Introduction to Partial Differential Equations

Olver, Peter J.

  • 出版商: Springer
  • 出版日期: 2016-08-23
  • 售價: $2,480
  • 貴賓價: 9.5$2,356
  • 語言: 英文
  • 頁數: 636
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3319347446
  • ISBN-13: 9783319347448
  • 其他版本: Introduction to Partial Differential Equations
  • 立即出貨 (庫存=1)



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.





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.


Peter J. Olver是明尼蘇達大學的數學教授。他廣泛的研究興趣集中在基於對稱性的微分方程方法的發展及其多樣的應用。他是超過130篇論文的作者,這些論文發表在主要的科學研究期刊上,並且還出版了其他4本書,包括權威的Springer研究生教材《Lie群在微分方程中的應用》,以及另一本本科教材《應用線性代數》。