Real analysis is the study of the foundations of calculus.  The goal is to provide formal definitions and  rigorous proofs of the key concepts of calculus, starting from axioms for the real numbers.

Course components

• Limits
• Continuity
• Uniform continuity
• Derivatives
• Integrals
• Sequences and series
• Convergence of Fourier series

Flath’s notes on the textbook A Radical Approach to Real Analysis by David Bressound.