Real Analysis

This was a second year analysis course that I taught at Imperial in 2016/17.

Contents:
  • Introduction: Recap, basic topology in $\mathbb{R}^n$
  • Chapter 1: Uniform continuity and convergence
  • Chapter 2: Integration in one variable
  • Chapter 3: Differentiation of maps $\mathbb{R}^n \to \mathbb{R}^m$
  • Chapter 4: Integration in several variables
  • Appendix: Differentiation in one dimension
Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Appendix
Complete notes
Problem sheet 1
Problem sheet 2
Problem sheet 3
Problem sheet 4
Problem sheet 5
Problem sheet 6
Problem sheet 7
Problem sheet 8
Problem sheet 9
Problem sheet A