ABSTRACT
This chapter discusses the most important class of Partial Differential Equations, the linear equations of the second order. By means of a definite transformation, one can transform the principal part of Equation to a certain standard form called canonical form. That transformation standardizes and simplifies the further analysis of the equation. The equation type is determined by the first three terms of, which contain derivatives of the second order. These terms form the principal part of the equation. The transformation is needed if at least one of the coefficients a and c is nonzero. The chapter considers three basic examples, the wave equation, the heat equation, and the Poisson equation.
