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.

7 %s göterimunit-format 19 _Öňki 121 soraglar 180 minut

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

  1. Classification and first-order equations

    3 _Öňki
  2. The heat equation and Fourier series

    4 _Öňki
  3. The wave equation

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

    3 _Öňki
  5. Fourier transforms and energy methods

    2 _Öňki
  6. Distributions and Sobolev spaces

    2 _Öňki
  7. 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%.

_Gün

Prices

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.

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.

Özüň işleýän bir parçany barla