Introduction to Partial Differential Equations and Hilbert Space Methods

THE USUAL TRINITIES The Usual Three Operators and Classes of Equations The Usual Three Types of Problems The Usual Three Questions (and the Other Three) The Usual Three Types of Boundary Conditions.'' The Usual Three Solution Methods (with Historical Remarks) Three Important Mathematical Tools Some Physical Considerations (and Examples) Elements of Bifurcation Theory Supplementary Discussions and Problems FOURIER SERIES AND HILBERT SPACE Lots of Separation of Variables Mathematical Justifications of the Method Fourier Series and Hilbert Space Fourier Series and Sturm-Liouville Equations Fourier Series and Green's Functions Fourier Series and Variational and Numerical Methods Some Unbounded Domain Considerations (and Continuous Spectra) Elements of Scattering Theory Supplementary Discussions and Problems Appendices: First-Order Equations Computational Methods Advanced Fluid Dynamics Selected Answers, Hints and Solutions Author Index Subject Index.