  A differential algebra of nonlinear generalized functions is presented as a
tool for a wide range of nonsmooth nonlinear problems. The power of the
differential algebra is used to do mathematical calculations or proofs; then
the final result is often a classical function or distribution which is not
solution in the classical or distributional sense. The aim of this text is to
invite the readers in applying this tool in their own research without
significant prerequisites by presenting its use on a sample of elementary
applications from mathematics and physics. This text is the written version of
a talk at the 2007 annual meeting of the AMS, NewOrleans, january 2007.
