Partial Differential Equations: Mathematical Techniques for Engineers

✍ Scribed by Marcelo Epstein (auth.)

• Publisher: Springer International Publishing
• Year: 2017
• Tongue: English
• Leaves: 261
• Series: Mathematical Engineering
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Vector Fields and Ordinary Differential Equations....Pages 3-24
Partial Differential Equations in Engineering....Pages 25-47
Front Matter....Pages 49-49
The Single First-Order Quasi-linear PDE....Pages 51-74
Shock Waves....Pages 75-88
The Genuinely Nonlinear First-Order Equation....Pages 89-112
Front Matter....Pages 113-113
The Second-Order Quasi-linear Equation....Pages 115-130
Systems of Equations....Pages 131-153
Front Matter....Pages 155-155
The One-Dimensional Wave Equation....Pages 157-182
Standing Waves and Separation of Variables....Pages 183-208
The Diffusion Equation....Pages 209-238
The Laplace Equation....Pages 239-252
Back Matter....Pages 253-255

✦ Subjects

Theoretical and Applied Mechanics;Partial Differential Equations;Mathematical Modeling and Industrial Mathematics