ABSTRACT
This chapter approaches the ideas of basic calculus by just looking at how far one can go with applying algebra alone. It looks carefully at a model of natural selection called viability selection. This is a model that is utilized in a typical calculus for biology course and is an example of applying limiting ideas. One of the benefits of the use of mathematics is that it allows us to build a very simplified model which nevertheless helps us understand general principles. These are biological versions of the famous Einstein gedanken experiments: i.e. thought experiments which help develop intuition and clarity. The smoothness of a function is reviewed. The chapter discusses the functional form of the frequency, limits, continuity, right and left hand slope limits, differentiability of a function at a point, and error form for differentiability of a function at a point.
