Humanity is like the Kronecker delta. We won't be one until we're all equal; so long as we're different we'll be nothing.
Now I'm going to go and spray paint some flowers onto the side of a VW Kombi Van or something.
Can anyone here check this proof for me please? Theorem 1.5.14 states that x is in the closure of A iff every neighbourhood of x intersects A.
[img]http://gyazo.com/27785bf2ad8e1020d80c4b6e760de87c.png[/img]
[img]http://gyazo.com/0a31ed10036affca0430ea480abc57d6.png[/img]
I realise that I probably could have defined the neighbourhood of x_i to be X_i after finitely many n but I prefered to seperate the two cases to make it clearer to myself what was happening when i > n (product topology is a bit trippy at times!)
Also, I apologise in advance if there is anything wrong with my LaTeX formatting, I'm still getting used to using it. (any tips greatly appreciated)
Edit: Just noticed an error, in the second case, its supposed to be X_i n A_i, not V_i n X_i.
Take Multivariable Calculus in community college they said.
It'll be easy they said.
Does anyone here have good experience with MATLAB?
sorta
I've been using it quite a lot lately.
Taking calc 1 at university and wow whats going on
[QUOTE=cody8295;47089768]Taking calc 1 at university and wow whats going on[/QUOTE]
Post questions you've got here. This thread has been so slow lately.
I have to write a script in MATLAB that is to transform a vector in discrete time.
For the independent variable:
[CODE]y[n] = x[an+b][/CODE]
For the dependent variable:
[CODE]y[n] = Ax[n] + B[/CODE]
The trouble that I'm having is being able to properly show/stem plot the time shifting, expansion, or contraction for the input of "a" and "b"
Here's an example:
[CODE]x[n] = [1 2 2 1 0 1 1 1 3]
n = [-4 -3 -2 -1 0 1 2 3 4]
a = 0.5
b = 0
A = 1
B = 0[/CODE]
The modified version would be from -8 to 8, and it would have gaps in the odd spots. I know that I have to use a for loop, but I don't know what to put in for the statement.
So if I understand this correctly, n is the time, x represents the value of some function at those specific points in time, and now you're trying to sample x at times an + b? The easiest way to do that would be to just use the [URL="http://www.mathworks.com/help/matlab/ref/interp1.html"]built in function for interpolation.[/URL]
So for your example it would look like this:
[CODE]>> interp1(n, x, a * n + b, 'nearest')
ans =
2 1 1 0 0 1 1 1 1
[/CODE]
Of course depending on what you're trying to achieve, you might want to use better interpolation methods instead of just taking the nearest sample.
What are some good books for Linear Algebra?
[QUOTE=frdrckk;47092479]What are some good books for Linear Algebra?[/QUOTE]
Learning for the first time, or what? I like Friedberg, Insel, and Spence. It might not be suitable for a first pass, though.
Then again, I didn't use it for a first pass so I don't really know. It feels to me like one of the only books that emphasizes both the calculations and theory pretty well.
[QUOTE=JohnnyMo1;47092794]Learning for the first time, or what? I like Friedberg, Insel, and Spence. It might not be suitable for a first pass, though.
Then again, I didn't use it for a first pass so I don't really know. It feels to me like one of the only books that emphasizes both the calculations and theory pretty well.[/QUOTE]
Yes, learning for the first time. But I will take a glance at the books you've mentioned. Thanks.
This is really, really basic shit but for some reason I just can't physically understand these proofs with the div & curl :
[img]https://dl.dropboxusercontent.com/u/888382/idontgetitatall.png[/img]
The fact that the solution for div is a workshop exercise is frustrating as I couldn't even do it in the workshop, and the Tutor's attempt at trying to explain it was awful.
Could someone ( aka all of you) who are considerably better at vector calculus please show a proof for it?
Have you tried writing out the i'th component of the left hand side and applying the chain rule? It's essentially a more simple but analogous version of the proof of (D) because it doesn't involve the Levi-Civita symbol.
[QUOTE=pebkac;47092468]So if I understand this correctly, n is the time, x represents the value of some function at those specific points in time, and now you're trying to sample x at times an + b? The easiest way to do that would be to just use the [URL="http://www.mathworks.com/help/matlab/ref/interp1.html"]built in function for interpolation.[/URL]
So for your example it would look like this:
[CODE]>> interp1(n, x, a * n + b, 'nearest')
ans =
2 1 1 0 0 1 1 1 1
[/CODE]
Of course depending on what you're trying to achieve, you might want to use better interpolation methods instead of just taking the nearest sample.[/QUOTE]
The thing is, the inputs are user-based so I have to make my code work for any inputs, but last thing I need for the code to be complete is for the stem plot to repeat its last inputs. With time contraction, the plot will get rid of some of the inputs and repeat their last inputs
For example:
[CODE]x[n] = [1 2 3 4 0 5 6 7 8][/CODE]
If I were to contract time by 1/2, then it would be
[CODE]x[n] = [1 1 1 3 0 6 8 8 8][/CODE]
The 1's and 8's were repeated, but I'm trying to figure how to phrase it in MATLAB so it only does those inputs
-snip- sorry nvm
[QUOTE=gangstadiddle;47096642]The thing is, the inputs are user-based so I have to make my code work for any inputs, but last thing I need for the code to be complete is for the stem plot to repeat its last inputs. With time contraction, the plot will get rid of some of the inputs and repeat their last inputs
For example:
[CODE]x[n] = [1 2 3 4 0 5 6 7 8][/CODE]
If I were to contract time by 1/2, then it would be
[CODE]x[n] = [1 1 1 3 0 6 8 8 8][/CODE]
The 1's and 8's were repeated, but I'm trying to figure how to phrase it in MATLAB so it only does those inputs[/QUOTE]
You could just pass 'extrap' as the last argument to interp1, this will tell it to use extrapolation for queries that fall outside the domain of the data. For nearest neighbor sampling, this means it will just repeat the first and last values when needed.
Can anyone explain to me if the reasoning in this proof is valid? I can't find anywhere that it would fail. (All those products should be from "i=1" and not "i" by the way. Just realised while posting this)
[img]http://gyazo.com/3efbdc37979e0154a82f4e2966011d5a.png[/img]
[img]http://gyazo.com/1d7319dfaae3f257014f09c3063fb8aa.png[/img]
[QUOTE=agentalexandre;47101583]Can anyone explain to me if the reasoning in this proof is valid? I can't find anywhere that it would fail. (All those products should be from "i=1" and not "i" by the way. Just realised while posting this)[/QUOTE]
A being an open set does not mean it is the product of open sets in each X_i, only that it is a (potentially infinite) union of such sets. (Think about what this would mean in R^2 - the only open sets are open squares?)
In general if you see a something along the lines of 'prove something about this structure built from finitely many smaller ones' it should scream induction.
It's trivial for n = 1
Then given the induction hypothesis, for n > 1 you can write your product as Y x X_n, where Y and X_n are connected, so [i]in fact[/i] you only really need to prove it for n = 2!
This case is fairly simple, and you should look at the subspaces {y} x X_n and Y x {x} (homeomorphic to X_n and Y respectively)
[QUOTE=Joey90;47104760]A being an open set does not mean it is the product of open sets in each X_i, only that it is a (potentially infinite) union of such sets. (Think about what this would mean in R^2 - the only open sets are open squares?)
In general if you see a something along the lines of 'prove something about this structure built from finitely many smaller ones' it should scream induction.
It's trivial for n = 1
Then given the induction hypothesis, for n > 1 you can write your product as Y x X_n, where Y and X_n are connected, so [i]in fact[/i] you only really need to prove it for n = 2!
This case is fairly simple, and you should look at the subspaces {y} x X_n and Y x {x} (homeomorphic to X_n and Y respectively)[/QUOTE]
Thanks! The counter example with R^2 cleared it up for me. I'm studying from Munkres and the proof for this theorem uses the induction reasoning on the strips but I was just wondering why what I had written would fail.
Integral of x*y*sin(x+y) at {(x,y): 0 <= x <= pi, 0 <= y <= pi}
I feel like I'm missing something after sinxcosy+sinycosx
[QUOTE=JohanGS;47114194]Integral of x*y*sin(x+y) at {(x,y): 0 <= x <= pi, 0 <= y <= pi}
I feel like I'm missing something after sinxcosy+sinycosx[/QUOTE]
At that point can't you just separate the variables and use a pretty straightforward integration by parts?
Yeah, I figured it out. Thanks anyway.
Can someone explain to me why the Final Value Theorem and Initial Value Theorem utilize the Laplace transform of the derivative? I saw this in my notes for my engineering class, but I didn't see a reason as to why the Laplace transform of the derivative was used.
snip
This seems like an entertaining exercise.
[QUOTE=Linkuya;47185283]Teacher asked me to write:
2 x 3 = 6
in the most complex way possible.
[img]http://i.imgur.com/Wdqohvp.jpg?1[/img]
Isn't math great?[/QUOTE]
Write 2 x 3 = 6 in as sophisticated a way as you can.
[editline]23rd February 2015[/editline]
[img]http://i.imgur.com/32V5KVR.jpg[/img]
Would using gamma-function identities be considered cheating? Because you could get some really freaky shit if you just found some representation of the gamma functions and then just filling in 4 (because 6=3!=Gamma(4))
Hell you could then recursively replace every 1 with some representation of Gamma(2).
For example
[IMG]http://quicklatex.com/cache3/ql_7fd3279fd679c58a230401347b4ef661_l3.png[/IMG]
though I'm too lazy to figure something out for the right hand side.
Also replace 1 with normalized gaussians where you change the integration variable so it gets a messed-up form :v:
Maybe there's some kind of double meaning to 'complex'...
[QUOTE=Number-41;47200584]Would using gamma-function identities be considered cheating? Because you could get some really freaky shit if you just found some representation of the gamma functions and then just filling in 4 (because 6=3!=Gamma(4))
Hell you could then recursively replace every 1 with some representation of Gamma(2).
For example
[IMG]http://quicklatex.com/cache3/ql_7fd3279fd679c58a230401347b4ef661_l3.png[/IMG]
though I'm too lazy to figure something out for the right hand side.
Also replace 1 with normalized gaussians where you change the integration variable so it gets a messed-up form :v:[/QUOTE]
Could somebody explain to me in either Spanish or English what this means
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