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, engineering, and elsewhere. The exposition
carefully balances solution techniques, mathematical rigor, and
significant applications, all illustrated by numerous examples.
Extensive exercise sets appear at the end of almost every
subsection, and include straightforward computational problems to
develop and reinforce new techniques and results, details on
theoretical developments and proofs, challenging projects both
computational and conceptual, and supplementary material that
motivates the student to delve further into the subject.
No previous experience with the subject of partial differential
equations or Fourier theory is assumed, the main prerequisites
being undergraduate calculus, both one- and multi-variable,
ordinary differential equations, and basic linear algebra. While
the classical topics of separation of variables, Fourier analysis,
boundary value problems, Green's functions, and special functions
continue to form the core of an introductory course, the inclusion
of nonlinear equations, shock wave dynamics, symmetry and
similarity, the Maximum Principle, financial models, dispersion and
solitons, Huygens'.
Principle, quantum mechanical systems, and more make this text
well attuned to recent developments and trends in this active field
of contemporary research. Numerical approximation schemes are an
important component of any introductory course, and the text covers
the two most basic approaches: finite differences and finite
elements.
Peter J. Olver is professor of mathematics at the University of
Minnesota. His wide-ranging research interests are centered on the
development of symmetry-based methods for differential equations
and their manifold applications. He is the author of over 130
papers published in major scientific research journals as well as 4
other books, including the definitive Springer graduate text,
Applications of Lie Groups to Differential Equations, and another
undergraduate text, Applied Linear Algebra.
A Solutions Manual for instrucors is available by clicking on
"Selected Solutions Manual" under the Additional Information
section on the right-hand side of this page. "
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