Recent content by Paradoxx

Sorry, the latex didn't work. Gonna edit this in one minute.

Homework Statement So my teacher, as we made the multipole expansion of Vector Potential (\vec A) decided to proof that the monopole term is zero doing something like this: ∫∇'⋅ (J.r'i)dV' = ∮r'iJ ndS' = 0 The first integral, "opening" the nabla: J⋅(∇r'i) + r'i(∇⋅J) this must be equals 0 J =...

Sorry, I know I have not been very clear, but I'm trying to understand (and failing) that's why... Here what I have (in the figure): I need to expand the first term, conserve only the linear term in "d". I need to get the last equation...but I have no idea about what I'm doing :(

For example,if I have ##(a+b)^n## , where n can be a fraction...I know I solve like: ##(a+b)^n= b^n +\left( ^n _1 \right)b^{n-1}a +\left( ^n _2 \right)b^{n-2}a^2+...## If I had ##(a-b)^n## I should alternate the signal + and -... But in the case ##(a+b+c)^n## or more precisely ##(a+b-c)^n## I...

Homework Statement So, I'm solving a dipole thing and I have these vectors: |r + d - r'| = (r² + d² - r'²)(1/2) Homework Equations I want to expand this but I have no idea how! I know I may have an infinite power series, but I may expand at the square terms tops... Before I needed to do the...

Ohhh, you are right! It worked now, thank you very much!

Ok, I realized that I must consider x and y and derivative in relation with time. v = dx/dt + dy/dt then v² would be (dx/dt + dy/dt)². I did the derivatives: x'= RΘ' + Rcos(Θ)Θ' and y' = Rsin(Θ)Θ', so x+y = RΘ' + RΘ' (cosΘ + sinΘ) Also, v² = ( RΘ' + RΘ' (cosΘ + sinΘ))² = (4R²Θ'² +...

Homework Statement Cycloidal Pendulum, with x= RΘ+RsinΘ and y = -RcosΘ I need to find the Lagragian. Homework Equations L = T - V The Attempt at a Solution I just want to know how do I find the velocity so I can find T, which is 1/2 mv². I thought it would be dx/dΘ but it didn't...

t = Ʃ Tn sin (n∏x/L) where f(t) = t = 2/L ∫ f(t) sin(n∏x/L) If the period 2L = 2, my limits on the integral will be 0 to 1?

Find the Fourier series solution to the differential equation x"+x=t It's given that x(0)=x(1)=0 So, I'm trying to find a Fourier serie to x(t) and f(t)=t, and I'm know it must a serie of sin... So here's my question...the limits of integration to the Bn, how do I define them? Will...

Yay! Thanks...I've got to do lots of exercises now to practice.

So n+1=3, n=2 And according to that formula I have to do f''(z0) Where my F(z) = 5z²-3z+2 F''(z)=10 F''(z)[(2∏i)/2!] = ∫5z²-3z+2 / (x-1)³ = 10i∏ Is it?

If you click with the right button and open it in a new tab you'll see it clearly. Or click in the image, then will appear a black image when you can barely see it, just click in this black image and it will open a new tab with the formula. Anyaway is just...

Here's the formula I know for cauchy's integral Where n is the radius, and f3(z) means I have to derivate F(z) 3times. At least it's what's on the only exercise we had in class...(f(z) was an exponencial at tha case) Decomposing it in partial fraction doesn't help. If was a function type...

Sorry, I know I'm really dumb :cry:...but anyways I have this Cauchy Int. Formula : ∫F(z)/((z-z0))n My doubt is about this countour, it just says it's a simple closed one with z =1.In this case, do I have a circle(for exemple) centred in (0,0) with r=1? Then my z0=1 and my n= 3 and my f(z)=...