Introduction

Why Real Analysis?

Real analysis is the rigorous foundation of calculus. It replaces intuition with precise definitions and proofs, giving you a deep understanding of limits, continuity, and convergence.

  • Epsilon-delta — master the precise language of limits and continuity.
  • Sequences and series — understand convergence, divergence, and the tools to tell them apart.
  • Differentiation and integration — the Riemann integral and the fundamental theorem, done right.
  • Hands-on — implement numerical approximations and verify theoretical results in Python.

What You Will Learn

  • Sequences, limits, and the completeness of the real numbers
  • Series convergence tests
  • Continuity and the intermediate value theorem
  • Differentiation and the mean value theorem
  • Riemann integration and the fundamental theorem of calculus
Next →