SECTION 1 - Introduction

Abstract

This chapter presents the differences in the nature of partial differential equations as compared to ordinary differential equations. The continuous and differentiable dependence of the solutions on the coefficients and initial data that is true for ordinary differential equations does not hold for partial differential equations. There is the need of a classification of partial differential equations in a completely different way than for ordinary differential equations. Most of the elementary partial differential equations come from applied problems; therefore, there is a need to find correct formulations of the problem to assure the uniqueness of the solutions and its continuous dependence on the a priori given data. The chapter discusses the study of partial differential equations of the first and second order equations, which are the most important in various applications. The chapter presents various equations such as line integral in the XY-plane, surface integral in the XYZ-space, integral over a surface, Green's theorem, Stokes' theorem, and divergence theorem.