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Partial Differential Equations

About this Title

Harold Levine, Stanford University, Stanford, CA

Publication: AMS/IP Studies in Advanced Mathematics
Publication Year: 1997; Volume 6
ISBNs: 978-0-8218-0775-0 (print); 978-1-4704-3797-8 (online)
DOI: https://doi.org/10.1090/amsip/006
MathSciNet review: MR1475701
MSC: Primary 35-01

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Table of Contents

Front/Back Matter

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Chapters

• Introduction
• Partial differentiation
• Solutions of PDE’s and their specification
• PDE’s and related arbitrary functions
• Particular solutions of PDE’s
• Similarity solutions
• Correctly set problems
• Some preliminary aspects of linear first order PDE’s
• Linear first order PDE’s with two independent variables
• First order nonlinear PDE’s
• Some technical problems and related PDE’s
• Linear first order PDE’s with two independent variables, general theory
• First order PDE’s with multiple independent variables
• Original details of the Fourier approach to boundary value problems
• Eigenfunctions and eigenvalues
• Eigenfunctions and eigenvalues, continued
• Non-orthogonal eigenfunctions
• Further example of Fourier style analysis
• Inhomogeneous problems
• Local heat sources
• An inhomogeneous configuration
• Other eigenfunction/eigenvalue problems
• Uniqueness of solutions
• Alternative representations of solutions
• Other differential equations and inferences therefrom
• Second order ODE’s
• Boundary value problems and Sturm-Liouville theory
• Green’s functions and boundary value problems
• Green’s functions and generalizations
• PDE’s, Green’s functions, and integral equations
• Singular and infinite range problems
• Orthogonality and its ramifications
• Fourier expansions: Generalities
• Fourier expansions: Varied examples
• Fourier integrals and transforms
• Applications of Fourier transforms
• Legendre polynomials and related expansions
• Bessel functions and related expansions
• Hyperbolic equations

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