I was a bit confused with the chronology of this when I got to this slide, since it seemed like boundary conditions would be specifically useful with the discrete Laplace and Dirichlet died before computers were thought about. But, when these were all originally made in the continuous sense (along the literal boundary of a set), each condition type has a distinct set of places in practice where it would be 'correct'---e.g. Dirichlet for places where we have a beam or node held at a fixed position in a mechanical system, and Robin is so useful in electromagnetism that they are also known as 'impedance boundary conditions'.
keenan
@clam Sure, you can talk about boundary conditions without discretizing first. Seeing the discrete picture can really help make it clear why boundary conditions are needed from the perspective of linear algebra. (And also boundary conditions can get kind of nasty, so sometimes better to hold off talking about them until closer to the end...)
I was a bit confused with the chronology of this when I got to this slide, since it seemed like boundary conditions would be specifically useful with the discrete Laplace and Dirichlet died before computers were thought about. But, when these were all originally made in the continuous sense (along the literal boundary of a set), each condition type has a distinct set of places in practice where it would be 'correct'---e.g. Dirichlet for places where we have a beam or node held at a fixed position in a mechanical system, and Robin is so useful in electromagnetism that they are also known as 'impedance boundary conditions'.
@clam Sure, you can talk about boundary conditions without discretizing first. Seeing the discrete picture can really help make it clear why boundary conditions are needed from the perspective of linear algebra. (And also boundary conditions can get kind of nasty, so sometimes better to hold off talking about them until closer to the end...)