ohmygod
[; \text{a function }f:(A_1 ,\mathcal{T}_1)\rightarrow (A_2 ,\mathcal{T}_2) \text{ is continuous everywhere} \Leftrightarrow;]
[; G_2 \epsilon \mathcal{T}_2 \Rightarrow G_1 \subset f^{-1}(G_2);]
Oh I already had it but I thought it was reddit-bound :V:
i wish i knew latex better
[editline]2nd June 2013[/editline]
but im too lazy to care
[editline]2nd June 2013[/editline]
[;I_{m_{G_{a_{y}}}};]
[; ;] = [; ;]
[; \xymatrix{ T \ar[r]^{\eta_T} \ar[dr]_{1_T} & TT \ar[d]^{\mu} \\ & T } \quad \xymatrix{ T \ar[r]^{T \eta} \ar[dr]_{1_T} & TT \ar[d]^{\mu} \\ & T } \quad \xymatrix{ TTT \ar[r]^{\mu_T} \ar[d]_{T\mu} & TT \ar[d]^{\mu} \\ TT \ar[r]_{\mu} & T } ;]
Oh it can do diagrams as well :v:
Guess it saves the time of prefixing everything with [url]http://www.codecogs.com/gif.latex?[/url]
Bradyns...
[; W_e <3 \lim_{for \to this} Y_{ou} for ;]
[QUOTE=mastoner20;40877893]Bradyns...
[; W_e <3 \lim_{for \to this} Y_{ou} for ;][/QUOTE]
[; I <3 (u_2) ;]
calc 3 final in 30 minutes!
that went fast, summer courses are fun
[QUOTE=Jo The Shmo;40886409]calc 3 final in 30 minutes!
that went fast, summer courses are fun[/QUOTE]
You're 28 minutes into it, but I hope you do well!
it was easy, the prof for this course is a grad student and he doesn't realize he's being too easy on us
the only one that stumped me was
[; \int_{0}^{1}\int_{x}^{x^\frac{1}{3}}\sqrt{1-y^{4}}\,\mathrm{d} y\,\mathrm{d} x ;]
I switched around the order of integration and did a bunch of tricky substitutions and integration by parts and i ended up needing to integrate arcsin(y), which I thought must have been wrong because I forgot how to do that even though its an easy trick
That's what I was afraid of, that I would forget all the integration tricks, since I haven't done any calc for an entire year before the start of may
But I ended up messing around and trying out lots of things like making it a triple integral, using polar coordinates, etc
and I figured out geometrically that part of it was the area of part of a circle which evaluated to [; \tfrac{\pi }{8} ;], but since that was for an integral in terms of [; u = y^{2} ;], I took the square root of it to make it in terms of y
(I should have noticed that even in terms of y, it's still [; \tfrac{\pi }{8} ;]
so I wrote down [; \sqrt{\frac{\pi }{8}} - \frac{1}{6} ;] , even though the answer is [; \frac{\pi }{8} - \frac{1}{6} ;] , and I also had a huge chuck of work done without geometric tactics that needed just ONE more step that I almost set up, so I'm sure I'll get decent part marks on it
Is there a plugin for Firefox that parse this inline TeX?
In the last lecture we had this semester, our lecturer put 3 puzzles on the board.
I've managed to write solutions to all 3, but here is my solution to the first...
The first puzzle is,
There is a wall and a floor which are orthogonal.
There is a point on a floor, and a point on a wall.
What is the shortest distance between the two points if you are an ant.
My attempt at characterizing a solution.
[QUOTE][IMG]http://i.imgur.com/FykpzpZ.png[/IMG][/QUOTE]
NB: The diagram was made in word, I tried to draw the Z plane, but I gave up as it was a pain in the ass to do.
A mathematician is a device for turning coffee into theorems.
A comathematician is a device for turning cotheorems into ffee.
Why does 0 keep losing at his debate club ?
[sp]He has no argument.[/sp]
Oh so I have a couple questions here:
If you have a function f(x) defined by:
f(x) = ...(f[sub]3[/sub](f[sub]2[/sub](f[sub]1[/sub](x))))...
with f(x) and f[sub]n[/sub](x) both differentiable, is f'(x) given by:
f[sub]1[/sub]'(x)*f[sub]2[/sub]'(f[sub]1[/sub](x))*... ?
Can you still use the Wronskian to determine the linear dependence of infinitely many functions?
[editline]5th June 2013[/editline]
[QUOTE=Joey90;40838462]Do you mean compose or multiply?
Either way it sounds pretty horrible...[/QUOTE]
I meant compose.
Indeed, it's super ugly and messy.
I'm going to be taking trigonometry next year, anyone give me any tips as to not look like a 5 year old that just opened a college quantum physics book? I've been very shit at math my entire life, only recently-last year- grasping intermediate algebra.
[QUOTE=Yahnich;40919831]can someone help me simplify this?
[; dU = Tdx\left (\sqrt{1+\frac{\partial^2Z}{\partial x^2}{}} -1 \right ) ;]
because i'm forgetting something obvious here
i should be getting this but i have no idea how
[;dU = Tdx\left (1+\tfrac{1}{2} \frac{\partial^2Z}{\partial x^2}{} -1 \right );][/QUOTE]
For small x:
[; \sqrt{1+x} \approx 1+\frac{x}{2};]
Yeah it's a taylor expansion around the origin.
[IMG]http://upload.wikimedia.org/math/7/1/3/713b1394e1acaa9a5bf87163060a363a.png[/IMG]
University of Antwerp, Physics (3rd year) :v:
I think I asked you a while ago, but I forgot what/where you studied
[QUOTE=Krinkels;40914568]Oh so I have a couple questions here:
If you have a function f(x) defined by:
f(x) = ...(f[sub]3[/sub](f[sub]2[/sub](f[sub]1[/sub](x))))...
with f(x) and f[sub]n[/sub](x) both differentiable, is f'(x) given by:
f[sub]1[/sub]'(x)*f[sub]2[/sub]'(f[sub]1[/sub](x))*... ?
[/QUOTE]
Firstly you have to be careful that the first function is even well defined! The best way to do it is to define g[sub]n[/sub] to be the composition of n functions, and then f = lim g[sub]n[/sub] - which you should check converges!
Supposing that is the case, and that the left hand side is also differentiable, you can certainly apply the chain rule on the g[sub]n[/sub] to get that form for the g'[sub]n[/sub].
So now we are reduced to showing that the limit of the derivatives of a sequence of functions is the derivative of the limit. In general this is not true, however
If the g'[sub]n[/sub] also converge to a function h, then that function [i]will[/i] be the derivative of f.
In other words, it does work provided everything converges.
[QUOTE=Krinkels;40914568]
Can you still use the Wronskian to determine the linear dependence of infinitely many functions?
[/QUOTE]
How would you use the Wronskian with infinitely many functions? Determinants of infinite matrices don't really exist...
Also, W=0 doesn't quite imply total linear dependence, although if the functions are 'nice' then it will.
Sounds like a fairly serious problem in Functional/Linear Analysis.
You also have to consider what linear independence of infinitely many functions even [i]means[/i] - do you allow only finitely many at a time (in which case, showing that f[sub]1[/sub]...f[sub]n[/sub] are LI for all n will show linear independence) or do you allow infinitely many nonzero terms, in which case you have to do it all 'simultaneously' which is quite hard!
For something like a Fourier series, you'd show the functions are orthogonal (with respect to some inner product on an appropriate function space), and then it's obvious that they are LI (at least in the finite sense).
[QUOTE=Krinkels;40914568]
I meant compose.
Indeed, it's super ugly and messy.[/QUOTE]
eek
I'd like to thank all of you, for this thread this will help me in my future endeavors for the military, hopefully for reading through this thread, khans academy, and pauls online notes, I will be able to score higher to get into a higher college category, thank you facepunch :smile:
this truly probably means as much to me as much as my life
Also if anyone were to point to me in the direction of any science discussions, kind of like this with resources and things to study, I'd be grateful,
[QUOTE=Roof;40930991]I'd like to thank all of you, for this thread this will help me in my future endeavors for the military, hopefully for reading through this thread, khans academy, and pauls online notes, I will be able to score higher to get into a higher college category, thank you facepunch :smile:
this truly probably means as much to me as much as my life
Also if anyone were to point to me in the direction of any science discussions, kind of like this with resources and things to study, I'd be grateful,[/QUOTE]
/sci/ board on 4chan made this repository:
[url]http://sites.google.com/site/scienceandmathguide/[/url]
Enjoy.
[QUOTE=Yahnich;40937613][;F \cdot \frac{\partial }{\partial t}F = \frac{1}{2}\frac{\partial }{\partial t}F^2;]
can anyone tell me what this rule is called or whatever, because it's one we got given to us but i like knowing the proofs and stuff and why it's allowed[/QUOTE]
An application of the chain rule?
[;\frac{\partial }{\partial t}F^2 = 2 F \cdot \frac{\partial F}{\partial t};]
[QUOTE=Yahnich;40946552]oh wow
wooooooow
woooooooooooooooooooooooooooooooooooooooooow
[editline]8th June 2013[/editline]
this happens when you do volume, surface and line integral for 3 days[/QUOTE]
don't worry. I looked at it and went "that looks like the chain rule... but wait... there's a 1/2 factor IT CAN'T BE THE CHAIN RULE WHAT IS IT" so I'm retarded as well.
I got stuck on that one too when[URL="http://www.sbfisica.org.br/rbef/pdf/070707.pdf"] I saw it for the first time in the exact solution to a pendulum[/URL] (step 4 to step 5)
I still don't get how the fuck you figure out all those steps to end up with an integral where the analytical solution has yet to come a few decades after (elliptic integrals)
Maybe that's why it took ~27 years lol
Does anyone know of a good website for maths puzzles (geometric, word problems, optimizations, etc)?
'Martin Gardner' style puzzles.
I might be showing my internet age, but sporcle has some pretty decent math puzzles behind some of them.
[url]http://www.math.utah.edu/~cherk/puzzles.html[/url] also has some little teasers, but not a real in depth endless amount. Scanning over them, it seems more like combinatorics riddles than anything.
Of course you've got Sudoku which is a pretty endless game.
Another application of small combinatorics with different board games: [url]http://www.math.com/students/puzzles/puzzleapps.html[/url]
If you have the extra cash, Luminosity is supposed to actually be pretty good at brain teasers, though I don't know how in-depth they are with the mathematics.
i hate luminosity ads
I do too, but I've still been told that their brain teasers are pretty good at what they're supposed to do.
Finished the front side of my resource sheet.
[QUOTE][IMG]http://i.imgur.com/QGEs1nR.jpg[/IMG][/QUOTE]
I should start an engraving business for fleas with jewelry.
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