Functions of several variables

By Gilbert Strang, E. Herman. Thermal Physics of the Atmosphere, 2021

224 citations recorded by the source corpus.

We previously covered some of the material in Simon and Blume’s Chapter 13, which explains why we don’t start the numbers at 13.1. We won’t cover sections 13.1 and 13.2 from S&B, but we will examine continuity in rather more detail than they do in section 13.4. We will start with continuity in metric spaces, look at a number of examples, and then consider continuity in general topological spaces. It turns out that the general definition will be useful in metric spaces too. For functions on the real line, a casual definition of continuity is that a function is continuous if you can draw its graph without lifting your pen from the paper. Of course, we will need a more formal definition.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/925cec7cb593ae4496b12802183a6c36e5887873