ABSTRACT
In this course we will discuss all possible functions which involve two variables and so look at functions from R2 into R, from R into R2 and from R2 into R2. We begin by considering functions from R2 into R and our objective is to obtain methods for finding maxima and minima. If the functions are arbitrarily behaved we get nowhere, so we have to make some assumptions-we will use the general term regularity conditions-on the functions considered. These regularity conditions usually relate to continuity and differentiability. First, however, we try and see, based on our one-dimensional experience, how we might proceed and then return to look more closely at what we need in order to proceed. The main onedimensional motivation is the following fundamental result.
