Partial Differential Equations: Methods and Applications

Partial Differential Equations: Methods and Applications, 1/e

Robert C. McOwen, Northeastern University

Published October, 1995 by Prentice Hall Engineering/Science/Mathematics

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Partial Differential Equations-Mathematics

Partial Differential Equations-Mechanical Engineering

Summary

Designed to bridge the gap between graduate-level texts in partial differential equations and the current literature in research journals, this text introduces students to a wide variety of more modern methods -- especially the use of functional analysis -- which has characterized much of the recent development of PDEs.

covers the modern, functional analytic methods in use today -- especially as they pertain to nonlinear equations.
maintains mathematical rigor and generality whenever possible -- but not at the expense of clarity or concreteness.
offers a rapid pace -- with some proofs and applications relegated to exercises.
unlike other texts -- which start with the treatment of second-order equations -- begins with the method of characteristics and first-order equations, with an emphasis in its constructive aspects.
introduces the methods by emphasizing important applications.
features important applications from physics and differential geometry -- e.g., Navier-Stokes, Klein-Gordon, Prescribed Scalar and Mean Curvature.
illustrates topics with many figures.
contains nearly 400 exercises, most with hints or solutions.
locates exercises near relevant topics.
provides chapter summaries.
lists references for further reading.

1. First-Order Equations.
2. Principles for Higher-Order Equations.
3. The Wave Equation.
4. The Laplace Equation.
5. The Heat Equation.
6. Linear Functional Analysis.
7. Differential Calculus Methods.
8. Linear Elliptic Theory.
9. Two Additional Methods.
10. Systems of Conservation Laws.
11. Linear and Nonlinear Diffusion.
12. Linear and Nonlinear Waves.
13. Nonlinear Elliptic Equations.
Hints and Solutions of Selected Exercises.
References.
Index.