# 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

## ELIGIBILITY

Students must meet eligibility requirements.

See the current Math Course Placement Chart here.

## 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 download—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 SYLLABUS & CALENDAR

Math 119A Syllabus (Spring 2024)

Math 119A Course Calendar (Spring 2024)

The specific Course Policy for your Math 119A section should be made available to you by your instructor.

## 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.

Majors that allow student to take Math 119A to complete the foundation math requirement include Biology, Physiology, Ecology and Evolutionary Biology, Molecular and Cellular biology, Psychological Sciences, Natural Resources, and a few other majors. Please consult your advisor before enrolling in Math 119A.

Math 119A is not a prerequisite to Math 129, Calculus II.

## FINAL EXAM Information

A final exam will be given for Math 119A on

Section 001 -

Section 002 -

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