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# Introduction to Differential Equations

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## Overview

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?

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.

## Syllabus

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

#### Taught by

David Jerison, Arthur Mattuck and Haynes Miller

## Reviews for edX's Introduction to Differential Equations 5.0 Based on 2 reviews

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• 4 star 0%
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Did you take this course? Share your experience with other students.

• 1
Wandalen W
5.0 2 years ago
by completed this course, spending 10 hours a week on it and found the course difficulty to be hard.
This valuable online course explains toughest topics in math quite well. It offers lots of practice what is good. The whole course is practice-based. Several problems from the course require making exhausting routine calculation producing long-long equation. MIT's online course uses teaching approach which is much closer to traditional teaching approach than Boston University's online course. Among drawbacks, MIT course often uses the help of postgraduates, which in fact don't have developed empathy so don't feel students and produce poor video lectures. Most lectures in the course are good. MIT course has visuals as well as Boston University's course what makes both able to extend intelligence of a participant. If you didn't take Paul Blanchard's course, I recommend you to start from his work, it's truly virtuosic and gives clearer understanding of the subject. Consider taking MIT course after. Both courses are definitely worth taking.
Jiting T
5.0 a year ago
by completed this course, spending 10 hours a week on it and found the course difficulty to be medium.
Wonderful course on differential equations. The teachers provide a nice computational tool to depict the dynamics of solving the equations, which is very useful for students to grasp the key ideas and concepts. And, this is the first course of a series course on differential equations offered by MIT, so it is the prerequisite for the later courses.