mirror of
https://github.com/vale981/phys512
synced 2025-03-04 17:11:42 -05:00
Clarifies that the last exervise in integration.md is for 3D
This commit is contained in:
parent
21c5c13fb7
commit
297711b38c
1 changed files with 2 additions and 2 deletions
|
@ -152,11 +152,11 @@ Another example is $W(x)=e^{-x}$ with integration limits $0$ to $\infty$. In thi
|
|||
|
||||
```{admonition} Exercise: Average velocity of the Maxwell-Boltzmann distribution.
|
||||
|
||||
Use Simpson's rule, Gaussian quadrature, and the general purpose integrator [`scipy.integrate.quad`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html) to evaluate the average velocity $\langle\left|v\right|\rangle$ for the [Maxwell-Boltzmann distribution](https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution).
|
||||
Use Simpson's rule, Gaussian quadrature, and the general purpose integrator [`scipy.integrate.quad`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html) to evaluate the average velocity $\langle\left|v\right|\rangle$ for the 3D [Maxwell-Boltzmann distribution](https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution).
|
||||
|
||||
For each method, check the numerical error comparing to the analytic result. How many points do you need to get to $0.1$% accuracy?
|
||||
|
||||
For Simpson's rule you can use your own implementation from above or you could try [`scipy.integrate.simpson`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.simpson.html)).
|
||||
For Simpson's rule you can use your own implementation from above or you could try [`scipy.integrate.simpson`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.simpson.html).
|
||||
|
||||
For Gaussian quadrature, try both Gauss-Hermite and Gauss-Laguerre. Which one is best?
|
||||
```
|
||||
|
|
Loading…
Add table
Reference in a new issue