Hi everyone,
Given a vector-valued function ##\vec{A}##, how do I show that:
$$\vec{\nabla} \times \left(\frac{\partial \vec{A}}{\partial x}\right) = \frac{\partial}{\partial x}(\vec{\nabla} \times \vec{A})$$
In other words, are the cross product and derivative commutative w/ each other? I...
I'm reading a textbook that says:
"The directional derivative in direction ##u## is the derivative of the function ##f( \mathbf x + \alpha \mathbf u)## with respect to ##\alpha##, evaluated at ##\alpha=0##. Using the chain rule, we can see that ##\frac {\partial}{\partial \alpha} f( \mathbf x...
Homework Statement
We're given the gaussian distribution: $$\rho(x) = Ae^{-\lambda(x-a)^2}$$ where A, a, and ##\lambda## are positive real constants. We use the normalization condition $$\int_{-\infty}^{\infty} Ae^{-\lambda(x-a)^2} \,dx = 1$$ to find: $$A = \sqrt \frac \lambda \pi$$ What I want...
I'm a 2nd-year physics undergraduate student at UC Berkeley. I think that it's about time I joined this community. I'm looking forward to asking and (hopefully?) answering questions with all of you.
Thank you.