Author | John, Fritz. author |
---|---|
Title | Partial Differential Equations [electronic resource] / by Fritz John |
Imprint | New York, NY : Springer US, 1971 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-9966-1 |
Descript | 221 p. online resource |
I โ 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 โ 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 โ 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 Duhamelโs principle -- 5. The potential equation in two dimensions -- 6. The Dirichlet problem -- 7. The Greenโs function and the fundamental solution -- 8. Equations related to the potential equation -- 9. Continuation of harmonic functions -- 10. The heat equation -- IV โ The Cauchy Problem for Linear Hyperbolic Equations in General -- 1. Riemannโs method of integration -- 2. Higher order equations in two independent variables -- 3. The method of plane waves -- List of Books Recommended for Further Study