Recent content by Justhanging

How do I propagate the standard error from the slope and intercept? For example: If I have the slope of a linear fit along with its standard error and I'm interested in a value derived from the slope how do I propagate it's error from the slope to the value of interest? X = (c1 -...

I have couple questions about this and I was hoping someone with some stats knowledge could clarify. First, when people report numbers such as 10 plus or minus 5, what does the 5 mean? Is it the standard deviation or the confidence interval or the variance? What is the relationship between...

I need straightforward answers not Quantum Mechanics.

Homework Statement What determines the order of the Molecular orbitals in heterodiatomics? The Attempt at a Solution In my book, I have NO with an order of 1s 2s 3s 1p 2p 4s Where s means sigma and p means pi. Also sometimes I see in the book the ordering being 1sigma...

Open sets would have none of its boundary points included in the set. Wow I made this question a lot harder than it needed to be. Thanks Dick.

So your saying the answer is false because the boundary of S need not be in S? But this then would only apply to open sets?

All the definitions I see are the same. The neighborhood of the point needs to have a point in the set and a point outside the set for it to be a boundary. For your quesition I would say 1 is a boundary because it has points outside of the set in its neighborhood. When you say an open set, are...

Am not exactly sure, but I seem to remember that interior points have a disk where all the area around the disk are within the set but boundary points have disk where some of the area of the disk is not within the set. The disk being so arbitrary disk with a very small radius. By this definition...

Homework Statement True or false: Let S be any set in R2. The boundary of S is the set of points contained in S which are not in the interior of S. Homework Equations The Attempt at a Solution Common sense tells me true. I don't really understand it though, if S is an open set...

Yes it means the gradient of f evaluated at the terminal point of the vector. My equation for differentiability taken from the book is: \lim_{(\Delta x, \Delta y)\rightarrow\ (0,0)}\frac {\Delta f - f_x (x_0, y_0)\Delta x - f_y(x_0,y_0) \Delta y}{\sqrt{(\Delta x)^2 + (\Delta y)^2}} = 0 If...

You sure know your latex, sorry its my first time and it was late. Everything is right except its the magnitude of h on the bottom not the absolute value. I don't if the notation is the same.

If all the first partial derivatives of f exist at \vec{x}, and if \lim_{\vec{h}\rightarrow\vec{0}}\frac {f(\vec{x})-(\nabla f(\vec{x}))\cdot\vec{h}}{||\vec{h}||} = 0 Then f is differentiable at \vec{x} Note: Its the magnitude of h on the bottom. First of all, I don't...

Ahh yes I see now. One last thing to clarify, the fraction in this equation is a scaler so really this equation is saying that it is a scaler multplied by a vector. Is this correct?\text{Proj}_\textbf{u}(\textbf{v} \times \textbf{w}) = \frac{\textbf{u} \cdot (\textbf{v} \times...

Honestly am still confused. I see that the top of the fraction is five but I don't know what u * u is on the bottom. And I still don't understand how to incorporate the other u outside the fraction. Am missing something here... you say that I can start cancelling once I get numbers but I only...

mag(u)2 = u * u Now I don't know if I can cancel some u's. I don't know what properties to apply here, my book doesn't mention anything about cancelling vectors like someone would cancel regular variables in algebra.