Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.


Topics - Shaghayegh A

Pages: 1 [2]
16
Chapter 2 / Solving the Burgers equation
« on: September 23, 2016, 07:29:07 PM »
In example 7 of chapter 2.1, we wish to solve $$u_{t}+uu_{x}=0.$$
The textbook says
$$\frac{dt}{1}=\frac{dx}{u}=\frac{du}{0}.$$
So far correct  The rest here are just your fantasies V.I.

We know $$\frac{\partial x}{\partial t}=u\;and\;\frac{du}{dt}=0\;so\;du=0\implies\frac{du}{0}=1$$
Why is $$\frac{dx}{u}=1?$$

17
Chapter 2 / question from 2.1 of textbook
« on: September 18, 2016, 07:45:39 PM »
Section 2.1 of the textbook states $$u_t a+u_x b$$ is the directional derivative of u in the direction l=(a,b). But there's an extra factor of $$\frac{1}{\sqrt{a^2+b^2}}$$ right? (which disappears if we set $$u_t a+u_x b$$ to 0). As in:

$$\nabla_{l}u \;. \frac{\bar{l}}{|\bar{l}|}=(\partial u/ \partial t \;\hat{t}\;+\;\partial u/ \partial x \; \hat{x}).\frac{ (a\hat{t}+b\hat{x})}{\sqrt{a^2+b^2}}=(u_t a+u_x b)\frac{1}{\sqrt{a^2+b^2}}$$?

Pages: 1 [2]