Recent content by eridanus

Let f : Rn -> R. Suppose that grad(f(x)) = 0 for all x in some open ball B(a, r). Show that f is constant on B(a, r). [Hint: use part (a) to make this a problem about a function of one variable] part (a) is show that for any two points x, y in B there is a straight line starting at x...

this is the diagram given http://www.columbia.edu/~kqc2101/circuit.gif so for Q_2 what would be the voltage drop V that charges C_2 in the equation Q=CV(1-e^{-t/\tau}) ?

A capacitor, a resistor, and another capacitor is connected in series. The first capacitor, C_1, has an initial charge of Q_0, and C_2 is initially uncharged. The switch is flipped at t=0, what is the charge on each capacitor as a function of time? So I thought Q_1 =...

I feel really dumb for asking this, but what? Simultaneously? I'm so confused

This is the problem: Let T be a complex linear space with a complex inner product <.,.>. Define T in L(V,V) to be Hermitian if <Tv,v> = <v,Tv> for all v in V. Show that T is Hermitian iff <Tv,w> = <v,Tw> for all v,w in V [Hint: apply the definition to v+w and to v+iw]. So this was my...

The first one seems right. Are you sure the answer is correct? For the second one, write out the equation that relates friction force with acceleration, and you should see that the mass cancels out.

I = (1e-10)10^(43.5/10)

faraday's law: E = N\Delta\Phi/\Delta t or induced voltage equals the number of loops times the change in flux over change in time direction matters because flux is a vector. so the change in flux would be (1.0 T)(1x10^-3 sqr. m)-(-1.0 T)(1x10^-3 sqr. m) change in flux is proportional to emf...

that looks right you can figure out the x displacement with pythagorean theorem, maybe drawing a diagram it will help

water and corneal tissue have about the same indices of refraction so light isn't as focused by the time it reaches the retina, as it would be after traveling through air first