Syllabus. Textbook information.
Day | Readings | Topics | Photos | Audio | More readings | HW due | Revision due |
1 | 1 | the real line; monotone sequences | zip | mp3 | zip (binomial theorem) | 5 | 11 |
2 | 2.1-4 | inequalities and estimates | zip | mp3 | 5 | 11 | |
3 | 2.5-6 | approximations and "for n large" | zip | mp3 | 7 | 12 | |
4 | 3.1,2,5 | proving limits from the definition | zip | mp3 | 7 | 12 | |
5 | 3.3,4 | infinite limits and a^{n} | zip | mp3 | 9 | 16 | |
6 | 4 | error term analysis | zip | mp3 | 9 | 16 | |
7 | 5.1 | limit laws | zip | mp3 | zip (-∞ and ∞·∞ limits) | 13 | 20 |
8 | 5.2-4 | comparison & location theorems; subsequences | zip | mp3 | jpeg (subsequence theorem) | 13 | 20 |
9 | 6.1-3 | completeness: Bolzano-Weierstrass | zip | mp3 | jpeg (summary) | 13 | 20 |
10 | 6.4 | Cauchy completeness | zip | mp3 | 16 | 22 | |
11 | 6.4 | proving sequences Cauchy | zip | mp3 | zip (strategies) xlsx (a sequence) zip (more examples) |
||
12 | 7 | infinite series | zip | mp3 | |||
13 | 7, 8 | ratio, root tests; power series | zip | mp3 | zip (solutions 1-4) | 19 | 27 |
14 | midterm exam (days 1-5) | ||||||
15 | 9 | real functions: basic properties | zip | mp3 | 19 | 27 | |
16 | 6.5, 10 | properties pointwise, local, and global | zip | mp3 | 19 | 27 | |
17 | 11 | continuity | zip | mp3 | 23 | 29 | |
18 | 11; 12.1-2 | continuity; IVT | zip | mp3 | 23 | 29 | |
19 | 12.3-4 | Inverse Function Theorem | zip | mp3 | |||
20 | 13.1-3 | Extreme Value Theorem | zip | mp3 | 23 | 29 | |
21 | 13.5 | Uniform Continuity | zip | mp3 | 26 | ||
22 | 14 | differentiability | zip | mp3 | zip (product and inverse rules) |
26 | |
23 | 14,15 | Mean Value Theorem | zip | mp3 | 26 | ||
24 | 17 | Taylor's Theorem | zip | mp3 | zip (proof of Taylor's Thm.) | 29 | |
25 | 18 | Riemann Integrability | zip | mp3 | zip
(solutions 5-10)
zip (integrability proofs) |
29 | |
26 | 18-19 | Riemann integrals, part I | zip | mp3 | zip (interval additon integrability) | ||
27 | 19 | Riemann integrals, part II | zip | mp3 | zip
(subinterval integrability)
zip (solutions 13-16, 21-23) |
29 | |
28 | 20 | Fundamental Theorems of Calculus | zip | mp3 | zip (more integral properties) | ||
29 | 22 | Uniform convergence and power series | zip | mp3 | zip (solutions 17-20, 24-27) | ||
Final Exam: Dec. 12, 3:30-6:30 |
Old exams:
Fall 2012:
1
2
Final
Fall 2013:
1
2
Final
Fall 2014:
Final
Fall 2015:
1
2
Final