Recent content by prasannaworld

Boiling Internal Energy - URGENT A quick question: dU = dQ - dW What are dU, dQ and dW during Boiling? I thought: -the particles do work, hence dW is + -dU increases as particles gain more energy so dQ = dU + dW - showing that heat flows in. Which made sense to me. Or is...

ok... I kept thinking of the Im(a*b) definition... Forgot completely about what exactly the Determinent is... Thanks for reminding me

http://en.wikipedia.org/wiki/Abuse_of_notation I don't want this thread to go too long. But can someone quickly explain to be how the Determinent method of evaluating the Cross Product is an "abuse". I cannot quite seem to grasp their explanation...

I hope this helps... "1" can be written as 1*cis(0 + 360n) where: - cis(x) = cos(x) + i*sin(x) - I am working in degrees... - n is any integer one can see that there may be an infinite no. ways of writing i depending on what n is... Now square rooting; the De Moivre's Theorem is...

I believe the easiest definition is that if you have a constant "e" and: f(x) = e^x (for all xER) then: f'(x) = e^x I vaguely try to explain this here... Please just PM me with criticizms :shy: http://prasannaworld.byethost4.com/mathematics_Calculus4.html

True... I still view that as the standard definition. To make it better how about: xER; obviously 0 can no longer work. Also on topic: I believe a "beautiful" definition in simple refers to one that is simple but a lot can be done with it/derived from it...

YES IT IS! Give me one "Definition" that boils to this one... Using this definition one can derive the Maclaurin Series for e... Using this definition one can use l'Hopital's Rule to derive: e = lim (1+1/n)^n x->inf And by defining ln(x) to be the inverse function of e^x...

Well call me premature if you will, but I reckon it is: e is a number such that: d/dx (e^x) = e^x I mean so much can be drawn from this...

Well here is a thought... Errors are usually (like Mathman said) linked with percentage error. So in you example we have (in Absolute Error): 0.0005 +/- .00001 g = 0.0005 +/- 20% 1.0005 +/- .00001 g = 1.0005 +/- .001% (wlthough you might ceil the value to 1%) Hence in practice, most of...

Okay I wish to try to construct an Epsilon-Delta Definition to prove the L'Hopital's Rule (0/0 form). Please correct me if I am wrong. http://mathforum.org/library/drmath/view/53340.html I found the above site. Scrolling down one would the proof. I can follow how an x constraint is...

I am trying to prove that the upper +limit of x^x, when x->0 converges to 1. So I started by converting x^x to e^(x ln(x)). I know that this eliminates the domain: x <= 0, but I still believe that I can still continue on. So here I tried to constrain the limit: x ln(x) (i.e. x->0, x ln(x)...

Yes. That is what I wanted. Still I think the best way for me to get this is convince myself by trying to prove a false limit (I obviously should not be able to...)

Okay for a simple finite limit: e.g. lim (3x) = 3 x->1 in the end I say: "Therefore for every |x - 3| < delta, there exists an epsilon such that |3x-3| < epsilon" Hence I can make delta really really small and the y bounds of epsilon will constrain the limit. So let's come to...

I believe that the definition of e is: e is such that when: y=e^x dy/dx = e^x Hence via the Taylor Series, the actual value of e can be found right?

Well that is what I thought. My equations were: I solved: m*d^2x/dt^2+b*dy/dx+ky = 0 k=spring constant m=mass p=drag constant (F=pv) x=displacement t=time A,B = Constants of Integration n1 = -p/2m + SQRT( (p/2m)^2 - k/m ) n2 = -p/2m + SQRT( (p/2m)^2 - k/m ) OverDamping: x...