Let f be analytic on {z : 0 < Im z < 1} and continuous on the closure of this set.
Suppose that f(z) = 0 if z is real. Show that f is identically zero.
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Arne wants to move in Leuven (54°N) with such a high speed that the vertical component of the Coriolis force cancels out the gravitational force. In which direction should he move to keep his speed as small as possible? How big is this speed? How big is the horizontal component of the Coriolis...
I've got some serious problems understanding Faradays law.
I think any changing magnetic field will create/induce an electric field through empty space. Is that correct? And if so, what is the direction of the field? I mean, the electric field vectors must have *some* direction, but I can't...
This shouldn't be too hard but I'm struggling.
Consider N identical particles in a box of volume V. The relation between their linear momentum and kinetic energy is given by E = c\left|\overrightarrow{p}\right|, where c is the speed of light. So, the Hamiltonian of the system is...
Does the Maxwell-Boltzmann speed distribution hold for all ideal gases or just for the mono-atomic ones? If it holds for all gases, why? What happens with the degrees of freedom, don't they change things?? I'm very confused.
We know the Maxwell-Boltzmann distribution for the energy and the speed of a molecule of an ideal gas. Using derivatives it is easy to see that the most probable speed for a gas molecule is given by sqrt(2kT/m), which corresponds to kinetic energy kT. Calculating the most probable energy, we get...