Talk:Scale analysis (mathematics)

Talk
Observe the difference between these two lines (in the right half of the page):


 * $${{\partial w }\over{\partial t }} + u {\frac{\partial w}{\partial x}} + v {\frac{\partial w}{\partial y}} + w {\frac{\partial w}{\partial z}} - {\frac{u^2 + v^2}{R}}= - { { \frac{1}{\varrho}}{\frac{\partial p}{\partial z}}} - g +2{\Omega u \cos \phi} + \nu ({\frac{\partial^2 w}{\partial x^2}}+{\frac{\partial^2 w}{\partial y^2}}+{\frac{\partial^2 w}{\partial z^2}}) $$,  (1)


 * $${{\partial w }\over{\partial t }} + u {\frac{\partial w}{\partial x}} + v {\frac{\partial w}{\partial y}} + w {\frac{\partial w}{\partial z}} - {\frac{u^2 + v^2}{R}}= - { { \frac{1}{\varrho}}{\frac{\partial p}{\partial z}}} - g +2{\Omega u \cos \phi} + \nu \left({\frac{\partial^2 w}{\partial x^2}}+{\frac{\partial^2 w}{\partial y^2}}+{\frac{\partial^2 w}{\partial z^2}}\right),\qquad(1) $$


 * The parentheses surrounding the sum of three partial derivatives look different.
 * The comma at the end of the line looks different.
 * The parenthesized number (1) at the end looks different.

Those are among the changes made by my recent edits. Also, on Wikipedia, although TeX looks good when "displayed", it often looks terrible when inline.

Observe, for example, the expression $$e^{\int_0^1 f(x)\,dx}\,$$. It's misaligned. The e should be at the same level as the preceeding and following letters; the integral should be a superscript.

Also, note that in non-TeX notation you don't need to write 3. 10; you can write 3 &times; 10 or 3 &middot; 10.

Notice the difference between


 * 10-3

and


 * 10&minus;3.

The second one is legible. Similar reasons apply to my other minor edits. Michael Hardy 21:22, 29 November 2006 (UTC)

"Rules of scale analysis"
Rule 3 and rule 4 can be combined and compacted down to be easier to understand:

Rule 3
A sum or difference of terms inherits the order of the highest-order term:

If $$c = a \pm b$$, then $$\mathcal{O}(c) = \max \left\{ \mathcal O (a), \mathcal O (b) \right\}.$$

~ Æolus (talk) 18:46, 24 November 2023 (UTC)