Backgrounds of Arithmetic and Geometry: An Introduction

Based on a course taught at Michigan State University, this work offers an introduction to partial differential equations (PDEs) and the relevant functional analysis tools which they require. The purpose of the course and the book is to give students a rapid and solid research-oriented foundation in areas of PDEs, such as semilinear parabolic equations, that include studies of the stability of fluid flows and of the dynamics generated by dissipative systems, numerical PDEs, elliptic and hyperbolic PDEs, and quantum mechanics