ABSTRACT
This chapter considers basic methods for solving first-order partial differential equations for an unknown function u(x, y) of two independent variables. The classical solution of an initial value problem for a first-order partial differential equation has to be continuously differentiable in the whole region where it is defined, including the line where the initial condition is imposed. The chapter examines the conditions for the existence and uniqueness of solutions of initial value problems. The general solution of a first-order equation includes anew n arbitrary function. The inverse transformation is successful, because the projections of characteristic curves on the plane (x, y) cross the projection of the initial curve transversally, i.e., neither of the characteristic curves is tangent to the initial curve anywhere.
