• Length:
    17 Weeks
  • Effort:
    10–12 hours per week
  • Price:

    Add a Verified Certificate for $149 USD

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  • Course Type:
    Instructor-led on a course schedule


Required: Multivariable calculus and ordinary differential equations.

Recommended: Some familiarity with partial differential equations and transport phenomena at the undergraduate level.


edX Prize 2019 Finalist

About this course

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In this course, you will learn how to formulate models of reaction-convection-diffusion based on partial differential equations and to solve them the old-fashioned way, by pencil and paper. You will also learn the art of approximation—how to obtain useful solutions by simplifying a model without sacrificing the key physics.

At MIT, 10.50 is a required subject for all first-year graduate students in chemical engineering, but it also attracts students from other departments. This online course is suitable for anyone interested in learning the principles of continuum modeling. Although the examples are mostly from chemical engineering, no prior knowledge is assumed, beyond basic undergraduate applied mathematics.

The modeling concepts and mathematical methods you learn in this course will advance your career in industry or academics. While your friends and co-workers may be able to run an experiment or computer simulation, you will also be able to derive simple formulae to explain the data and guide rational design. There is growing demand for such mathematical skills in most technical careers and graduate programs today.

Attribution:By Kevin R Johnson, CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/), via Wikimedia Commons.

What you'll learn

Skip What you'll learn
  • Models of diffusion, heat conduction, fluid flow
  • Exact and approximate solution of partial differential equations
  • Scaling, dimensional analysis, and similarity solutions
  • Perturbation methods, matched asymptotic expansions
  • Fourier series, eigenfunction expansions

There will befive chapters, each containing lightboard lecture videos, online tutorials, and a homework assignment, followed by a final exam.

  1. Continuum Models (conservation equations and boundary conditions, stochastic and thermodynamic models of diffusion)
  2. Mathematical Formulation (dimensionless variables, dimensionality reduction, pseudosteady approximation)
  3. Scaling (dimensional analysis, similarity solutions)
  4. Asymptotics (regular and singular perturbations, matched asymptotic expansions)
  5. Series Expansions (Fourier series, eigenfunction expansion)

Meet your instructors

Martin Bazant
E. G. Roos (1944) Professor of Chemical Engineering and Professor of Mathematics
Massachusetts Institute of Technology

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Who can take this course?

Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.