# Search results

5. ### Creating intuition about Laplace & Fourier transforms

Hey everyone, I've been reading up a bit on control systems theory, and needed to brush up a bit on my Laplace transforms. I know how to transform and invert the transform for pretty much every reasonable function, I don't have any technical issue with that. My only problem is that some...
6. ### Confused about the Equivalence Principle and Inertial Reference Frames

Hey everyone, I started reading up on GR a couple of days ago, and I'm somewhat stuck on the concept of a free-falling IRF. I understand that an observer on a free-falling small spaceship would experience the laws of physics in a rather simple form, eliminating the need for a force of gravity...
7. ### Proving that a solution to an IVP is unique and infinitely differentiable

Homework Statement \frac{d^2y}{dt^2} + t\frac{dy}{dt} + t^3y = e^t;\ \ \ y(0) = 0, \ \ y'(0) = 0 Show that the solution is unique and has derivatives of all orders. Determine the fourth derivative of the solution at t = 0. 2. The attempt at a solution I'm somewhat lost here... Trying to...
8. ### Proving that an integral is a pure imaginary

Homework Statement Show that \int_{\gamma}\ f^*(z)\ f'(z)\ dz is a pure imaginary for any piecewise smooth closed curve \gamma and any C^1 function f whose domain contains an open set containing the image of \gamma 2. The attempt at a solution I have tried to approach it from some...
9. ### Probability fluid velocity and quantum entanglement question

Hey everyone, I'm a second year undergraduate student in aerospace engineering and I've been learning a bit of quantum mechanics for the past few weeks, for recreational purposes. I've been following this textbook: http://www-thphys.physics.ox.ac.uk/people/JamesBinney/qb.pdf On pages 40-41...