Transcription of Partial Differential Equations
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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.
Figure 1.4: Oscillating string utt = c24u, where u = u(x,t), c is a positive constant, describes oscillations of mem-branes or of three dimensional domains, for example. In the one-dimensional case utt = c2uxx describes oscillations of a string.
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