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...Partial dierential equations lecture notes erich miersemann department of mathematics leipzig university version october contents introduction examples from variational problems ordinary exercises rst order linear quasilinear alinearization method initial value problem cauchy nonlinear in two variables n r hamilton jacobi theory classication second normal form elliptic systems theorem kovalevskaya appendix real analytic functions hyperbolic one dimensional wave equation higher dimensions case inhomogeneous amethod riemann boundary oscillation a string membrane fourier transform denition properties pseudodierential operators parabolic poisson s formula heat maximum principle uniqueness black scholes fundamental solution representation conclusions the dirichlet neumann mixed green function for ball...