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.

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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!

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

Meet The Faculty

John Wesley Cain

John Wesley Cain

Senior Lecturer on Mathematics, Harvard University

John Wesley Cain is a Senior Lecturer on Mathematics at Harvard University. His academic interests lie at the interface of mathematics, medicine, and biology. Prior to arriving at Harvard in 2015, he spent 10 years as a mathematics professor in Virginia after completing his PhD at Duke University in 2005.

Juliana Belding

Juliana Belding

Professor of the Practice in Mathematics, Boston College

Juliana Belding is a Professor of the Practice in Mathematics at Boston College. Her primary interests are mathematics teaching and learning at the undergraduate and K12 level. Previously, she was a Preceptor at Harvard University, where she began work with colleagues on curricula to help students connect ideas of calculus to other fields. She received her PhD in algebraic number theory and cryptography at the University of Maryland in 2008.

Peter M. Garfield

Peter M. Garfield

Professor of Mathematics, University of California, Santa Barbara

Peter M. Garfield is teaching faculty at the University of California Santa Barbara. His main academic interests are in undergraduate pedagogy and curriculum development, particularly in the introductory university courses (calculus, linear algebra, and differential equations). Before accepting a permanent job at UCSB, he taught for eight years as a Preceptor at Harvard University. His PhD in differential geometry was from the University of Washington, and he has also taught at the University of Toronto and Case Western Reserve University.

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