| Jan 9 |
1.1–1.3 |
Real numbers as an ordered field, bounds, supremum, infimum, completeness of the real numbers |
| Jan 12 |
1.4–2.1 |
Natural numbers, induction, rational and irrational numbers, absolute value, sequences, limits |
| Jan 16 |
2.1–2.2 |
Bounded sequences, properties of limits |
| Jan 19 |
2.3–2.4 |
Monotonic convergence criterion, subsequences, Bolzano-Weierstrass Theorem |
| Jan 23 |
2.5–2.6 |
Cauchy sequences, limit sup, lim inf |
| Jan 26 |
3.1, 3.2 |
Series, alternating series, boundedness criterion, Cauchy criterion |
| Jan 30 |
3.2, 3.3 |
Convergence tests, absolute convergence |
| Feb 2 |
4.1, 4.2 |
The topology of Rn, convergence in Rn |
| Feb 6 |
4.3 |
Open and closed sets in Rn |
| Feb 9 |
4.4 |
Compact sets, the Heine-Borel Theorem |
| Feb 13 |
5.1 |
Limits of functions |
| Feb 16 |
5.2, 5.3 |
Continuity |
| Feb 20–24 |
|
Reading week |
| Feb 27 |
5.3 |
Properties of continuous functions |
| Mar 2 |
1.1–5.2 |
Midterm test |
| Mar 6 |
5.4, 5.5 |
Inverse functions, uniform continuity |
| Mar 9 |
6.1, 6.2 |
Derivatives |
| Mar 13 |
6.3, 6.4 |
Local extrema, Rolle's Theorem, Mean Value Theorem |
| Mar 16 |
7.1, 7.2 |
The Riemann integral, integrability |
| Mar 20 |
7.2, 7.3 |
Properties of the integral, The Fundamental Theorem of Calculus |
| Mar 23 |
7.4, 8.1 |
Improper integrals, sequences and series of functions, pointwise convergence |
| Mar 27 |
8.2, 8.3 |
Uniform convergence, Weierstrass M-test, properties of uniform convergence |
| Mar 30 |
9.1, 9.2 |
Power series |
| Apr 3 |
9.3, 9.4 |
Taylor series, Fourier series |
| Apr 6 |
Notes |
Review |