  The problem of Laplacian growth is considered within the Loewner-equation
framework. A new method of deriving the Loewner equation for a large class of
growth problems in the half-plane is presented. The method is based on the
Schwarz-Christoffel transformation between the so-called `mathematical planes'
at two infinitesimally separated times. Our method not only reproduces the
correct Loewner evolution for the case of slit-like fingers but also can be
extended to treat more general growth problems. In particular, the Loewner
equation for the case of a bubble growing into the half-plane is presented.
