Many phenomena in the world around us can be described with the help of functions. These functions by themselves are usually too complicated to understand, but we can already learn a lot from approximations. This is where mathematical analysis comes in: Mathematical analysis is about making and proving rigorous statements about the approximate behavior of functions. In Analysis 2 we continue our rigorous study of the approximate behavior of functions. We will now learn to approximate functions by affine functions and by polynomials, which are still simple, but can approximate better than the constant functions seen in Analysis 1. We will also see how these approximations give us important information about the functions we study.