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Learn techniques to interpret and solve differential equations

XSeries Program in
18.03x Differential Equations

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.

Learner Testimonials

"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)

Expert instruction
5 high-quality courses
1 year 2 months
4 - 7 hours per week
For the full program experience

Courses in this program

  1. MITx's 18.03x Differential Equations XSeries Program

  2. 3–6 hours per week, for 14 weeks

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

  3. 2–5 hours per week, for 10 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.

  4. Started Jan 11, 2023
    5–8 hours per week, for 9 weeks

    Learn how to use linear algebra and MATLAB to solve large systems of differential equations.

  5. Started Mar 22, 2023
    5–8 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.

  6. 3–6 hours per week, for 10 weeks

    An intro to the mysteries of the frequency domain and Laplace transform and how they're used to understand mechanical and electrical systems.

  7. 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.

Meet your instructors
from Massachusetts Institute of Technology (MITx)

Experts from MITx committed to teaching online learning

Also in Math at edX


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