Partial Differential Equations

Mathematical Techniques for Engineers
Softcover Nachdruck of the original 1. Auflage 2017
ISBN: 978-3-319-85597-4
Verlag: Springer International Publishing

Buch, Englisch, 255 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 4161 g

Reihe: Mathematical Engineering

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.

Zielgruppe

Research

Autoren/Hrsg.

Epstein, Marcelo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.