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Analysis of Transport Phenomena I: Mathematical Methods

Graduate-level introduction to mathematical modeling of diffusion, convection, and chemical reactions.

Este curso está archivado
17 semanas estimadas
10–12 horas por semana
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Sobre este curso

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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.

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edX Prize 2019 Finalist

De un vistazo

  • Institución: MITx
  • Tema:Ingeniería
  • Nivel:Advanced
  • Prerrequisitos:

    Required: Multivariable calculus and ordinary differential equations.

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

  • Idioma:English
  • Transcripción de video:English

Lo que aprenderás

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  • 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

Plan de estudios

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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)

Acerca de los instructores

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Lamentablemente, las personas residentes en uno o más de los siguientes países o regiones no podrán registrarse para este curso: Irán, Cuba y la región de Crimea en Ucrania. Si bien edX consiguió licencias de la Oficina de Control de Activos Extranjeros de los EE. UU. (U.S. Office of Foreign Assets Control, OFAC) para ofrecer nuestros cursos a personas en estos países y regiones, las licencias que hemos recibido no son lo suficientemente amplias como para permitirnos dictar este curso en todas las ubicaciones. edX lamenta profundamente que las sanciones estadounidenses impidan que ofrezcamos todos nuestros cursos a cualquier persona, sin importar dónde viva.

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