# Mathematics of Biological Systems: a Calculus-Based Approach (Math 119A)

## COURSE OBJECTIVES AND EXPECTED LEARNING OUTCOMES:

Students will learn how to interpret and develop calculus-based models of biological systems that describe how quantities change in realistic and relevant settings drawn from physiology, neuroscience, ecology and evolution. They will also learn the rudiments of a programming language (SageMath/Python) sufficient to graph functions, plot data and simulate systems of differential equations.

Students who successfully complete this course are expected to be able to:

- Create dynamical models of verbally described biological systems
- Quantify and interpret changes in dynamical systems using software
- Explain homeostasis in terms of positive and negative feedback
- Classify equilibria in one- and two-dimensional systems and use that information to interpret long term biological behaviors of modeled systems

## PREREQUISITES

Completion of college algebra (Math 112) or PPL 60+ or SAT I MSS 640+ or ACT MATH 26+

## COURSE MATERIALS

The following course materials are required for Math 119A:

- Textbook:
**Modeling Life: The Mathematics of Biological Systems**by Garfinkel, Shevtsov and Guo, Springer 2017, (ebook) ISBN 978-3-319-59731-7, or ISBN 978-3-319-59730-0 (Hardcover). The ebook is available to University of Arizona students through the library at no cost, and a softcover edition can be purchased through their link for $25. Click Modeling Life: The Mathematics of Biological Systems to downloadâ€”you will have to log in to your UAccess account. - Software: Cocalc/Sagemath. (Details on access will be posted on D2L, cost $14/semester)

## COURSE DESCRIPTION

Math 119A is a course using real examples developing and studying models of biological dynamical systems using concepts from calculus. Students taking this course will learn how to interpret and develop calculus-based models of biological systems that describe how quantities change in realistic and relevant settings drawn from physiology, neuroscience, ecology and evolution. They will also learn the rudiments of a programming language sufficient to graph functions, plot data and simulate systems of differential equations.

This course is intended for students in the biological sciences or those interested in pursuing a career in medicine and does not require any prior knowledge of calculus or of programming.

- Physiology, Molecular and Cellular Biology, Biology and Ecology and Evolutionary Biology majors can use this course together with a course in Statistics such as Math 263 to satisfy their mathematics requirements.