I am not exactly sure where to post this but this seems like a fine place


I am looking for a predesigned spread sheet (excel or whatever else) that you can use to create a bibliography of all the books you have read. Like a chart with title/author/publisher/year ETC. The main goal is to be able to write down concepts / interesting passages / excerpts next to a book. I often find myself thinking "hmm where did I read that". With such a list it would be more or less easily findable.

Does anyone use something like that? Esp Academics I am sure must organize their reading somehow in this fashion.

Looking at the integral tests I find some functions I do not know.

What are
ctg, tg, ch, sh, th?

If they're cotangent, tangent, hyperbolic cosine, hyperbolic sine and hyperbolic tangent, I hate them.

I have not seen those abbreviations before. Usually it is

cot
tan
sinh
cosh
tanh

In math and the sciences the challenge isn't so much tracking concepts and passages as it is properly recording and formatting citations for a bibliography. This is because one needs to write them in a way compatible with LaTeX, the canonical "program" for typesetting mathematics. I've only used it a bit myself, but you might consider BibDesk (http://bibdesk.****************/) if you've got a Mac. This might not be what you're looking for -- I don't know how conducive it is to making notes or recording excerpts. as it was created for somewhat of a different purpose. But it's worth a look.

"the integral tests"?

From bobboufl11's link - the integrals competition had several test papers available, using strange abbreviations for trig functions.

Confirmed, I hate them.

Can somebody please explain to me what co-variation means?

Incidence of rape and ice cream sales.

They co-vary.

When it is warm, rapists rape more.

When it is warm, people buy more ice cream.

Or, if you are still stuck on Kelly, read: http://en.wikipedia.org/wiki/Covariation_model

Looking for a little excel help, I was referred over here.

I'm learning to use the regression tool on stocks in excel 2010 but i'm having trouble interpreting the data when you use multiple benchmarks. My R^2 goes up maybe 10%, but P-value increases to nearly .4 (1- p-value gives you the coefficient confidence) and 95% upper/lower confidence boundaries include 0. How do I know if the new benchmark is relevant to the stocks movements or should be included in the overall model?

I can include the full regression data if necessary.

In regression R^2 always goes up when you add another variable.

Okay. So what is the determining factor of relevance for a new independent variable? I should have mentioned the adjusted R^2 and F increased as well. Does the 95% upper/lower mean I should auto discard this benchmark?

i'm confused, because adj. R^2 and F have increased, but t-stat p-value and 95% confidence levels have decreased in desirability. Is there an overall "best statistic" for judging your confidence in a variable? My stats classes were a while back, and i'm rusty at best

ya that seems strange. I didnt go into more detail because I'm sure someone can answer it better than I. You can do individual t test on each variable by analyzing the coefficients in the regression model and their standard errors and one with highest p value is the worst one

tyvm

Still can't see the distinction between co-vary and correlation though D:

Correlation is normalized by the standard deviations of your rv's.

corr(X,Y) = cov(X,Y) / (sigma_X * sigma_Y)

Simple linear algebra question if someone could help quickly.

Determine the standard basis for the orthogonal complement when S is given by the following: span ((1,0,2) , (1,1,1))

Do you know about Gram-Schmidt orthonormalization?

Ahhh yes. Forgot about that. Could you explain it possibly? The section in my book is very very poorly written.

in R^3 you have 3 dimensions, meaning you can span the entire room with three vectors.
Any two vectors, not linearly dependent, will define a two dimensional subspace (a plane). There will be a third dimension left over. Any vector not in the plane will suffice to generate the third dimension. We don't need an arbitrary one here though, we need an orthogonal one. A trick would be just to calc the box product of the two vectors - that gives a third one thats orthogonal.

Or just run some numbers in your head. (2,x,-1) is orthogonal to the first one. (-2,1,1) is orthogonal to the second. So (2,-1,-1) should be orthogonal to both.


(i hope I understood the question correctly)

GS algorithm:
1. Choose a vector to be your first basis vector (You can normalize it if you want)
2. Given the other vector, subtract the inner product with it and your first vector.
3. Check that the inner product with your two vectors is zero and you have orthogonal basis vectors that span your original space!

Note, if you had more basis vectors, you'd need to subtract the inner product with each from all of the other ones you've already orthogonalized.

Ty. And ty also, Internet

Progressing through Trig... now on Sum/Difference Identities...

If 0 < A <= pi, and sin(x - pi/2) = A* cos(x), then the number A = ?

Using the sine difference identity:

sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

sin(x - pi/2) = sin(x)cos(pi/2) - cos(x)sin(pi/2)
= sin(x)*0 - cos(x)*1
= -1 * cos(x)

So... I have A = -1, but the question specifies, 0 < A <= pi.

Not sure what number in the interval (0,pi] is equivalent to -1. The number A is not a radian measure, so it's not like I can just add 2pi? Even so, -1 + 2pi > pi so... I'm a little stuck here. Should I be adding 2pi to sin(x - pi/2)? i.e., is sin(x - pi/2) equivalent to sin(x + 3pi/2)?

Thanks.

typo in the problem for sure. They meant 0 < x <= pi. This is a superfluous condition, of course, but as you point out, A=-1 is the only solution (that holds for all x).

Thanks, Wyman. Indeed there was a typo in the problem. We submit our homework online and get instant grading, and -1 was correct. However, I think I'm running into a similar problem without any success this time.

If sin(2x) - cos(2x) = sqrt(2) * sin(2x + A*pi), then the number 0 < A = ? < 2

I divide the left side by sqrt(2), or multiply each term by the reciprocal, for:

sin(2x)*(1/sqrt(2)) - cos(2x)*(1/sqrt(2)) = sin(2x + A*pi)

sin(2x)*cos(pi/4) - cos(2x)*sin(pi/4) = sin(2x + A*pi)

I recognize the left side of the equality as the sine of difference formula:

sin(a-b) = sin(a)*cos(b) - cos(a)*sin(b)

So, using the above identity, a = 2x, and b = A*pi... therefore A = -1/4, but again -1/4 is not in the interval 0< A < 2. Also, entering -1/4 is incorrect per the homework software. Am I missing something here?

Thank you.


EDIT: Tried a little harder. Apparently this problem was a bit different that my previous one. For the sine function's intents and purposes, sin(2x + A*pi) = sin(2x + A*pi + 2pi)? Because I when I used 7/4 instead of -1/4 for A, the answer is correct. But I'm a little confused now, because I thought I would be able to do this with my previous problem as well?

You have the equality
sin(2x + A) = sin(2x - pi/4).

The equality holds for A = -pi/4. It also holds for A=7pi/4, A = 15pi/4, and in general, A = 7 * pi/4 + 2n*pi, where n is any integer. That's because sin is periodic, with period 2*pi.

In the previous problem, however, you had
A cos(x) = -cos(x).
This only holds when A=-1 (just divide both sides by cos(x)!)

The difference is that in this current problem, the A is *inside* the argument of the sin function.