Partial Differential Equations - Softcover

Inhaltsangabe

I - The Single First Order Equation.- 1. The linear and quasi-linear equations.- 2. The general first order equation for a function of two variables.- 3. The general first order equation for a function of n independent variables.- II - The Cauchy Problem for Higher Order Equations.- 1. Analytic functions of several real variables.- 2. Formulation of the Cauchy problem. The notion of characteristics.- 3. The Cauchy problem for the general non-linear equation.- 4. The Cauchy-Kowalewsky theorem.- III - Second Order Equations with Constant Coefficients.- 1. Equations in two independent variables. Canonical forms.- 2. The one-dimensional wave equation.- 3. The wave equation in higher dimensions. Method of spherical means.Method of descent.- 4. The inhomogeneous wave equation by Duhamel's principle.- 5. The potential equation in two dimensions.- 6. The Dirichlet problem.- 7. The Green's function and the fundamental solution.- 8. Equations related to the potential equation.- 9. Continuation of harmonic functions.- 10. The heat equation.- IV - The Cauchy Problem for Linear Hyperbolic Equations in General.- 1. Riemann's method of integration.- 2. Higher order equations in two independent variables.- 3. The method of plane waves.- List of Books Recommended for Further Study.

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