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Partial Differential Equations

Partial Differential EquationsLecture NotesErich MiersemannDepartment of MathematicsLeipzig UniversityVersion October, 20122 Contents1 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 .. Initial value problem of Cauchy .. Nonlinear Equations inRn.. Hamilton-Jacobi theory .. Exercises .. 593 Linear Equations of second order .. Normal form in two variables .. Quasilinear Equations of second order .. Quasilinear elliptic Equations .. Systems of first order .. Examples .. Systems of second order .. Examples .. Theorem of Cauchy-Kovalevskaya .. Appendix: Real analytic functions .. Exercises.

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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