Syllabus (includes schedule).
Office hours: MW 1--3, TR 1--5 at LBV 321; email: david.milovich@tamiu.edu
Textbook corrections (for first printing).
Day | Readings | Topics | Photos | Audio | Other | HW |
1 | 1.1-2 | introduction; proof techniques | zip | mp3 | 1.2 #7,10,12 | |
2 | 1.3-4 | sup and inf; completeness | zip | mp3 | 1.3 #11; 1.4 #8 | |
3 | 1.4-5 | completeness; cardinality | zip | mp3 | 1.5 #3 | |
4 | 2.1-2 | sequences and series | zip | mp3 | course outline, pictoral (jpeg) |
2.2 #2,7 |
5 | 2.3 | limit theorems | zip | mp3 | 2.3 #10,13 | |
6 | 2.4 | Monotone Convergence Theorem | zip | mp3 | 2.4 #5 | |
7 | 2.5 | Bolzano-Weierstrass Theorem | zip | mp3 (incomplete) |
2.5 #1,2 | |
8 | 2.6 | Cauchy sequences | zip | mp3 | 2.6 #3,4 | |
9 | 2.7 | infinite series properties | zip | mp3 | more solutions (pdf) | 2.7 #1,9 |
10 | 3.2-3 | open, closed, compact sets | zip | mp3 | more solutions (pdf) | 3.2 #15; 3.3 #6 |
11 | 4.1-2 | functional limits | zip | mp3 | 4.2 #5,9 | |
12 | 4.3 | continuity | zip | mp3 | more solutions (pdf) | 4.3 #1,11 |
13 | 4.4 | continuity and compactness | zip | mp3 | 4.4 #7 solved two ways
(pdf). The "Subsubsequence Lemma" (pdf). |
4.4 #3,6 |
14 | 4.5 | Intermediate Value Theorem | zip | mp3 | Days 1--7 one-page outline
(jpeg). more 4.5 solutions (zip) |
4.5 #6 |
16 | 5.1-2 | derivatives | zip | mp3 | more 5.2 solutions (zip) | 5.2 #9,10 |
17 | 5.3 | Mean Value Theorems | zip | mp3 | 5.3 #5 | |
19 | 6.1 | power series introduction | zip | mp3 | See 8.3 for an Euler's sum proof | |
20 | 6.2-3 | uniform convergence | zip | mp3 | 6.2 #9, 6.3 #6 | |
21 | 6.4-5 | power series | zip | mp3 | 6.5 #2,8 | |
24 | 6.6 | Taylor series | zip | mp3 | 6.6 #7 | |
25 | 7.2 | integrals defined | zip | mp3 | ||
27 | 7.2-4 | properties of integrals | zip | 7.3#1 | ||
28 | 7.2-4 | Fundatmental Theorems of Calculus | zip | Dec. 5 Q & A (zip) | ||
Final Exam (Dec. 11, 3:30-6:30) |
Old exams:
Fall 2012:
1,
2,
Final
Fall 2013:
1,
2,
Final
Fall 2014:
Final
Fall 2015:
1,
2,
Final
Fall 2016:
Midterm,
Final