코스 · Graduate
Partial Differential Equations
Transport, heat, wave and Laplace equations, Fourier methods, energy and maximum principles, weak derivatives, Sobolev spaces, well-posedness and scaling.
A graduate course in partial differential equations that starts with classification and characteristics and ends with the tools used to study the Navier-Stokes equations. You solve the four model equations by hand (characteristics, separation of variables, Fourier series and transforms, d'Alembert, Green's functions), then learn the methods that work without formulas: maximum principles, energy estimates, distributions and weak derivatives, Sobolev spaces, a priori estimates and scaling.
It assumes multivariable calculus, ordinary differential equations, linear algebra and a first course in analysis, and it prepares you for the fluid dynamics course.
다음에 오는: Multivariable-Calculus, Differential-Equations, Linear-Algebra, Analysis
코스에 대해
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Classification and first-order equations
3 레슨 -
The heat equation and Fourier series
4 레슨 -
The wave equation
2 레슨 -
Laplace's equation, maximum principles and Green's functions
3 레슨 -
Fourier transforms and energy methods
2 레슨 -
Distributions and Sobolev spaces
2 레슨 -
Well-posedness, estimates and scaling
3 레슨
마지막 시험
모든 단위에서 질문, 가장 어려운 것들 마지막. 입력 답변은 대수학 시스템에 의해 표시됩니다; 증거와 사진 작업 모델에 의해 읽어; 그럼 사람이 결과가 발표되기 전에 전체 종이를 검토. 통과하고 자신의 링크와 함께 인증서를 얻을. 통과 표시: 70%.
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