Lecture Notes and Videos on Introduction to Analysis I
|
Copyright: I (Bala Krishnamoorthy) hold the copyright
for all lecture scribes/notes, documents, and other
materials including videos posted on these course web
pages. These materials might not be used for commercial
purposes without my consent.
|
Scribes from
all lectures so far (as a single big file)
| Lec | Date | Topic(s) | Scribe | Video |
| 1 |
Aug 19 |
syllabus,
notation for logical statements, contrapositive proof,
proof by contradiction, proof by induction
|
Scb1
|
Vid1
|
| 2 |
Aug 21 |
sets and operations, union, intersection, distributive laws, set
difference, De Morgan's laws, Cartesian product
|
Scb2
|
Vid2
|
| 3 |
Aug 26 |
problem on Cartesian product, families of sets, set
operations over families, functions, composition,
pre/image
|
Scb3
|
Vid3
|
| 4 |
Aug 28 |
pre/images commute with \(\cup,\cap\) or not (for
\(\cap\)), injective, surjective \(f\)'s, relation,
equivalence relation, partition
|
Scb4
|
Vid4
|
| 5 |
Sep 2 |
\(\{[x]\}_{x \in X}\) under \(\sim\) partitions \(X\),
equivalence classes of fruits, countability, Cartesian
product of countable sets
|
Scb5
|
Vid5
|
| 6 |
Sep 4 |
\(\mathbb{Q}\) is countable, \(\mathbb{R}\) is
uncountable, triangle inequality (two versions),
convergence, \(\{x_n\}\)\(\to\)\(a \Rightarrow\)\(
\{Mx_n\}\)\( \to\)\( Ma\)
|
Scb6
|
Vid6
|
| 7 |
Sep 9 |
convergence in \(\mathbb{R}^m\), continuity, \(f_i\)
continuous \(\Rightarrow f_1 + f_2 - f_3\) is,
\(g(x)\) continuous & \(g(a) \neq 0 \Rightarrow
1/g(x)\) is
|
Scb7
|
Vid7
|
| 8 |
Sep 11 |
completeness, bounded set, \(\mathbb{R}\) complete but
\(\mathbb{Q}\) is not, monotone/bounded sequence, sup,
inf, lim sup, lim inf
|
Scb8
|
Vid8
|
| 9 |
Sep 16 |
\(\lim\sup\)\(/\)\(\inf
a_n\)\(=\)\(b\)\(\Leftrightarrow\)\(\lim
a_n\)\(=\)\(b\), Cauchy sequences, continuity with
sequences, intermediate value theorem (IVT)
|
Scb9
|
Vid9
|
Last modified: Tue Sep 16 17:33:07 PDT 2025
|