MHB Finding Lagrangian description of position from Eularian velocity description

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The discussion focuses on converting Eulerian velocity descriptions into Lagrangian position descriptions in fluid dynamics. Participants emphasize the importance of correctly formatting LaTeX code for mathematical expressions to facilitate clear communication. The use of specific tags for inline math is highlighted as essential for proper parsing. There is a brief mention of the technical aspects of LaTeX formatting. Overall, the thread serves as a guide for effectively using LaTeX in mathematical discussions.
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\infty
 
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nemo surfs said:
\infty

Hello and welcome to MHB, nemo surfs! (Wave)

In order to get $\LaTeX$ to parse, you need to enclose the code in tags. The easiest method (for inline math) is to use the $\Sigma$ button on our toolbar, which will generate $$$$ tags, and put the cursor between the tags so you can then add your code. For example:

$$\infty$$

generates:

$$\infty$$
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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