<p>lol ok /<em>woo hoo comprimises</em>/</p>
<p>how about october?</p>
<p>chocolatechippancakember.... 18 seconds /<em>yay compromises... especially when I WIN!!!</em>/</p>
<p>hahaha november= teddybearsyrupember</p>
<p>how many days in a week? since we're making our own calendar.</p>
<p>
[quote]
Holomorphic functions are central to the study of complex analysis. These functions are defined on the complex number plane C (with values that make C complex-differentiable at every point). What makes a holomorphic function so powerful is that the function can be described by its Taylor Series because the implication is that it is infinitely differentiable.</p>
<p>We will let B be an open subset of C and f. f is complex differentiable at some point z* of B if
f'(z<em>) =
lim (f(z)-f(z</em>))/(z-z<em>)
z-->z</em>
This limit is taken over all series of complex numbers approaching z* and for all these series, the difference quotient must approach f'(z<em>). We know through intuition that f is complex differentiable at z</em>. If we approach z* from the direction p, then our image graphs will approach f(z<em>) from the direction f'(z</em>)p. This concept is analagous to real differentiability in that it obeys the rules of differentiation (product, quotient, chain).
But the essence of the relationship between complex differentiability and real differentiability lies in the following.
f(x+iy) = a(x,y) + ib(x,y) is a holomorphic complex function, with a and b being the first partial derivatives with respect to x and y and satisfy the Cauchy-Riemann equations. But the converse is NOT true. Here is a simple converse: if a and b have partial derivatives that are continuous and satisfy the C-R equations, then f is holomorphic. A different and more complex converse is the Looman-Menchoff Theorem, which is a real pain to prove.</p>
<p>Note: If f is complex differentiable at every point z* in B, then we say that f is holomorphic on B. </p>
<p>Here are some examples of holomorphicity:
The sine, cosine, and exponential function are all holomorphic on C, as is the main branch of the logarithmic function. The square root function can be written as squareroot(z) = e^(.5*log(z)). Thus the square root function is holomorphic whenever log(z) is holomorphic.</p>
<p>It is difficult to discuss conformal mappings and holomorphicity more in depth without first touching on Shwarz Lemma, automorphisms on D and H, and the Riemann Mapping Theorem.</p>
<p>ChaosTheory?
[/quote]
</p>
<p>Nice. That's wazzapnin'. :cool:</p>
<p>Abraham and the Tablets! You guys really took the paffle seriously...lol. Who knew that it would revolutionize the world?</p>
<p>oh, it's going to revolutionize more than just the world! don't you understimate the prolific power of the paffle!</p>
<p>Hmm...I remember yesterday when the paffle was just in its infancy. Good times. Good times.</p>
<p>Yes... the Information Age has officially ended... and the Paffle Age has begun! By the year 2100, everyone will eat the same meals: french toast for breakfast, waffles for lunch, and pancakes for dinner. Male children will be named Pafflo and females will be named Pafflina. It will be a wonderful, wonderful time.</p>
<p>yes, LesOs, the Paffle Age has begun! today is not tuesday, june 26th.
it is waffle, illegitimatebreakfastchildmonth 26th.</p>
<p>yay, and i'm a founding member of the UPPT (the United Paffle Protectors of Tomorrow).</p>
<p>^if i do say so myself, i think that's one of the better named months :D</p>
<p>^^Ok, I was gone whenever the whole name changes happened, so iamapeach, would you please inform me of the new names?</p>
<p>here:
days
sunday will be Paffleday
Monday will be Waffle
Tuesday will be Pancake
Wednesday will be Maple Syrup
Thursday will be Butter
Friday will be...umm..Grizzly Bear Day
and Saturday is french toast</p>
<p>months
January= waffleironary
February= doughember
March= Tastebud
April= findauntjemima
May = Breakfasember
June= illegitimatebreakfastchildmonth</p>
<p>[edit] oh, and we added all the other months except december. i forgot to update this, though.</p>
<p>Thanks, MBP. What happened to the other months? Did you guys get lazy?</p>
<p>that was all we had the last time i updated it.
... and I got lazy and didn't add them... oh well. it should be in the last three pages (and if you wouldn't mind, copy and paste them into a post to update :) plz).</p>
<p>edit: your work will be handsomely rewarded</p>
<p>i don't believe we ended up naming november or december. any suggestions?</p>
<p>oct= chocolatechippancakember
nov= teddybearsyrupember</p>
<p>so we still need december</p>
<p>pafflemania... you can't beat the classics</p>
<p>Did we skip September?</p>