Real Analysis
Calculus & Analysis
Rigorous foundations of calculus: the real number system, sequences, continuity, differentiation, Riemann integration, series of functions, and metric spaces.
Learning Objectives
- Prove properties of the real numbers using the completeness axiom
- Analyze convergence of sequences and series rigorously
- Distinguish continuity from uniform continuity and apply Cantor's theorem
- Prove and apply the Mean Value Theorem
- Understand Riemann integration and the Fundamental Theorem of Calculus
- Apply the Banach fixed-point theorem to existence proofs
Lessons
1
Foundations: The Real Number System & Completeness
35 min
2
Sequences & Series: Convergence Criteria
35 min
3
Continuity & Uniform Continuity
35 min
4
Differentiation & the Mean Value Theorem
35 min
5
Riemann Integration
35 min
6
Sequences & Series of Functions
35 min
7
Metric Spaces & Completeness
35 min
Quick Practice
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Key Concept Flashcards
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