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Massachusetts Institute of Technology

Introduction to Differential Equations

Massachusetts Institute of Technology via edX


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.

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.

The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Pageto learn more and to enroll in the modules.

Photo by user: bizoo_n. Copyright © 2016 Adobe Systems Incorporated. Used with permission.


Please note: edX Inc. has recently entered into an agreement to transfer the edX platform to 2U, Inc., which will continue to run the platform thereafter. The sale will not affect your course enrollment, course fees or change your course experience for this offering. It is possible that the closing of the sale and the transfer of the edX platform may be effectuated sometime in the Fall while this course is running. Please be aware that there could be changes to the edX platform Privacy Policy or Terms of Service after the closing of the sale. However, 2U has committed to preserving robust privacy of individual data for all learners who use the platform. For more information see the edX Help Center.


Unit 1

  1. Introduction to differential equations and modeling
  2. Complex numbers
  3. Solving first order linear differential equations

Unit 2

  1. The complex exponential
  2. Sinusoids
  3. Higher order linear differential equations
  4. Characteristic polynomial

Unit 3

  1. Harmonic oscillators
  2. Operators
  3. Complex replacement
  4. Resonance

Unit 4

  1. Graphical methods and nonlinear differential equations
  2. Autonomous equations
  3. Numerical methods

Taught by

David Jerison, Arthur Mattuck and Haynes Miller


5.0 rating, based on 7 Class Central reviews

Start your review of Introduction to Differential Equations

  • Profile image for Chris Harding
    Chris Harding
    I have a BS in chemical engineering. I averaged 96% over the 5 units of study. The material was mostly new to me. Although I had a high average, I only averaged so high because I took copious notes from the lecture notes, practice problems, and videos....
  • Anonymous

    Anonymous completed this course.

    This course is excellent! Although the title of it is 'Introduction to Differential Equations', but it covers a lot. The course has a lot of practise problems to help us learn the concepts and apply different methods in solving linear differential equations. Every unit has two to three lessons, every lesson has recitation proplem. And at the end of the unit, there are two problem sets. I think the course is difficult but it's properly challenging. The reading notes explain everything so well and I think if you devote enough time, you can totally understand them totally. Another great course from MITX!
  • Profile image for Ayur Tadimalla
    Ayur Tadimalla

    Ayur Tadimalla completed this course and found the course difficulty to be medium.

    This course is a rigorous primer to differential equations. It is well structured, the lectures are informative and Professor Mattuck is extremely witty! There are recitations and HW assignments which require critical thinking, and solidify the material...
  • Casper

    Casper completed this course.

    Great introduction to differential equations. The course alternates between theory and practical applications, which helps a great deal in understanding the theory.
    This course allowed me to understand, model and solve real world problems (from electrical engineering, economics to biology).
  • Anonymous

    Anonymous completed this course.

    This was my first course with MIT but will not be the last( for sure).Teachers and staff was really supportive and active, felt like I was therein real class room.My favorite was Prof. Muttuck!! He is phenomenal...Looking forward to be with MIT .
  • Wandalen

    Wandalen completed this course, spending 10 hours a week on it and found the course difficulty to be hard.

    This valuable online course explains toughest topics in math quite well. It offers lots of practice what is good. The whole course is practice-based. Several problems from the course require making exhausting routine calculation producing long-long equation....
  • Jiting Tian completed this course, spending 10 hours a week on it and found the course difficulty to be medium.

    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. And, this is the first course of a series course on differential equations offered by MIT, so it is the prerequisite for the later courses.

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