Partial Differential Equations
Equations of mathematical physics; classification of linear equations and systems. Existence and uniqueness problems for elliptic, parabolic, and hyperbolic equations. Eigenvalue problems for elliptic operators; numerical methods.
Partial Differential Equations: Methods and Applications, McOwen, Prentice Hall, 2nd edition.
This course is a classical introduction to the subject of Partial Differential Equations including first-order equations by the method of characteristics and the linear second-order equations which arise in mathematical physics: the wave equation, the Laplace equation, and the heat equation. The class will also provide some exposure to a variety of more modern methods, especially the use of functional analysis, semigroups and fixed point techniques for studying nonlinear partial differential equations.
(Johnson 2017 )