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.

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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.

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.

**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.

### Course Syllabus

**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

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