Partial Differential Equations: a Genuine Introduction to

This introduction to the theory of partial differential equations is written for the reader who likes rigorous and unhurried mathematical texts, and understands that reading such texts actually saves the time and effort. The main topics of the book cover the standard topics in an undergraduate course in PDE:

• we give a detailed account on change of variables in PDEs;
• consider first-order linear and semilinear equations (obtaining general solutions with the use of method of characteristics);
• study characteristic systems associated with first-order quasilinear equation and their first integrals;
• description of solution sets of first-order quasilinear equations;
• method of characteristics for first-order quasilinear equations, and
• second-order semilinear equations.

The books is essentially, save a number of references to the multi-variable calculus and ordinary differential equations, self-contained. Throughout the book we give numerous, detailed, and workable examples on the use of Maple and the popular online resource Wolfram Alpha for dealing with problems in the theory of partial differential equations.