| SES # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Monotone sequences; completeness; inequalities | |
| 2 | Estimations; limit of a sequence | Assignment 1 due |
| 3 | Examples of limits | Assignment 2 due |
| 4 | Error term; limit theorems | |
| 5 | Subsequences, cluster points | Assignment 3 due |
| 6 | Nested intervals, Bolzano-Weierstrass theorem, Cauchy sequences | Assignment 4 due |
| 7 | Completeness property for sets | |
| 8 | Infinite series | Assignment 5 due |
| 9 | Infinite series (cont.) | |
| 10 | Power series | Assignment 6 due |
| 11 | Functions; local and global properties | Assignment 7 due |
| 12 | Exam 1 (open book) | Exam 1 |
| 13 | Continuity | Assignment 8 due |
| 14 | Continuity (cont.) | Assignment 9 due |
| 15 | Intermediate-value theorem | Assignment 10 due |
| 16 | Continuity theorems | Assignment 11 due |
| 17 | Uniform continuity | |
| 18 | Differentiation: local properties | Assignment 12 due |
| 19 | Differentiation: global properties | Assignment 13 due |
| 20 | Convexity; Taylor's theorem (skip proofs) | |
| 21 | Integrability | Assignment 14 due |
| 22 | Riemann integral | Assignment 15 due |
| 23 | Fundamental theorems of calculus | |
| 24 | Improper integrals, convergence, Gamma function | Assignment 16 due |
| 25 | Stirling's formula; conditional convergence | Assignment 17 due |
| 26 | Exam 2 (open book) | Exam 2 |
| 27 | Uniform convergence of series | |
| 28 | Continuity of sum; integration term-by-term | Assignment 18 due |
| 29 | Differentiation term-by-term; analyticity | Assignment 19 due |
| 30 | Continuous functions on the plane | Assignment 20 due |
| 31 | Quantifiers and Negation | Assignment 21 due |
| 32 | Plane point-set topology | Assignment 22 due |
| 33 | Compact sets and open sets | |
| 34 | Differentiating integrals with respect to a parameter | Assignment 23 due |
| 35 | Leibniz and Fubini theorems | Assignment 24 due |
| 36 | Improper integrals with a parameter | |
| 37 | Differentiating and integrating improper integrals | Assignment 25 due |
| 38 | Countability; sets of measure zero | |
| 39 | Introduction to Lebesgue integral; review | Assignment 26 due |
| 40 | Three-hour final exam during finals week (open book) | Final exam |