Here's the new fence I've been building. Boundary conditions play an important part in Physics. The laws of Physics are very general. In fact, they were often stated as proportionalities. For example, Newton just said that acceleration was proportional to resultant force. To make the differential equations fit one particular example, particular numbers need to be inserted. These are often called boundary conditions. eg speed at time zero. http://hyperphysics.phy-astr.gsu.edu/hbase/diff.html#c4 Another boundary problem I've come across this year involves the setting of coordinates in abstract mathematical spaces. These can often have many dimensions. x and y axes don't work well when the space is curved, so the space is often thought of as being sections of flat x,y planes that are patched together; hence the boundaries. I've been trying to understand tensors, which I think are going to be independent of the choice of local coordinates and allow you to make transformations within the mathematical space.
