Kurslar · 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.
Comes after: Multivariable-Calculus, Differential-Equations, Linear-Algebra, Analysis
Kurs
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Classification and first-order equations
3 _Öňki -
The heat equation and Fourier series
4 _Öňki -
The wave equation
2 _Öňki -
Laplace's equation, maximum principles and Green's functions
3 _Öňki -
Fourier transforms and energy methods
2 _Öňki -
Distributions and Sobolev spaces
2 _Öňki -
Well-posedness, estimates and scaling
3 _Öňki
The final exam
Her bir bölümden soraglar, iň kynlary soňuna çenli. Ýazan jogaplar aljebra sistemasy tarapyndan nyşanlanýar; subutnama we surata alnan iş bir model tarapyndan okalýar; soňra bir adam siziň netijeňizi çap etmekden öň ähli kagyzy synlaýar. Geçiň we öz baglanyşygy bilen bir şahadatnama alyň. Geçir: 70%.
_GünPrices
Kursy geç
$39
Her bir bölüm soragy, bir tekrar bilen sonky synag, we 20 öz işiň barlagy, bir kurs üçin.
Bir soňky synag
$15
Bir kursyň soňky bir sessiýasy, nyşanlan we gözden geçirilmiş. Maddeyi örän gowy bilýän we ony synap görmek isleýän biri üçin.
Her bir kurs
$19/10 minut
Her kursda ähli soraglar we finallar (ýolda iki final) we aýda 100 iş barlaglary. Siziň hasabyňyzdan kes.
Iş barlaglary
$9
On barlag: her bir işleýäniň suratyny ýükle, ýa-da ony ýaz, we nädip hata düşendigini gör.
Kurslar çaltdan satyn almak üçin açyldy. Her bir kursyň leksiýalary we ilkinji soragy indi açyldy.