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February 11th, 2015, 11:11 AM   #1
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Math Focus: Calculus
Analytic functions?

I am jumping into complex analysis, and getting really confused with some theory.
So I get that a function is analytic when cauchy-reimann rules apply (in almost all points)
My question is, is there a shortcut to know when a function is analytic without differentiating?
What if it's given as a function of z->f(z). Do I have to put in x+iy and then differentiate.
Also can I get an example of a non analytic function.


Also this is loosely tied to this topic, but could you throw in an example of a non harmonic function aswell?

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February 13th, 2015, 05:44 PM   #2
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There are a number of ways of defining "analytic function" but, honestly, the Cauchy-Riemann equations are the simplest way of determining whether or not a function is analytic. f(z)= |z| is neither analytic nor harmonic. f(z)= Re(z) and f(a)= Im(a) are other examples.
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