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
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.
There will be five chapters, each containing lightboard lecture videos, online tutorials, and a homework assignment, followed by a final exam.
Continuum Models (conservation equations and boundary conditions, stochastic and thermodynamic models of diffusion)
Mathematical Formulation (dimensionless variables, dimensionality reduction, pseudosteady approximation)
Scaling (dimensional analysis, similarity solutions)
Asymptotics (regular and singular perturbations, matched asymptotic expansions)
Series Expansions (Fourier series, eigenfunction expansion)
Required: Multivariable calculus and ordinary differential equations.
Recommended: Some familiarity with partial differential equations and transport phenomena at the undergraduate level.