Recent content by Cole A.

@HS-Scientist: Thanks for your answer.

Homework Statement Prove that if x^2 + y = 13 and y \neq 4 , then x \neq 3 .Homework Equations N.A.The Attempt at a Solution The proof itself is simple enough: suppose x^2 + y = 13 and y \neq 4 . Suppose for the sake of contradiction that x = 3 . Then \begin{align*} (3)^2 + y &= 13...

I'm sorry for my lack of feedback. This one line provided a great deal of clarification. I appreciate your input, both of you.

Thank you for the responses, everyone.

I'm reading an introductory E&M textbook (with an electrochemical emphasis, so charge carriers are ions rather than electrons), and the wording my book uses to describe current is giving me a great deal of confusion that I was hoping someone could help me resolve. My understanding is as...

I'm having trouble understanding the relationship between a system's energy level and its stability (in a general sense). My understanding is that chemical and physical systems experience a driving force that pushes them toward the lowest possible energy state (ignoring quasi-steady states...

Thank you for clearing things up.

This clarified things immensely for me. Thank you.

This is a really basic point that I am getting held up on. In probability theory, we use PDFs and PMFs to describe random variables. (The term "random variable" carries a certain connotation of "unpredictable variations when repeated.") For example, the number of heads we will see in 50...

(I'd like to preface this with the warning that the following question may be a very dumb one.) My understanding is that current density (or flux) \vec{J} = \vec{J}(x, y, z) is the rate of flow of charge (or the current) per unit area. (Units of \frac{\text{C/s}}{\text{cm}^2} .) Say...

Ugh, I was starting to suspect I was wasting time because of a typo in the book. I attached the relevant portion of the textbook page as an image, where the above equality is listed along with a couple other vector identities. Thanks for the extra input (and sanity check).

Homework Statement (From Plonsey, R. and R. C. Barr, "Bioelectricity: A Quantitative Approach") Show \nabla^2 r = 0 given r = \sqrt{x^2 + y^2 + z^2}. Homework Equations \nabla = \frac{\partial}{\partial x}{\bf i} + \frac{\partial}{\partial y}{\bf j} +...