Syllabus for Math 122 - Calculus for the Life Sciences II

This course introduces integral calculus from a dynamical systems perspective and includes a review of trigonometry. Topics from biology motivate the studies in integral calculus primarily through the solution of differential equations. The models demonstrate how biological problems can be analyzed with mathematical methods. The course consists of 2 lectures and a computer lab each week. The computer lab extends the lecture topics to more complicated mathematical models, while teaching important computer and communication skills. Below is a list of the main topics covered.

1. Review of Differential Calculus - Applications in biology using optimization review the main ideas from Math 121, Differential Calculus.
2. Trigonomic functions - The periodic functions sine and cosine are applied to several biological examples.
3. Newtonâs method - Finding roots of nonlinear functions is important in biological equilibrium analysis.
4. Differential Equations - Malthusian growth and radioactive decay are studied. Linear differential equations are applied to radiant cooling and mixing or pollution problems. Numerical simulation of the differential equations is introduced. Separation of variables show other biological applications.
5. Integration - Antiderivatives and integration by substitution solve certain biological problems. Riemann sums introduce the definite integral and is applied to area problems. Models with linear differential equations use integrals for analyzing toxic build up.
6. Qualitative Analysis of Differential Equations - Lotka-Volterra models and competition models are analyzed. Numerical methods for two-dimensional models help visualize the model behavior.