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Last updated:

November 4, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This is the first semester of a two-semester sequence on Differential Analysis.

Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.

Course Curriculum

  • Continuous Functions Unlimited
  • Measures and σ-algebras Unlimited
  • Measureability of Functions Unlimited
  • Integration Unlimited
  • Hilbert Space Unlimited
  • Test Functions Unlimited
  • Tempered Distributions Unlimited
  • Convolution and Density Unlimited
  • Fourier Inversion Unlimited
  • Sobolev Embedding Unlimited
  • Differential Operators Unlimited
  • Cone Support and Wavefront Set Unlimited
  • Homogeneous Distributions Unlimited
  • Spectral Theorem Unlimited
  • Problems Unlimited
  • Solutions Unlimited
  • References Unlimited

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Massachusetts Institute of Technology
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