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Implicit Derivatives Explination by Simon Nodgefield - Thu, 10 Jul 2014 23:33:41 EST ID:BE8EyBvj No.14199 Ignore Report Reply Quick Reply
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So here's an excerpt from my textbook, but it's not verbose enough for me.
So they take the derivative of the y^2 = 2y(dy/dx)
My confusion comes from, why is that (dy/dx) still being multiplied to it? Should it not have disappeared because we just took the derivative?

For instance, (dx/dy)(x^2) = 2x
It does not equal = (2x)(dy/dx)

You see? Why is it staying there? What's going on?
Edward Gummlehall - Fri, 11 Jul 2014 03:53:38 EST ID:Gw2IN3ba No.14202 Ignore Report Quick Reply
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>For instance, (dx/dy)(x^2) = 2x

This is incorrect. You seem to be confusing the function dx/dy for the operator d/dx. The excerpt you posted is making use of a result in calculus known as the chain rule. The chain rule states that if you have a function f(y(x)), you can calculate its derivative using this formula: d/dx f(y(x)) = (df/dy)*(dy/dx). So to use the excerpt as an example, in this case f(y(x)) = y^2. So df/dy = 2y, but because you don't have an expression for y as a function of x to differentiate, you just leave the dy/dx as is. So multiplying the derivative of the outside function (df/dy = 2y) by the derivative of the inside function (dy/dx) gives you the total derivative with respect to x: d/dx (y^2) = 2y dy/dx.

Simon Nodgefield - Fri, 11 Jul 2014 12:45:58 EST ID:BE8EyBvj No.14206 Ignore Report Quick Reply
>So to use the excerpt as an example, in this case f(y(x)) = y^2
Well I guess this is where I'm confused. Why/how can the chain rule be applied here?
If we apply the chain rule to y^2, why don't we apply it to x^2?

>confusing the function dy/dx for the operator d/dx
So.. if you use d/dx on an X, then since x is on the top/bottom, they cancel out. But if you use it d/dx on a y, they don't cancel, and you're left with dy/dx.
That's how I'm understanding it, is that wrong?
Martin Haddleberk - Fri, 11 Jul 2014 20:57:18 EST ID:Gw2IN3ba No.14208 Ignore Report Quick Reply
>If we apply the chain rule to y^2, why don't we apply it to x^2?

You can, but it's trivial. So we would have f(x(x)) = x^2. Applying the chain rule you get: df/dx = (df/dx)*(dx/dx) = [d/dx (x^2)]*(dx/dx) = (2x)*(1) = 2x.

>So.. if you use d/dx on an X, then since x is on the top/bottom, they cancel out. But if you use it d/dx on a y, they don't cancel, and you're left with dy/dx.
That's how I'm understanding it, is that wrong?

Pretty much, that's how it works. d/dx (f) tells you by what factor to multiply to an infinitesimal increase in x to get an infinitesimal increase in f. So d/dx (x) yielding 1 just tells you that for an infinitesimal increase in x, you need to multiply by a factor of 1 to get an infinitesimal increase in x.

End behavior of derivatives of wave functions. by Cedric Sidgefut - Sun, 06 Jul 2014 18:17:11 EST ID:yGgK6aCs No.14175 Ignore Report Reply Quick Reply
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Hey /math/! I'm working through every single problem of Griffith's textbook on Quantum Mechanics to prepare for the course, and I've come across a question that I wanted to ask you guys. Often I'm having to evaluate expressions from infinity to negative infinity. With wave functions these terms always disappear because of their end behavior. In my mind, this must be true of their higher derivatives as well. I'm wondering if my intuition is wrong, and if it's not, is there a relatively pretty proof of it? Thanks in advance.
Fuck Blimblestock - Sun, 06 Jul 2014 22:50:17 EST ID:p8Vzq3fC No.14176 Ignore Report Quick Reply
>Often I'm having to evaluate expressions from infinity to negative infinity. With wave functions these terms always disappear because of their end behavior.
Isn't it with the |w|^2 that the total integral needs to be finite?

Intuitively, I think you're right, but also can't do a proof.

The case for monotonic functions would be easy to prove,but not all wave functions are monotonic.
Fuck Blimblestock - Sun, 06 Jul 2014 22:58:39 EST ID:p8Vzq3fC No.14177 Ignore Report Quick Reply
Also, for the monotonic proof it's very easy. By definition for a monotonic function that also approaches 0 as gets larger/smaller, lim x->infinity f(x)-f(x+dx) = 0. Therefor, f'(x) approaches 0 as x increases.

Shit, wait. That doesn't necessarily mean the integral from -infinity to infinity is finite, does it? Fuck man. I literally just picked up my old analysis textbook to get this shit sorted.
Martin Poffinghall - Sun, 06 Jul 2014 23:18:05 EST ID:yGgK6aCs No.14179 Ignore Report Quick Reply
Well I don't really care what the integral evaluates to, as long as all higher derivatives approach zero on both sides. I'm so n00b that I haven't even done analysis and I'm tinkering with these complex functions. Touch and go, my nigga.
Martin Haddleberk - Fri, 11 Jul 2014 20:09:05 EST ID:Gw2IN3ba No.14207 Ignore Report Quick Reply
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The wave functions in QM are what are known as square-integrable functions. These are functions that satisfy the condition that the function multiplied by its complex conjugate integrated from - infinity to + infinity must yield a finite value. But Griffiths mentions on page 14 (Second Edition) that in addition to (not as a consequence of) this requirement, the wave function must also go to zero at + or - infinity. So the higher derivatives of wave functions must go to zero at + or - infinity from this second requirement and the simple fact that the derivative of a constant (in this case zero) is zero.

Learn math from the very beginning by Cornelius Bappernick - Fri, 20 Jun 2014 20:32:26 EST ID:arK+ls13 No.14106 Ignore Report Reply Quick Reply
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How can I learn math from the bottom up? I want to start at the beginning, understand all the concepts, and really have an education in math. Basically I want to start over.

I know how to add, subtract, multiply, divide, and I know a little about real numbers and whole numbers, imaginary numbers, all that stuff. I'm really good at basic algebra, but I don't really "understand" it, nor can I name everything about it. I know nothing about calculus or geometry, or trigonometry.

I heard that math is the "Language of the Universe" so I want to learn it so I can understand science well. Thanks
3 posts omitted. Click Reply to view.
Polly Honeylock - Fri, 27 Jun 2014 15:31:53 EST ID:MXyuPRIu No.14137 Ignore Report Quick Reply
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If you can do all the exercise on the first chapter, you've got a pretty good idea of what math is
Shit Nocklestirk - Mon, 30 Jun 2014 03:28:52 EST ID:e1p9nP+4 No.14145 Ignore Report Quick Reply
If you are comfortable enough with your algebra, I would suggest that you read and work through (aka do every fucking exercise) in Spivak's Caluclus or Apostol's Calculus. I never used Apostol, some people swear by it. Spivak has the advantage that he starts from the very beginning and discusses number systems and the usual axioms and that will help orient your thinking in the right directions.

Don't waste time on Euclidean geometry (I study algebraic geometry and I don't know shit about that subject), and certainly don't try jumping directly into topology as is suggested above.
James Goshhall - Fri, 04 Jul 2014 19:23:28 EST ID:8Js26kRu No.14167 Ignore Report Quick Reply
What I would recommend to you is trying to push along further in your math and pay careful attention to how you are learning. Then I would go back to earlier subjects and review through the material so you can see what you missed and why you didn't understand that in the first place. This will help you strategically in more complicated mathematics. You may actually be able to pick up some new information from just studied subjects by going over it again with a better foundation and be more capable of abstract thought instead of just plugging in calculations.
Matilda Wankinnure - Sat, 05 Jul 2014 22:06:32 EST ID:kFCSHfPa No.14173 Ignore Report Quick Reply
Holy shit, I was just working on the first chapter of that exact book. Spooky.
Clara Weckleman - Fri, 11 Jul 2014 00:13:27 EST ID:hd9LVxdX No.14201 Ignore Report Quick Reply
I actually did start over too.

https://www.khanacademy.org/ you can learn from the ground up. Sheldon Axler's books are also the best out there, because they assume you have little knowledge and are self contained. For example his Trigonometry stuff in his book 'Precalculus' assumes you don't remember any Trig. Google his name and buy/pirate his books.

http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/ Is a good book as it gives a broad overview of all math without having to do rigorous proofs.

All the math you missed for graduate school is higher level but one of the best books out there.

If you want the ultimate understanding in Math, basically as good as you can get without starting to specialize since it's impossible to know everything, and you already have some undergraduate self studying done (ie: you know calculus, you know discrete math already, you know probability)

  1. Principles of Mathematical Analysis by Rudin
  2. Algebra by Artin (and Sheldon Axler's Linear Algebra done right)
  3. Topology by Munkres
  4. Princeton's Companion to Mathematics http://press.princeton.edu/titles/8350.html
Comment too long. Click here to view the full text.

Need help getting back into math. by Edward Druggledock - Mon, 07 Jul 2014 22:21:07 EST ID:kQQi+WA1 No.14182 Ignore Report Reply Quick Reply
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I made it through Calculus when I was in highschool. But it's been 6 years and I just started at a community college. I just need help getting started again. They put me in college algebra or MTH 111. And I'm looking at my first homework assignment. It's supposed to be review but I'm having a little trouble.
(5/2)x + (1/4)x = (7/4)x
Fractions are confusing me. I just put the x with the numerator since x = (x/1) and simplified it to 11x/4 = 7x/4.
Is that right? Not even sure what to do next, hopin you guys can help or point me to a web site that can.
Also, I forgot how much school sucks. I think math will be cool though once I really get back into it. Thanks guys!
5 posts omitted. Click Reply to view.
Edward Druggledock - Mon, 07 Jul 2014 23:30:07 EST ID:kQQi+WA1 No.14188 Ignore Report Quick Reply
Ok, sorry everybody for doing my homework here. I found a site called purplemath.com that's pretty helpful. If you know of any other websites that are helpful let me know though. Thanks!
Edward Druggledock - Tue, 08 Jul 2014 00:18:50 EST ID:kQQi+WA1 No.14189 Ignore Report Quick Reply
I do need help remembering how to factor actually. I understand how to find a common factor in some equations but I need to someone to show me how they go about factoring something like this:
x^2 + 15x + 56
I know the answer is (x+8) (x+7)
I just don't know how to get there. I mean sort of but not really. I'm about to go to work so if someone can show me their work on how to get that answer in the next couple hours I would really appreciate it!
Edward Druggledock - Tue, 08 Jul 2014 02:29:11 EST ID:kQQi+WA1 No.14190 Ignore Report Quick Reply
shit nevermind this whole thread, I am struggling so hard, but it's slowly coming back.
Jack Bagglebut - Tue, 08 Jul 2014 19:59:35 EST ID:Dn4zhXKX No.14191 Ignore Report Quick Reply
With these simple factorization problems, where the answer looks like (x+a)(x+b) and you have to figure out a and b,
think of how (x+a)(x+b) multiplies out

x^2+ax+bx+ab = x^2+(a+b)x+ab

In this case, we have x^2+15x+56
So you have to find two numbers that simultaneously multiply to 56, AND add to 15.
Start with ab=56
In the whole numbers, there are a few different pairs that multiply to 56: (1,56),(2,28),(4,14),(7,8)
But only one of these pairs adds up to 15.
Clara Weckleman - Thu, 10 Jul 2014 23:51:01 EST ID:hd9LVxdX No.14200 Ignore Report Quick Reply
https://www.khanacademy.org/ has everything from kindergarten to college math in short video presentations. Look up fractions, radicals whatever you need.

Also go buy Sheldon Axler's "Precalculus' Version 2. Either used or pirate it.
Math will actually make sense if you read it. It assumes you have zero highschool knowledge and is self contained.

Measuring how evenly spread out numbers are by Frederick Punderstet - Thu, 26 Jun 2014 18:46:12 EST ID:lH5+Lnwt No.14126 Ignore Report Reply Quick Reply
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Is there a decent formula for measuring how "diverse" a set of values are?
For instance if I have 5 values between 0 and 1...
0, 0.25, 0.5, 0.75, 1 = maximum diversity
0, 0, 0, 0, 0, = minimum diversity
1, 1, 1, 1, 1, = minimum diversity also

So I want to measure how close the differences between the values are to 0.25, ideally in a way that will return 1 in the best case and 0 in the worst case.

Any ideas? Thanks
3 posts omitted. Click Reply to view.
Walter Binnerchodge - Thu, 26 Jun 2014 23:11:10 EST ID:HbNSsmiC No.14130 Ignore Report Quick Reply
Just at first glance it would appear that this may be workable for finite sets.

Given a metric space (A, d) then we can define a diversity function

dv (AxA) = sum from j=1 to |AxA| d ((x, y)) j / |AxA|

Or the sum of all distance for all cartesian pairs divided by the set size of the cartesian product.
Walter Binnerchodge - Thu, 26 Jun 2014 23:46:48 EST ID:HbNSsmiC No.14132 Ignore Report Quick Reply
I didn't read the post after about being normalized but I think if you choose all cartesian pairs that dont have a distance of zero and divide by that set size and the size of the max distance on the interval.
Phineas Clondlefield - Mon, 30 Jun 2014 14:57:15 EST ID:d64DnQ1v No.14150 Ignore Report Quick Reply
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In an ideally diverse set the distance between consecutive elements would be (max - min)/num_elements

Couldn't you just take the average of the distance between every consecutive element and then see how much this average deviates from the ideal distance?
Reuben Pisslefoot - Mon, 30 Jun 2014 19:15:37 EST ID:jkYtMoE5 No.14153 Ignore Report Quick Reply
Standard deviation seems like it could be used here.
But putting the answers on a 0-1 scale of minimum to maximum diversity is the hard part
Rebecca Cessleford - Thu, 10 Jul 2014 16:56:48 EST ID:Vnayk5eu No.14198 Ignore Report Quick Reply

This guys correct. Given a partially ordered set A and a diversity mapping dvr: A -> [0,1] then for max diversity we should have it such that each consecutive pair should have a distance of (max(A)-min(A))/|A|.

dvr(A) = ((sum(i = 0 to |A|-1) (a_i-a_i+1))/|A|)/((max(A)-min(A))/|A|)

have I discovered this? by Isabella Surrylodge - Fri, 27 Jun 2014 02:59:35 EST ID:ySRm4RKM No.14133 Ignore Report Reply Quick Reply
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David Sibbledure - Fri, 27 Jun 2014 13:18:40 EST ID:p8Vzq3fC No.14136 Ignore Report Quick Reply
Discovered what?
Nigger Winkinpat - Sat, 05 Jul 2014 17:44:54 EST ID:Dn4zhXKX No.14171 Ignore Report Quick Reply
Probably. You can call it Surrylodge's Lemma. Although if your proof is computer assisted, it might be controversial.

OK math lets count by Beatrice Trotwater - Sat, 24 May 2014 17:18:16 EST ID:Le9Cy2Bo No.14031 Ignore Report Reply Quick Reply
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11 posts and 3 images omitted. Click Reply to view.
Nicholas Bablinglock - Sun, 29 Jun 2014 10:57:19 EST ID:KRSGkVa1 No.14140 Ignore Report Quick Reply
Reuben Pisslefoot - Mon, 30 Jun 2014 19:14:03 EST ID:jkYtMoE5 No.14152 Ignore Report Quick Reply
Nigger Smallford - Tue, 01 Jul 2014 19:51:57 EST ID:MTIV7/tU No.14156 Ignore Report Quick Reply
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My nigga.

This picture is called fuck numbers.
Betsy Cruzzlelat - Fri, 04 Jul 2014 13:27:06 EST ID:p8Vzq3fC No.14166 Ignore Report Quick Reply
for those that don't know https://www.youtube.com/watch?v=w-I6XTVZXww
It's a pretty fantastic video, especially if you watch the one about 1/2-1/2+1/2-1/2...
Phoebe Crarrynat - Fri, 04 Jul 2014 23:27:31 EST ID:yHx/72Ow No.14168 Ignore Report Quick Reply

not this again...

The sum of the natural numbers is NOT -1/12, this is part of something called Ramanujan summation where you *ASSIGN* values to divergent series so that you can deal with them concretely. It does not mean that if you added all the natural numbers you would get -1/12, that is troll science and the video is completely and totally misleading.

1+2+3+4+... is a divergent series and you cannot add it up to get a negative number, or any number at all for that number. 1-1+1-1+... is not 1/2. Ramanujan is used in the specialized study of infinite series and it is FALSE to say that these things really add up to what is claimed in the video. It really sickens me the way these "educated" people dumb down extremely specialized things to produce something that is completely false in the end. Ugh.

Die math die! by Cyril Bardville - Tue, 01 Jul 2014 20:39:22 EST ID:dZa7zeXl No.14157 Ignore Report Reply Quick Reply
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Math sucks and this board should die
CrazyFolksTribe !loJSOMZg0g - Wed, 02 Jul 2014 00:26:26 EST ID:8i+nkfnL No.14160 Ignore Report Quick Reply

I\neq 1 by Esther Suvingmuck - Sun, 29 Jun 2014 22:33:39 EST ID:3EegWVCd No.14143 Ignore Report Reply Quick Reply
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On page 39 of Emil Artin's Galois Theory, should the equation


instead read

(x^2-x+1)^3-I*x^2(x-1)^2=0 ?

That confused me a good bit. I just want to be sure I reached the correct conclusion. You can find the book here:
Shit Nocklestirk - Mon, 30 Jun 2014 05:13:11 EST ID:e1p9nP+4 No.14147 Ignore Report Quick Reply

Yeah, you're correct. He is showing that that the element x is algebraic over the field k(I) by writing down a specific polynomial that it satisfies. Since the polynomial has degree 6, he obtains the desired bound on the degree of the extension as well.
James Hippersore - Mon, 30 Jun 2014 13:39:41 EST ID:k3j5GQQF No.14148 Ignore Report Quick Reply
thanks bro

Math training by James Cubberson - Mon, 16 Jun 2014 18:14:57 EST ID:LFUhSvVn No.14089 Ignore Report Reply Quick Reply
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I want to be able to solve the problems presented here and similar by the end of the summer, I'm currently at about calculus 2 level engineering math.

How much more do I need to study and what exactly is it that I need to study in order to be able to solve all the problems presented here, I have a lot of time on my hands so I hope my brain is up for it.
Angus Broddleshit - Tue, 17 Jun 2014 21:06:14 EST ID:Dk8yywxc No.14093 Ignore Report Quick Reply
Linear Algebra and Differential Equations, in terms of United States college semesters, normally you would take calculus 3 and then linear algebra and differential equations, so you are two semesters away.

If you go looking around on Amazon or something like that, you should be able to find good textbooks that are readable for independent study for an edge when you take these classes. Personally, I would look for proof based treatments of these subjects to get the most out of it but as an engineering student you may not be required to do much of that. However, if you get a good introductory level linear algebra text for example it should ease you into the proofs and it will help with all your other math classes.
Fanny Podgesick - Wed, 18 Jun 2014 07:07:44 EST ID:LFUhSvVn No.14097 Ignore Report Quick Reply
Is #2 a basic linear algebra problem? Or does it already border on functional analysis?
Wesley Supperspear - Sun, 22 Jun 2014 10:28:28 EST ID:8NZnQ0yA No.14112 Ignore Report Quick Reply
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The second problem should be provable in a basic linear algebra context since the algebraic structure is just a finite dimensional real vector space without the additional structure that usually allows for functional analysis type study.
Walter Binnerchodge - Thu, 26 Jun 2014 23:26:11 EST ID:HbNSsmiC No.14131 Ignore Report Quick Reply
#3 is an application of mean value and intermediate value theorem from calculus
Shit Nocklestirk - Mon, 30 Jun 2014 03:18:39 EST ID:e1p9nP+4 No.14144 Ignore Report Quick Reply
(1) is single variable calculus.

hint: for the "only if" . assume that both u_n are convergent and the sum is infinite and obtain a contradiction nearly immediately.

the "if" follows from the monotone convergence theorem and the sequence comparison test

(2) is standard linear algebra
hint: diagonalize!!!!!!! eigenvectors are your friend.

(3) is single variable calculus and very simple

hint: see the comment of the person above

(4) is interesting, but doesn't entail and ODE tools or anything
hint: look at Taylor series solutions to the equation to get form a conjecture for the shape of the solutions, then prove conjecture using standard integration techniques. this will be easy for (a) and tricky for (b).

Vector Calc by Rebecca Clobberforth - Sun, 29 Jun 2014 20:48:28 EST ID:wer7kd6a No.14142 Ignore Report Reply Quick Reply
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round 3 of trying to type this on a damn forum

Suppose f is any function with continuous second-order partial derivatives such that f(0,0)=0 and (,0) is a critical point of f. Write an expression for the second-degree Taylor polynomial, Q, of f at (0,0)

multiply 0 by Charles Pickman - Sat, 28 Jun 2014 18:22:13 EST ID:tsVlvxIF No.14138 Ignore Report Reply Quick Reply
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how is it that when you multiply something by 0 the answer is 0? say i have 3 carrots and i multiply the carrots 0 times, would i still have 3 carrots?
Samuel Bluttingham - Sat, 28 Jun 2014 20:05:05 EST ID:8PJ0nVdr No.14139 Ignore Report Quick Reply
Bob Bob - Sun, 29 Jun 2014 20:33:18 EST ID:Dk8yywxc No.14141 Ignore Report Quick Reply

1*3 = 3 right?

0*3 = (1-1)*3 = 3 - 3 = 0

So you would have 0 carrots.

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