Course Handouts
This page contains all handouts, and the homework assignments organized by topic. Each handout includes problems, proofs, and definitions for you to work through. Homework assignments are available below.
▸ Handouts
- Completeness and Order Properties
- Axioms of Real Numbers (Part 1) [pdf]
- Axiom of Completeness (Part 2) [pdf]
- Consequences of Completeness (Part 1) [pdf]
- Consequences of Completeness (Part 2) [pdf]
- Sequences and Series
- Sequences and Limits [pdf]
- The Limit Theorems (Part I) [pdf]
- The Limit Theorems (Part II) [pdf]
- The Cauchy Criterion [pdf]
- Monotone Convergence Theorem and Infinite Series [pdf]
- Subsequences and Bolzano-Weierstrass [pdf]
- Properties of Infinite Series [pdf]
- Basic Topology of ℝ
- Open Sets, Closed Sets, Limit Points [pdf]
- Compact Sets [pdf]
- Perfect Sets [pdf]
- Connected Sets [pdf]
- Functional Limits and Continuity
- Limit of a function [pdf]
- Continuous functions [pdf]
- Compact sets and Uniform continuity [pdf]
- Intermediate Value Theorem [pdf]
- Sequence of Functions
- Pointwise and Uniform convergence [pdf]
- Uniform convergence and Derivatives [pdf]