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2
students
Created by:
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
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1520
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Students
Massachusetts Institute of Technology
