Recent content by vvarma
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Graduate Total derivatives-how to get them, what they look like.
snipez90: Thanks so much for the help. (b) Using Df(x)=Dx dot L(x) + x dot DL(x) gives me Df=2(x dot L(x)) since derivatives of linear functions are the linear functions themselves and x in above map can be called Id(x) which, along w/ L(x), is linear. Is that possibly correct? (c) The... -
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Graduate Total derivatives-how to get them, what they look like.
I'm fairly confused as to how to get the total derivative of a function from Rn to Rm. I know the definition and the meaning, i.e. best linear approximation to a function at given point, but my book, Rudin's Principles of Mathematical Analysis, is lacking in examples of how to actually get them... -
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Graduate Velocity of red light vs. blue light in water - qualitative reasoning?
@vanhees71 I'll definitely check out that source. Thank you. @jambaugh Thanks for the reciprocal argument. It seems possible to me that I might be using the wrong w-k relationship to show this result due to a mislabeling on the part of my professor. Just to verify: is the graph of w(k) for... -
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Graduate Velocity of red light vs. blue light in water - qualitative reasoning?
Every source I have referred to says red light is faster in water than blue light. However, nearly all descriptions/explanations depend on refractive indices and 'bending' to show that blue light is slowed to a greater extent. Instead, I'm wondering if a more precise explanation based on...