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Introduction to Partial Differential Equations (Undergraduate Texts in Mathematics), Peter J. Olver Introduction to Partial Differential Equations (Undergraduate Texts in Mathematics)
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Book details
Author : Peter J. Olver
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Pages : 636 pages
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Publisher : Springer 2016-09-14
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Language : English
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ISBN-10 : 3319020986
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ISBN-13 : 9783319020983
Book Synopsis
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 solutions, 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.