Calculus or Analysis I Notes

These notes provide a rigorous reconstruction of calculus from the ground up. Starting with the Field Axioms and the Completeness of the Real Numbers, we develop the $\epsilon-N$ definition of convergence, explore the topology of the real line (Bolzano-Weierstrass, Cauchy sequences), and conclude with a comprehensive treatment of Infinite Series.

Notes

Real Analysis I

Note: I really recommend reading Analysis 1 by Tao along side my notes it helps to get both perspectives.

Real Analysis I (If my notes are too dense you can use this instead.)

Prerequisites

(Recommended for induction and field axioms)

Algebra Notes Logic Notes Set Theory

Recommendations

• Understanding Analysis - Stephen Abbott (Highly recommended for intuition)
• Analysis I - Terence Tao (For a constructive approach to the number system)