Lectures |
Sections in Text |
Brief Description |
Day 1: 9/24 |
1.1, 1.2, 1.3, and 1.5 |
Notation; Background material; Why proofs? |
Day 2: 9/26 |
2.2 |
Real numbers as infinite decimals |
Day 3: 9/29 |
2.3, 2.4 |
Limits; Basic properties |
Day 4: 10/1 |
2.5 |
Least upper bound property of R |
Day 5: 10/3 |
2.6, 2.7 |
Subsequences; Cauchy sequences |
Day 6: 10/6 |
2.7 |
More about sequences, their subsequences, lim inf and lim sup |
Day 7: 10/8 |
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First midterm exam |
Day 8: 10/10 |
4.1, 4.2 |
R^n as normed vector space and metric space |
Day 9: 10/13 |
4.3 |
Topology of R^n |
Day 10: 10/15 |
4.3, 4.4 |
Topology of R^n; Compact subsets and the Heine-Borel theorem |
Day 11: 10/17 |
3.1, 3.2 |
Series; Convergence tests for series |
Day 12: 10/20 |
3.2, 3.4 |
Alternating series; Absolute and conditional convergence |
Day 13: 10/22 |
3.4 |
Rearrangement of series |
Day 14: 10/24 |
2.8 |
Cardinality |
Day 15: 10/27 |
3.3, 4.4 |
The number e; The Cantor set
|
Day 16: 10/29 |
5.1, 9.1 |
Limits of functions; Continuous functions on metric spaces |
10/29 |
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Second midterm exam (in the evening) |
Day 17: 10/31 |
5.3 |
Properties of continuous functions |
Day 18: 11/3 |
5.3 |
Properties of continuous functions |
Day 19: 11/5 |
5.4, 5.5 |
Compactness and extreme values; Uniform continuity |
Day 20: 11/7 |
5.6, 5.2 |
Intermediate Value Theorem; Discontinuous functions |
Day 21: 11/10 |
5.2, 5.7 |
Discontinuous functions; Monotone functions |
Day 22: 11/12 |
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Third midterm exam |
Day 23: 11/14 |
6.1 |
Differentiable functions |
Day 24: 11/17 |
6.2 |
Mean Value Theorem |
Day 25: 11/19 |
6.3 |
Riemann integral |
Day 26: 11/20 |
6.3 |
Riemann integral |
Day 27: 11/21 |
6.3, 6.4 |
Riemann integral; Fundamental theorem of calculus |
Day 28: 11/24 |
6.6 |
Measure zero and Lebesgue's theorem |
Day 29: 12/1 |
8.1, 8.2, 8.4 |
Limits of functions; Pointwise and uniform convergence; Series
of functions |
Day 30: 12/3 |
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Review of Chapter 6 |