# Calendar

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