Analysis of Transport Phenomena: Series Expansions

Graduate-level introduction to mathematical modeling of heat and mass transfer (diffusion and convection), fluid dynamics, chemical reactions, and phase transformations.

Analysis of Transport Phenomena: Series Expansions

Graduate-level introduction to mathematical modeling of heat and mass transfer (diffusion and convection), fluid dynamics, chemical reactions, and phase transformations.

Analysis of Transport Phenomena is a series of the following nine MOOC modules:

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In these MOOCs, you will learn to formulate mathematical models of transport phenomena based on partial differential equations and to solve them 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. Applications include heat and mass transfer, fluid flow, waves, hydrodynamic instabilities, convection, phase transformations and electrochemical transport.

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 engineering applications 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 formulate models, make scaling estimates, and derive simple analytical approximations. There is growing demand for such mathematical skills in most technical careers and graduate programs today.

What you'll learn

  • Fourier series and eigenfunction expansions
  • Sturm–Liouville theory
  • Generalized Fourier series: Bessel functions, spherical Bessel functions, and Legendre polynomials

Prerequisites

Required: multivariable calculus and ordinary differential equations

Recommended: undergraduate-level exposure to partial differential equations, heat and mass transfer, and fluid dynamics; previous modules of 10.50x as needed.

Meet your instructors

  • Featured image for Martin Bazant
    Professor of Chemical Engineering & Mathematics
  • Featured image for Joey Gu
    Lecturer & Digital Learning Scientist in Chemical Engineering

Who can take this course?

Because of U.S. Office of Foreign Assets Control (OFAC) restrictions and other U.S. federal regulations, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba, Syria, North Korea and the Crimea, Donetsk People's Republic and Luhansk People's Republic regions of Ukraine.