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 .
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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