Introduction

Understanding Calculus through real analysis, complex analysis, and measure theory

Because we so often forget material we learn, I'm recording my understanding of analysis here.

Outline:

• Real Analysis

  • Real numbers

  • Topology: open, compact, connected

  • Functions, limits and continuity

  • Differentiation: mean value, Taylor,

  • Series and convergence

  • Integration

Althought dry, Apostol's Mathematical Analysis is a helpful reference.

• Complex Analysis (start with Weselyan notes)

  • Complex plane

  • ...