Partial Differential Equations

បន្ទាប់​ពី: Multivariable-Calculus, Differential-Equations, Linear-Algebra, Analysis

វគ្គ

1. Classification and first-order equations

   3 មេរៀន
   ∂What a PDE is, and how to classify one∂First-order linear equations and characteristics∂Nonlinear first-order equations and shocks
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

2. The heat equation and Fourier series

   4 មេរៀន
   ∂The heat equation: where it comes from∂Separation of variables∂Fourier series: coefficients, convergence and Parseval∂The heat equation on an interval
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

3. The wave equation

   2 មេរៀន
   ∂The wave equation and d'Alembert's formula∂The vibrating string: modes and energy
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

4. Laplace's equation, maximum principles and Green's functions

   3 មេរៀន
   ∂Laplace's equation and harmonic functions∂Maximum principles and uniqueness∂Green's functions and the fundamental solution
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

5. Fourier transforms and energy methods

   2 មេរៀន
   ∂The Fourier transform and the heat kernel∂Energy methods: uniqueness, stability and decay
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

6. Distributions and Sobolev spaces

   2 មេរៀន
   ∂Distributions and weak derivatives∂Sobolev spaces and embeddings
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

7. Well-posedness, estimates and scaling

   3 មេរៀន
   ∂Well-posedness in the sense of Hadamard∂A priori estimates, local and global existence∂Scaling and criticality: why dimension matters
   ចូល​ដើម្បី​ធ្វើ​សំណួរ

តម្លៃ

វគ្គ​សិក្សា​បើក​សម្រាប់​ទិញ​ឆាប់ៗ​នេះ ។ មេរៀន និង​សំណួរ​ដំបូង​នៃ​វគ្គ​សិក្សា​នីមួយៗ​គឺ​បើក​ឥឡូវ ។

ពិនិត្យ​មើល​ផ្នែក​មួយ​នៃ​ការងារ​របស់​អ្នក​ផ្ទាល់