Differential Equations

Overview

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

During this Differential Equations programme from Massachusetts Institute of Technology (MIT) Massachusetts Institute of Technology - MITx we will develop the  mathematical tools needed to solve linear differential equations, understand 2x2 systems of first-order linear and nonlinear differential equations. 

We will use linear algebra to solve systems of more than two differential equations. As well as, explore the use of Fourier series to analyze the behavior of and solve ordinary differential equations (ODEs) and separable partial differential equations (PDEs). In the last course of the series, we will consider frequency domain and Laplace transform to help us appreciate their effects on mechanical and electrical systems.

What you will learn

• Use differential equations to model real-world phenomena

• How to solve linear differential equations as well as how to use matrix methods to solve systems of differential equations

• How to use graphical methods to understand the qualitative behavior of linear and nonlinear systems

• Formulate and solve eigenvalue and eigenvector problems

• How to solve ODEs and separable PDEs using Fourier series inputs and boundary conditions

XSeries Details

This is a series of five courses that are best taken in the following order: 18.031x, 18.032x, 18.033x, 18.03Fx, and 18.03Lx. 18.03Lx is the exception, as the course can be taken at any point after 18.031x.