Partial Differential Equations

An Introduction to Theory and Applications

Nonfiction, Science & Nature, Mathematics, Differential Equations, Calculus
Cover of the book Partial Differential Equations by Michael Shearer, Rachel Levy, Princeton University Press
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Author: Michael Shearer, Rachel Levy ISBN: 9781400866601
Publisher: Princeton University Press Publication: March 1, 2015
Imprint: Princeton University Press Language: English
Author: Michael Shearer, Rachel Levy
ISBN: 9781400866601
Publisher: Princeton University Press
Publication: March 1, 2015
Imprint: Princeton University Press
Language: English

This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.

Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs.

  • Provides an accessible yet rigorous introduction to partial differential equations
  • Draws connections to advanced topics in analysis
  • Covers applications to continuum mechanics
  • An electronic solutions manual is available only to professors
  • An online illustration package is available to professors
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This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.

Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs.

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