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Massachusetts Institute of Technology

Multivariable Calculus 3: Theorems and Applications

Massachusetts Institute of Technology via MITx Online

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Overview

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We live in a multivariable world. Explore elegant theorems connecting differentiation, integration, and geometry in higher dimensions, and learn how to apply them to solve real world problems. Part 3 of 3.

Syllabus

  • Compute surface integrals that measure flux through spheres, cylinders, and parametrized surfaces
  • Compute line integrals that represent work done by vector fields along curves in space
  • Determine whether a vector field is conservative and construct corresponding potential functions
  • Apply the Divergence Theorem to relate surface flux to volume integrals
  • Compute the curl of a vector field and interpret its physical meaning as local rotation
  • Apply Stokes’ Theorem to relate circulation around a curve to the flux of curl through a surface
  • Analyze physical problems involving fluid flow, electromagnetism, and diffusion

Taught by

Lawrence Guth and Denis Auroux

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