Core unitUnit 10 of 24
Real Analysis
Develop a rigorous understanding of calculus through formal definitions, limits, continuity, and convergence.
Difficulty
Beginner
Estimated study
200 hours
Duration
Self-paced
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About this unit
Unit overview
This unit establishes the rigorous foundations of calculus on the real numbers. You will work carefully with limits, continuity, differentiation, integration and convergence, learning to prove the results often assumed in introductory calculus.
Learning outcomes
What you’ll learn
- 01Use completeness and topology of the real line
- 02Prove results about sequences and series of numbers and functions
- 03Analyse continuity, uniform continuity and differentiability
- 04Develop rigorous theories of integration and convergence