ABSTRACT
The discussion of limits, continuity and differentiation on a real line is made easier because the way one measures distance between objects or numbers, is quite easy. This chapter illustrates the Euclidean norm or Euclidean metric along with a typical two dimensional vector. Functions of two variables are described using the base grid and the surface mesh. The functions are combined into a utility function such as DrawSimpleSurface, which manages the different graphing choices using boolean variables like DoGrid to turn a graph on or off. If the boolean variable DoGrid is set to one, the grid is drawn. The chapter describes the continuity of a two dimensional function and partial derivatives. It is very useful to have an analytical way to discuss tangent planes and their relationship to the real surface to which they are attached. The Chain rule in two variables is reviewed along with tangent plane approximation error and Hessian approximations.
