MATH 4630 Handouts

Handouts - Real Analysis

Chapter 1: Completeness

• Axiom of completeness I
• Axiom of completeness II
• Consequences of completeness I
• Consequences of completeness II

Chapter 2: Sequences and Series

• Limits of sequences
• Limit theorems I
• Limit theorems II
• Monotone convergence theorem
• Subsequences and BWT
• Cauchy sequences
• Infinite series

Chapter 3: Basic Topology of R

• Open and Closed sets
• Compact sets
• Perfect sets
• Connected sets

Chapter 4: Functional Limits and Continuity

• Functional limits
• Continuous functions
• Continuity and compactness
• Intermediate value theorem

Chapter 5: Sequences and Series of Functions

• Pointwise and Uniform convergence
• Uniform convergence and derivatives