This modern take on partial differential equations does not require
knowledge beyond vector calculus and linear algebra. The author
focuses on the most important classical partial differential
equations, including conservation equations and their
characteristics, the wave equation, the heat equation, function
spaces, and Fourier series, drawing on tools from analysis only as
they arise. Within each section the author creates a narrative that
answers the five questions: What is the scientific problem we are
trying to understand? How do we model that with PDE? What
techniques can we use to analyze the PDE? How do those techniques
apply to this equation? What information or insight did we obtain
by developing and analyzing the PDE? The text stresses the
interplay between modeling and mathematical analysis, providing a
thorough source of problems and an inspiration for the development
of methods.
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