Transforming Spaces, Transforming Shapes - Ken McKelvie

29th January 2005
In some branches of mathematics it is useful to be able to transform one Cartesian coordinate space into another where the variables of the second space are expressed as functions of the variables of the first. When doing this, an important, but often overlooked skill, is the ability to work out how the "shape" of a specified region in the first space is transformed into a usually different "shape" in the second. In this session we concentrate on two-dimensional spaces, namely planes. A key feature of all the given examples and exercises is that when tracing the boundary of a transformed region, segment-by-segment, you should have the satisfaction of finishing up back at the point at which you started. If there any gaps in your boundary then you need to look again!