MHB Linear Approximation: Intro to Physics Problem

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Linear approximation is frequently utilized in physics to simplify complex problems by estimating values near a given point. The discussion highlights the importance of understanding this concept as a foundational tool in physics. Participants express a sense of uncertainty about their initial attempts but receive reassurance that their approach appears correct. The conversation suggests a willingness to explore further examples to solidify understanding. Overall, linear approximation serves as a critical method for solving introductory physics problems effectively.
karush
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https://www.physicsforums.com/attachments/1614
never done this before so this is an intro problem
it mentioned that LA is used in Physics a lot
hopefully correct no ans in bk(Speechless)
 
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karush said:
https://www.physicsforums.com/attachments/1614
never done this before so this is an intro problem
it mentioned that LA is used in Physics a lot
hopefully correct no ans in bk(Speechless)
Looks good to me.

-Dan
 
I post a couple more...
 

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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