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Introduction to Partial Differential Equations [2014] [PDF]

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Description

 							
  
  Title: Introduction to Partial Differential Equations
  Series: Undergraduate Texts in
Mathematics
  Author: Peter Olver 
  Format: PDF
  Hardcover: 652 pages
 
Publisher: Springer; 2014 edition (November 9, 2013)
  Language: English
  ISBN:
9783319020983
  
  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.
  
  
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