Partial Differential Equations
Partial Differential EquationsLecture NotesErich MiersemannDepartment of MathematicsLeipzig UniversityVersion October, 20122Contents1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equations from variational problems . . . . . . . . . . . . . . Ordinary differential Equations . . . . . . . . . . . . . Partial differential Equations . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Equations of first Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . Quasilinear Equations . . . . . . . . . . . . . . . . . . . . . . A linearization method . . . . . . . . . . . . . . . . . Initial value problem of Cauchy . . . . . . . . . . . . . Nonlinear Equations in two variables.
Chapter 1 Introduction Ordinary and partial differential equations occur in many applications. An ordinary differential equation is a special case of a partial differential equa-
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