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Partial differential equationsmathem...

Epstein, Marcelo.

Partial differential equationsmathematical techniques for engineers /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Partial differential equationsby Marcelo Epstein.
其他題名:	mathematical techniques for engineers /
作者:	Epstein, Marcelo.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xiii, 255 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Partial.
電子資源:	http://dx.doi.org/10.1007/978-3-319-55212-5
ISBN:	9783319552125$q(electronic bk.)

Partial differential equationsmathematical techniques for engineers /
Epstein, Marcelo.

Partial differential equationsmathematical techniques for engineers /[electronic resource] :by Marcelo Epstein. - Cham :Springer International Publishing :2017. - xiii, 255 p. :ill. (some col.), digital ;24 cm. - Mathematical engineering,2192-4732. - Mathematical engineering..

Vector fields and ordinary differential equations -- Partial differential equations in engineering -- The single first-order quasi-liner PDE -- Shock waves -- The genuinely nonlinear first-order equation -- The second-order quasi-linear equation -- Systems of equations -- The one-dimensional wave equation -- Standing waves and separation of variables -- The diffusion equation -- The Laplace equation.

This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.

ISBN: 9783319552125$q(electronic bk.)

Standard No.: 10.1007/978-3-319-55212-5doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

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520 $a This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.
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