Syllabus for Math 121 - Calculus for the Life Sciences I

This course introduces differential calculus from a dynamical systems perspective. Examples from biology motivate topics in differential calculus. A modeling approach shows how Calculus applies to many fields in the life sciences. The course consists of 2 lectures and a computer lab each week. The computer lab extends the lecture topics to more complicated mathematical models from biological applications, while teaching important computer and communication skills. Below is a list of the main topics covered.

1. Linear models - A review of lines and how they apply to basic biological models.
2. Least Squares - Least squares analysis is briefly discussed to allow fitting biological data throughout the course.
3. Functions - Quadratic functions are reviewed, and other functions, such as rational and square root functions are discussed, including domains, graphs, and asymptotes. A variety of functions are applied to biological problems.
4. Allometric Models - Power law fit to data has important biological applications.
5. Exponentials and logarithms are reviewed along with logarithmic plots.
6. Discrete Dynamical Models - Malthusian growth, linear discrete dynamical models, logistic growth, and other nonlinear models are introduced. Qualitative behavior of these models is studied.
7. Derivative - Growth rates, velocities, and tangent lines motivate the derivative. Limits and continuity are discussed. Rules of differentiation are given for the power law. The derivative is applied to graphing and the stability analysis of discrete dynamical and growth models. Differentiation of e^x and ln(x) is presented. The product, quotient, and chain rules are shown and applied to biological problems.
8. Optimization - Differential calculus is used to find maxima and minima for biological problems.