Landau Growth for Students Part I Initial Valuie Problem

This paper is internded to demonstrate to students that electron Landau growth of plasma waves is an easily understood and computed phenomenon. This derivation does not use the usual Fourier-Laplace transform technique with the inversion and final result being obtained by contour integration and residue theory. Instead, a simple treatment, following the original work of Vlasov, is used. Landau´s original solution is recovered both for growth and decay, but only the growing part rigorously satisfies the initial assumptions.