课程 · 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.
之后的来: Multivariable-Calculus, Differential-Equations, Linear-Algebra, Analysis
课程
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Classification and first-order equations
3 经验教训 -
The heat equation and Fourier series
4 经验教训 -
The wave equation
2 经验教训 -
Laplace's equation, maximum principles and Green's functions
3 经验教训 -
Fourier transforms and energy methods
2 经验教训 -
Distributions and Sobolev spaces
2 经验教训 -
Well-posedness, estimates and scaling
3 经验教训
期末考试
每个单位的问题,最难回答的问题最后。输入的答案以代数系统为标志;证据和照片工作用模型读取;然后一个人在结果发布之前审查整份文件。通过并获得带有其链接的证书。 通行证: 70%.
签署日期