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
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.
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.
"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.” - Jiting (completed this course, spending 10 hours a week on it and found the course difficulty to be medium)
"Interesting course. Lectures, homeworks and review exercises of any part are really well setup. One of the best MOOC on topic of differential equations." - Gaetano (completed this course, spending 4 hours a week on it and found the course difficulty to be medium)
"Another excellent course from MIT. The lecture videos are excellent and so are the exercises. This course also has MATLAB based exercises which is wonderful. The problem sets are excellent and so are the staff and the community teaching assistants who are always there to help any time." - Dna47a (completed this course, spending 8 hours a week on it and found the course difficulty to be medium)
Courses in this program
MITx's 18.03x Differential Equations XSeries Program
- Started Sep 15, 20212–5 hours per week, for 8 weeks
In order to understand most phenomena in the world, we need to understand not just single equations, but systems of differential equations. In this course, we start with 2x2 systems.
- Started Apr 21, 20215–8 hours per week, for 11 weeks
Learn to use Fourier series to solve differential equations with periodic input signals and to solve boundary value problems involving the heat equation and wave equation.
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.
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