(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Please see the attached pdf file, which is the bottom of page 365 from the 3rd edition of the book. This is a lesson about (generalized) waves, and f(z,t) is the vertical displacement of the medium at point z, time t. F is net force and T is the tension on the string in the picture.

I don't understand how we get from the tangents of angles to partial derivatives in this derivation. I've asked a professor about this before, and he said something about tangent lines to curves being connected to derivatives, but it didn't make sense because the tangent line to a curve is a different use of tangent than what I have here, tangent the trig function. Is there some connection between the two?

Also, the last step (from first to second partial derivatives) seems too hand wavy to be legitimate.

2. Relevant equations

None for my first question.

For my second question, I understand that it involves the definition of the derivative:

[tex]\lim_{\Delta z \to 0} \frac{\frac{\partial f(z+ \Delta z)}{\partial t} -

\frac{\partial f(z)}{\partial t}}{\Delta z} = \frac{\partial^{2} f}{\partial t^{2}}[/tex]

What I'm not sure about is if it's mathematically sound to just multiply both sides of that equation by [tex]\Delta z[/tex], seeing as how one side has a limit.

3. The attempt at a solution

I have no idea.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Griffith's E&M Derivation

**Physics Forums | Science Articles, Homework Help, Discussion**