In recent years, due primarily to the proliferation of computers,
dynamical systems has again returned to its roots in applications. It is
the aim of this book to provide undergraduate and beginning graduate
students in mathematics or science and engineering with a modest
foundation of knowledge. Equations in dimensions one and two constitute
the majority of the text, and in particular it is demonstrated that the
basic notion of stability and bifurcations of vector fields are easily
explained for scalar autonomous equations. Further, the authors
investigate the dynamics of planar autonomous equations where new
dynamical behavior, such as periodic and homoclinic orbits appears.