 |
Taylor series
|
6.6
|
|
| April 23 |
Special topic III
|
|
Exam 3 due April 23rd by 6pm Central time, tex and pdf |
| April 26 |
Convergence of functions
|
7.1
|
|
| April 28 |
Uniform convergence
|
7.2
|
|
| April 28 |
Uniform convergence of power series
|
7.3
|
Final Exam due May 10th by 6pm Central time, No late work accepted, tex and pdf |