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Preface

This book is a continuation of our book Bandura A. I., Ovchar I. Ye., Tymkiv I.R.

Partial differential equations: lectures. – Ivano-Frankivs’k: IFNTUOG, 2018. –
138 p.
It provides an introduction to the basic methods to solve partial differential
equations (PDEs) and to the techniques that have proved useful in analyzing them.
Our purpose is to provide for the student a broad perspective on the subject, to

illustrate the rich variety of phenomena encompassed by it and to impart a working
knowledge of the most important techniques of analysis of the solutions of the
equations. One of the most important techniques is the method of separation of

variables (Fourier’s method). Many textbooks heavily emphasize this technique to
the point of excluding other points of view. The problem with that approach is
that only certain kinds of partial differential equations can be solved by it, whereas
others cannot. In this book it plays a very important but not an overriding role.
This is an undergraduate textbook. It is designed for juniors and seniors who are

science, engineering, or mathematics majors. Graduate students, especially in the
sciences, could surely learn from it, but it is in no way conceived ofas a graduate
text.

The main prerequisite is a solid knowledge of calculus, especially multivariate.
The other prerequisites are small amounts of ordinary differential equations and of
linear algebra, each much less than a semester’s worth. However, since the subject
of partial differential equations is by its very nature not an easy one, we have
recommended to our own students that they should already have taken full courses

in these two subjects.
The presentation is based on the following principles. Motivate with physics but
then do mathematics. Focus on the three classical equations: All the important
ideas can be understood in terms of them.

Our book contains guidelines for solutions of typical problems on partial differ-
ential equations.
Many useful exercises with full solutions are presented in the textbook. Answers
and hints to Supplementary problems of every section are included at the end of

this book.
The authors welcome reader’s suggestions for improvement of future editions of
this book.

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