Recent content by filter54321

Ignore the first part. Sine/cosine is a simple counterexample. Still wondering about the second part. Thanks

Is the antiderivative of an even function even? Specifically, given an even function g(x)=g(-x) will the following function be even? Odd? For constant a>0, r a dummy variable h(x,t) = Definite Integral [ g(r) dr, FROM x-at TO x+at] Asking whether or not h(x,t)=h(-x,t) This is the...

When formally proving trig identities using algebra are you allowed to divide? Ordinarily I wouldn't think twice about this. Sure, the trig function by which you are dividing might take on 0, but not for all angles. We divide by potential zeros all the time. My advisor was being very coy...

...actually, I think I was confusing myself. The x,y in the definition don't have to be matching up with the x,y from the complex number z. The x,y in the definition correspond to the real and imaginary parts of an arbitrary complex z.Would you plug this into the definition? real: x/(x^2+y^2)...

How do you write e^(1/z) in the other form? z = x+yi So we should be able to right it using this definition of e^z, no? e^z = e^x * [cos(y) + i * sin(y)] I pushed some numbers around the page for a while but I can't get 1/(x+i*y) to split into anything nice. Is there a trick?

I'm in real analysis classes but my calculus is shaky when I hit things that aren't plug and chug. How do you evaluate this integral and why can you ignore the dx differential? The more theoretical details, it smells like some flavor of the Fundamental Theorem of Calculus or Leibniz's Rule...

I'm studying the Poisson Process (rate R) and I'm hung up on the issue of dependence. This seems like and easy question but I have no background in probability whatsoever. By definition, the number of events in disjunction time intervals are independent. Okay. Fine. But say we have an...

You can n-sect any arbitrary angle with a ruler and compass. You just need to get really lucky.

I had a terrible adjunct professor in ODEs and got little or no theory. I'm not in PDEs and my much better professor just (re)introduced convolutions while generalizing the heat equation to Rn - unfortunately it was not a reintroduction for me. Later chapters in the book deal with...

Are there "imaginary" numbers other than i? I'm taking a class in complex analysis and the professor wrote the textbook so I'm getting most of it. There is one elephant in the room though, and I haven't been able to make office hours to clear it up. Are there "imaginary" numbers other than...

Ah. Typo. y''-xy'=0

Homework Statement Find the first 6 terms of the power series expansion centered at 0 for the general solution for y -xy'=0. Then find the coefficient of the x38 term. Homework Equations General solution is of the form: y=a0+a1x+a2x2+a3x3+a4x4+a5x5+... If you factor out the ao and...

Right side corrected, should be y''-2y'+y=(ex)/x

Homework Statement Find the general solution for: y''-2y'+y=ex/x Homework Equations NONE - not an initial value problemThe Attempt at a Solution Solve the homogeneous first: r2-2r+1=0 r=1 as a double root So: y1=c1ex y2=c2xex ...but what in God's name is the form for the particular Y (based...

I know what it looks like, it's a common example in calculus. It bounces up and down as you go to 0 with ever increasing frequency. How does that have anything to do with the boundary methodology outlined in my original post?