This textbook is designed for a one-year course covering the fundamentals of partial
differential equations, geared towards advanced undergraduates and beginning graduate
students in mathematics, science, and engineering. No previous experience with the subject
is assumed, while the mathematical prerequisites for embarking on this course of study
will be listed below. For many years, I have been teaching such a course to students
from mathematics, physics, engineering, statistics, chemistry, and, more recently, biology,
finance, economics, and elsewhere. Over time, I realized that there is a genuine need for
a well-written, systematic, modern introduction to the basic theory, solution techniques,
qualitative properties, and numerical approximation schemes for the principal varieties of
partial di?erential equations that one encounters in both mathematics and applications. It
is my hope that this book will ?ll this need, and thus help to educate and inspire the next
generation of students, researchers, and practitioners.