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Created by:

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Last updated:

December 24, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This course introduces three main types of partial differential equations

diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

Course Curriculum

  • Introduction to PDEs Unlimited
  • Introduction to the heat equation Unlimited
  • The heat equation: Uniqueness Unlimited
  • The heat equation: Weak maximum principle and introduction to the fundamental solution Unlimited
  • The heat equation: Fundamental solution and the global Cauchy problem Unlimited
  • Laplace’s and Poisson’s equations Unlimited
  • Poisson’s equation: Fundamental solution Unlimited
  • Poisson’s equation: Green functions Unlimited
  • Poisson’s equation: Poisson’s formula, Harnack’s inequality, and Liouville’s theorem Unlimited
  • Introduction to the wave equation Unlimited
  • The wave equation: The method of spherical means Unlimited
  • The wave equation: Kirchhoff’s formula and Minkowskian geometry Unlimited
  • The wave equation: Geometric energy estimates Unlimited
  • Classification of second order equations Unlimited
  • Introduction to the Fourier transform; Fourier inversion and Plancherel’s theorem Unlimited
  • Introduction to Schrödinger’s equation Unlimited
  • Introduction to Lagrangian field theories Unlimited
  • Transport equations and Burger’s equation Unlimited

About the instructor

5 5

Instructor Rating

1

Reviews

1520

Courses

1823

Students

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Massachusetts Institute of Technology
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