Introduction to Analysis

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