Partial Differential Equations: Mathematical Techniques for Engineers

ISBN-13: 9783319855974 / Angielski / Miękka / 2018 / 255 str.

Marcelo Epstein

Recenzje

"The book would be accessible to strong undergraduates with some multivariable calculus, basic linear algebra and ordinary differential equations. The author provides references at each stage to several of the standard texts, including those of Garabedian and John. This would be a good textbook for an introduction to PDEs or as a supplement to a more standard mathematical treatment." (William J. Satzer, MAA Reviews, maa.org, July, 2017)

Spis treści

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.

Blurb

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.