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

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

## Prerequisites

Single variable calculus

### About this course

How do you design:

• A boat that doesn’t tip over as it bobs in the water?
• The suspension system of a car for a smooth ride?
• Circuits that tune to the correct frequencies in a cell phone?

How do you model:

• The growth of antibiotic resistant bacteria?
• Gene expression?
• Online purchasing trends?

The answer: Differential Equations.

Differential equations are the language of the models we use to describe the world around us. In this mathematics course, we will explore temperature, spring systems, circuits, population growth, and biological cell motion to illustrate how differential equations can be used to model nearly everything in the world around us.

We will develop the mathematical tools needed to solve linear differential equations. In the case of nonlinear differential equations, we will employ graphical methods and approximation to understand solutions.

The five modules in this series are being offered as an XSeries on edX. Please visit the Differential Equations XSeries Program Page to learn more and to enroll in the modules.

Photo by user: bizoo_n. Copyright © 2016 Adobe Systems Incorporated. Used with permission.

### What you'll learn

• Use linear differential equations to model physical systems using the input / system response paradigm.
• Solve linear differential equations with constant coefficients.
• Gain intuition for the behavior of a damped harmonic oscillator.
• Understand solutions to nonlinear differential equations using qualitative methods.

Unit 1

1. Introduction to differential equations and modeling
2. Complex numbers
3. Solving first order linear differential equations

Unit 2

1. The complex exponential
2. Sinusoids
3. Higher order linear differential equations
4. Characteristic polynomial

Unit 3

1. Harmonic oscillators
2. Operators
3. Complex replacement
4. Resonance

Unit 4

1. Graphical methods and nonlinear differential equations
2. Autonomous equations
3. Numerical methods

## Meet your instructors

David Jerison
Professor of Mathematics
Massachusetts Institute of Technology
Arthur Mattuck
Emeritus Professor of Mathematics
Massachusetts Institute of Technology
Haynes Miller
Professor of Mathematics
Massachusetts Institute of Technology
Jennifer French
Lecturer & Digital Learning Scientist
Massachusetts Institute of Technology
Kristin Kurianski
Postdoctoral Associate
Massachusetts Institute of Technology

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### Who can take this course?

Unfortunately, learners from one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. EdX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.