The calendar here is tentative, and the topics discussed and specific
dates are subject to change. Numbers in parentheses denote the corresponding
section from Ross, Elementary Analysis, unless specified as
"Lebl", in which case it is from Lebl, Basic Analysis.
| Fri. 8/30 |
Sets, induction (Lebl 0.3.1-2) |
| Mon. 9/2 |
No class |
| Wed. 9/4 |
Functions, field axioms (Lebl 0.3.3, Ross 3) |
| Fri. 9/6 |
Real numbers, inf and sup (3, 4) |
| Mon. 9/9 |
Completeness axiom, infinity (4, 5) |
| Wed. 9/11 |
Sequences, limits of sequences (7, 8) |
| Fri. 9/13 |
Properties of limits of sequences (9) |
| Mon. 9/16 |
Monotone sequences, lim inf and lim sup (10) |
| Wed. 9/18 |
Cauchy sequences (10) |
| Fri. 9/20 |
Subsequences and Bolzano-Weierstrass theorem (11) |
| Mon. 9/23 |
Subsequences and Bolzano-Weierstrass theorem (11) |
| Wed. 9/25 |
Midterm 1 |
| Fri. 9/27 |
Properties of lim inf and lim sup (12)
|
| Mon. 9/30 |
Series (14) (add/drop deadline) |
| Wed. 10/2 |
Alternating series, integral tests (15) |
| Fri. 10/4 |
Absolute convergence (Lebl 2.6) |
| Mon. 10/7 |
Continuous functions (17) |
| Wed. 10/9 |
Properties of continuous functions (18) |
| Fri. 10/11 |
Uniform continuity (19) |
| Mon. 10/14 |
Limits of functions (20) |
| Wed. 10/16 |
Differentiation (28) |
| Fri. 10/18 |
Mean value theorem (29) |
| Mon. 10/21 |
Applications of Mean Value Theorem, L'Hospital's Rule
(29,30) |
| Wed. 10/23 |
Riemann integration (32) |
| Fri. 10/25 |
Properties of the Riemann integral (33) |
| Mon. 10/28 |
Fundamental theorem of calculus (34) |
| Wed. 10/30 |
Integration by parts, Riemann-Stieltjes
integral (34,35) |
| Fri. 11/1 |
Midterm 2 |
| Mon. 11/4 |
Power series (23) |
| Wed. 11/6 |
Uniform convergence (24) |
| Fri. 11/8 |
Uniformly Cauchy power series (25) |
| Mon. 11/11 |
No class |
| Wed. 11/13 |
Integration and differentiation of power
series (26) |
| Fri. 11/15 |
Weierstrass's approximation theorem (27) |
| Mon. 11/18 |
Taylor's theorem (31) |
| Wed. 11/20 |
Metric spaces (Lebl 7.1) |
| Fri. 11/22 |
Open and closed sets (Lebl 7.2) |
| Mon. 11/25 |
Connectedness, closure and boundary (Lebl 7.2) |
| Wed. 11/27 |
Sequences in metric spaces (Lebl 7.3) |
| Fri. 11/29 |
No class |
| Mon. 12/2 |
Cauchy sequences, completeness (Lebl 7.4) |
| Wed. 12/4 |
Compactness (Lebl 7.4) |
| Fri. 12/6 |
Continuous functions on metric spaces (Lebl 7.5) |
| Thurs. 12/19 |
Final exam 7-10pm |