A Local Existence and Uniqueness Theorem for First Order Differential Equations

As a student in Math 22b, taught by Dr. Dusty Grundmeier, I learned introductory proof-based vector calculus with some exposure to limits and continuity. However, I was interested in getting more exposure to real analysis, so for my final project I learned about existence and uniqueness theorems for differential equations and wrote an expository paper presenting a simple case of such a theorem.