# Introduction to Differential Equations (edX)

Scientists and engineers understand the world through differential equations. You can too.

Category: Mathematics

## Description

Scientists and engineers understand the world through differential equations. You can too.

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.

## 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.

## Syllabus – Introduction to Differential Equations edX Course

**Unit 1**

- Introduction to differential equations and modeling
- Complex numbers
- Solving first-order linear differential equations

**Unit 2**

- The complex exponential
- Sinusoids
- Higher-order linear differential equations
- Characteristic polynomial

**Unit 3**

- Harmonic oscillators
- Operators
- Complex replacement
- Resonance

**Unit 4**

- Graphical methods and nonlinear differential equations
- Autonomous equations
- Numerical methods

## Instructors

- David Jerison
- Arthur Mattuck
- Haynes Miller
- Jennifer French

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