Partial Differential Equations: Methods and Applications, 2nd edition

Published by Pearson (October 29, 2002) © 2003

  • Robert C. McOwen
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For a one-year, graduate-level course in Partial Differential Equations.

Designed to bridge the gap between introductory texts in partial differential equations and the current literature in research journals, this text introduces students to the basics of classical PDEs and to a wide variety of more modern methods—especially the use of functional analysis—which has characterized much of the recent development of PDEs. Throughout, the results are almost completely self-contained.



Introduction.


 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.


Appendix on Physics.


Hints and Solutions for Selected Exercises.


References.


Index.


Index of Symbols.

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