The research carried out under this grant centered in the main on partial differential equations, with one exception, the work of Visiting Professor Pollaczek. Professor Pollaczek prepared a technical report summarizing his researches on stochastic problems arising in a group of telephone lines. He also lectured on selected topics in analysis, specifically, Legendre polynomials, Fermas theorem and linear integral equations. The work of other authors dealt with the construction of non-linear boundary problems for non linear partial differential equations for which the solution is unique either unconditionally or under prescribed conditions. More precisely they considered a quasi-linear partial differential equation.