# 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

PPL 60+ or SAT I MSS 640+ or ACT MATH 26+ or one recent course from MATH 112 ,113, 116, 120R, or 122A.

Test scores expire after 1 year. Some students may need to take Math 100, then Math 112 first.

## 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.

## FINAL EXAM Information

**A final exam will be given for Math 119A on Thursday, December 17th from 8:00am - 10:00am. **

*See instructor or syllabus for more details regarding your final exam.*