Schedule
Lecture | Date | Topic | Reading* | Notes |
1 | Aug 29 | Natural numbers and Mathematical Induction | 1 | |
Sept 1 | Labor Day (No Class) | |||
2 | Sept 3 | Field Axioms and Rational Numbers | 2 | |
3 | Sept 5 | Real numbers | 3 | HW 1 due |
4 | Sept 8 | Completeness axiom and infinity | 4,5 | |
5 | Sept 10 | Sequences and Convergence | 7 | |
6 | Sept 12 | Proofs | 8 | HW 2 due |
7 | Sept 15 | Properties of sequences | 9 | |
8 | Sept 17 | Monotone and Cauchy sequences | 10 | |
9 | Sept 19 | Subsequences | 11 | HW 3 due |
10 | Sept 22 | Bolzano-Weierstrass Theorem | 11 | |
11 | Sept 24 | limsup and liminf | 12 | |
12 | Sept 26 | Series | 14 | HW 4 due |
13 | Sept 29 | Series | 14 | |
14 | Oct 1 | Convergence tests | 15 | |
Oct 3 | Midterm I | |||
15 | Oct 6 | Metric spaces | 13 | |
16 | Oct 8 | Metric spaces | 13 | |
17 | Oct 10 | Metric spaces | 13 | HW 5 due |
18 | Oct 13 | Continuity | 17 | |
19 | Oct 15 | Properties of continuous functions | 18 | |
20 | Oct 17 | Uniform continuity | 19 | HW 6 due |
21 | Oct 20 | Uniform continuity | 19 | |
22 | Oct 22 | Limits of functions | 20 | |
23 | Oct 24 | Limits of functions | 20 | HW 7 due |
24 | Oct 27 | Differentiation | 28 | |
25 | Oct 29 | Mean Value Theorem and Rolle's Theorem | 29 | |
26 | Oct 31 | The Riemann Integral | 32 | HW 8 due |
32 | Nov 3 | The Riemann Integral | 32 | |
Nov 5 | Midterm II review | |||
Nov 7 | Midterm II | |||
28 | Nov 10 | Properties of the Riemann integral | 33 | |
29 | Nov 12 | Fundamental theorem of calculus | 34 | |
30 | Nov 14 | Power series | 23 | HW 9 due |
31 | Nov 17 | Uniform convergence | 24 | |
32 | Nov 19 | Uniform convergence | 25 | |
33 | Nov 21 | Differentiation and integration of power series | 26 | HW 10 due |
34 | Nov 24 | Taylor series | 31 | |
35 | Nov 26 | Weierstrass function | ||
Nov 28 | Thanksgiving (No Class) | |||
36 | Dec 1 | Taylor series | 31 | |
37 | Dec 3 | Metric spaces | 21 | HW 11 due |
Dec 5 | Metric spaces | 21 | ||
Dec 10 | HW 12 due | |||
Dec 12 | Exam review session | |||
Dec 18 | Final exam |
*The numbers in the reading column refer to chapters in the course textbook
Ross, Kenneth A. Elementary Analysis. Springer, 2013.