## What you'll learn

- Authentic examples and case studies of how calculus is applied to problems in other fields
- How to analyze mathematical models, including variables, constants, and parameters
- Appreciation for the assumptions and complications that go into modeling real world situations with mathematics

## Course description

In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work.

Through a series of case studies, you’ll learn:

• How standardized test makers use functions to analyze the difficulty of test questions;

• How economists model interaction of price and demand using rates of change, in a historical case of subway ridership;

• How an x-ray is different from a CT-scan, and what this has to do with integrals;

• How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks;

• How the Lotka-Volterra predator-prey model was created to answer a biological puzzle;

• How statisticians use functions to model data, like income distributions, and how integrals measure chance;

• How Einstein’s Energy Equation, E=mc2 is an approximation to a more complicated equation.

With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions.

This course provides a unique supplement to a course in single-variable calculus. Key topics include application of derivatives, integrals and differential equations, mathematical models and parameters.

This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms.

This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!

## Associated Schools

### Harvard Faculty of Arts & Sciences

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