• Length:
    10 Weeks
  • Effort:
    3–6 hours per week
  • Price:

    FREE
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  • Institution
  • Subject:
  • Level:
    Intermediate
  • Language:
    English
  • Video Transcript:
    English

Prerequisites

Single-variable Calculus (derivatives, integrals and basics of differential equations); College or AP/IB High School Level

About this course

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!

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 your instructors

John Wesley Cain
Senior Lecturer, Mathematics
Harvard University
Juliana Belding
Professor of the Practice in Mathematics
Boston College
Peter M. Garfield
Teaching Faculty
University of California Santa Barbara

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Frequently asked questions

Using Desmos in this Course This course uses Desmos ( https://www.desmos.com/ ), an online graphing calculator, to illustrate examples. Your use of the Desmos platform or any content hosted by Desmos is subject to the Desmos terms of service at https://www.desmos.com/terms and privacy policy at https://www.desmos.com/privacy.

If you do not wish to use the Desmos platform or view content hosted by Desmos, you may not be able to complete the course. This course does NOT require you to make your own individual user account on Desmos. Desmos is a separate entity and is not directly affiliated with HarvardX or edX.

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