Calculus or Analysis III Notes

Notes

Real Analysis III

Note: While these notes provide a self-contained path through analysis-based calculus, I highly recommend consulting Satish Shirali & H. L. Vasudeva’s Multivariable Analysis (Springer) to gain a comprehensive perspective. Specifically, this text is invaluable for its rigorous handling of Euclidean topology and the General Derivative; I suggest working through the exercises in my notes first to establish a theoretical foundation before tackling their challenging proof-based questions.

(Some other recommendations include, tom apostle calc 2, calculus on manifolds by spivak etc etc.)

Prerequisites

(Recommended for induction, field axioms, sequences)

• Algebra Notes
• Logic Notes
• Set Theory
• Real Analysis I
• Real Analysis II

Recommendations

• Multivariable Analysis by Satish Shirali & H. L. Vasudeva (Highly recommended for just the problem sets)

• Multivariable Calculus by Michael Taylor (Highly recommended for intuition)