Recent content by Atropos

Wow, I'm an idiot. I was so hung up on the cosine part of the sum that I completely forgot about the monotonic series u_n. I was only paying attention to the fact that cosine was sinusoidal ad therefore f_n>f_n+1>0 couldn't apply. ...but it does apply to u_n. Thank you for pointing that...

Homework Statement Show that if \vartheta is any constant not equal to 0 or a multiple of 2\pi, and if u_{0}, u_{1}, u_{2} is a series that converges monotonically to 0, then the series \sum u_{n} cos(n\vartheta +a) is also convergent, where a is an arbitrary constant. Homework...

Are you sure the summation is from 0 to \infty, because ln(n) doesn't exist for n=0. Maybe it's supposed to be a trick question?

i know that \nabla(\nabla\bullet\vec{u}) - \nabla\times\nabla\times\vec{u} = \nabla^{2}\vec{u} i dunno, what about this?.. Solve this equation for \nabla\times\nabla\times\vec{u}, then substitute into your equation, and simplify the resulting equation. The first term of your equation...

Integration of the series expansion and contour integration are pretty useful. Laplace transforms too. There's also the Howitzer Cannon of integration techniques: differentiation with respect to a parameter.

\vec{}Forget what I wrote in my last post. I think I found a way to solve this using only algebra. Let me sum up the problem as I understand it. Let me know if it's correct or not. **A circular disc of uniform density, mass M and radius R is rolling without slipping on the ground. Initially...

im having issues with LaTeX

There's no force that restores the wheel to its upright position, but there is a force that resists any change in the position. Before we can figure out what that force is, we need to make a few assumptions. (1) Because the wheel is rolling, it is rotating about a fixed axis, so it has angular...

As this my first post, I'm not sure if this is the right place to ask this question. But textbooks are learning materials, so I think it's alright. I enjoy learning new things in math, but textbooks are very expensive. I'd really hate to spend $100+ on a book, only find out that it isn't...