In this project, we start off by discussing results from an eclectic pool of topics like Differential Geometry, Functional Analysis and Differential Toplogy, such as analytic concepts like Frechet derivatives and geometry of manifolds. We slowly move on to an in-depth analysis of ODEs and PDEs, including results pertaining to their existence and uniqueness, as well as some methods of simplifying
... [Show full abstract] and solving them. The project culminates in a discussion of Distribution Solutions of PDEs and some geometric interpretations.