Math and science

[Oversleep]

19 minutes ago, Silverblade5 said:

Has anyone here ever tried creating a function that took the number of rectangles in a Riemann integral as an input and the resulting area as an output? Is there a name for this?

I believe Riemann integral is the limit of such funtion. With number of rectangles reaching infinity.

[Oversleep]

Programmers (and maybe not only them!) will laugh.

(It's pretty old, but... gold.) https://www.destroyallsoftware.com/talks/wat

[Silverblade5 he/him]

5 hours ago, Oversleep said:

Programmers (and maybe not only them!) will laugh.

(It's pretty old, but... gold.) https://www.destroyallsoftware.com/talks/wat

I love it.  

{}+{}=NaN

JAHAHAHAHAHAHA

[Silverblade5 he/him]

How would I solve S [cos(3x^2)]dx ?

S [4^x]dx ?

S [x^x]dx ?

S [1/(3-x^3)^.5]dx ?

[Oversleep]

I just realized I don't remember anything from my mathematical analysis courses.

That's bad.

@Silverblade5, have you tried Wolphram?

[Silverblade5 he/him]

2 minutes ago, Oversleep said:

I just realized I don't remember anything from my mathematical analysis courses.

That's bad.

@Silverblade5, have you tried Wolphram?

Yes. That generally only gives results. I want the process.

[AliasSheep]

3 minutes ago, Oversleep said:

I just realized I don't remember anything from my mathematical analysis courses.

That's bad.

@Silverblade5, have you tried Wolphram?

Wolfram is a lifesaver

[Chaos he/him]

6 hours ago, Silverblade5 said:

How would I solve S [cos(3x^2)]dx ?

S [4^x]dx ?

S [x^x]dx ?

S [1/(3-x^3)^.5]dx ?

The first and third integrals don't have closed form anti derivatives and you'd need to use infinite series. That might not work great on the third one though, but works easily on the first.

The second integral is easy. Rewrite it to e^((ln4)x) and use a u sub.

The final integral is also very difficult. It may also not have a closed form antiderivative. But I am looking at these literally as I'm heading to bed.

Long story short, as someone who has taught Calc 2 for many semesters, three of those integrals would be things I'd never ask. (Well, I could ask the first in the context of Taylor series.) So don't worry about it. There might be some crazy integration table thing for 2 and 4, but no one remembers that stuff nor is it important to derive the very hard integration table formulas. If it isn't taught in Calc 2 it is unlikely to be an easy thing.

Edited August 24, 2016 by Chaos

[Silverblade5 he/him]

If I had an infinite series and I knew it was a Taylor Series, how could I find the function it's approximating?

ex: E(n=0,infinite)e*2^n*(x-1)^n/n!

Edited August 27, 2016 by Silverblade5

[Silverblade5 he/him]

I recently encountered a circuit where the resistors are in a triangular mesh that's neither in series nor in parallel. I can't figure out how to network it. Anyone that can help?

[PantsForSquares he/him]

You're going to have to use Kirchoff's Laws. If you have a diagram, I can help with that.

Kirchoff's Laws come in two rules, which help you set up a system of equations to solve for them. They are as follows:

• Junction Rule: If a current splits into two paths, the algebraic sum of the two currents is equal to the current just prior to the split.
• Loop Rule: In a closed loop, the sum of all voltage differences is equal to 0.

Basically, you can use the Junction Rule to name currents in terms of other currents (ie, if one current is I_1, and it branches into two currents, you can write the first as I_2 and the second branch as I_1-I_2), and the Loop Rule allows you to put everything into a system of two/three equations that's fairly straightforward.

Edited September 26, 2016 by PantsForSquares

[Silverblade5 he/him]

8 minutes ago, PantsForSquares said:

You're going to have to use Kirchoff's Laws. If you have a diagram, I can help with that.

I know how to do it with Kirchoff's Laws. However, my teacher told me that while it might be very hard, it's still possible to do it with networking. That's what I want to figure out.

[PantsForSquares he/him]

If it's not explicitly in a series/parallel configuration, then you're going to need Kirchoff's Laws. The sole reason the laws are used is because you can have combinations that aren't possible to solve with just straight series/parallel configuration rules. I'm not an electrical engineer/physicist, so I'm not sure if there are any other methods, but my physics professor made it pretty clear that Kirchoff's Laws are the only reliable way to solve for non-parallel/circuit configurations.

[JUQ he/him]

On 9/26/2016 at 6:18 PM, PantsForSquares said:

If it's not explicitly in a series/parallel configuration, then you're going to need Kirchoff's Laws. The sole reason the laws are used is because you can have combinations that aren't possible to solve with just straight series/parallel configuration rules. I'm not an electrical engineer/physicist, so I'm not sure if there are any other methods, but my physics professor made it pretty clear that Kirchoff's Laws are the only reliable way to solve for non-parallel/circuit configurations.

Maybe ze is meant to derive Kirchoff's laws?

On 7/2/2016 at 11:45 AM, Silverblade5 said:

Has anyone here ever tried creating a function that took the number of rectangles in a Riemann integral as an input and the resulting area as an output? Is there a name for this?

I haven't, but it seems possible, if pointless. I did once re-arrange the exponential interest formula so that one could determine the approximation of e required to get the desired increments (days, months, or years), which is a sort of similar thing.

[Silverblade5 he/him]

Thank you math teacher for updating my database of nerd swears! A motherfunction shift indeed! 

[Orlion Blight he/him]

Ha! That's pretty clever!

[Silverblade5 he/him]

I've got a question on L'hopitile's rule.

If we were to take the limit of tan(x) as x approaches pi/2, we'd say it doesn't exist, because it's a vertical asymptote and it doesn't approach the same infinity from both sides. However, if we express it as sin(x)/cos(x) and apply L'hopitile's rule, we get lim x>pi/2 -cos(x)/sin(x). Evaluating at pi/2, we get 0/1, which is 0. These are two very different answers. What's going on here?

[Oversleep]

@Silverblade5 it's because you can't apply de l'Hospital here. What is the limit of sin(x) as x approaches pi/2? What is the limit of cos(x) as x approaches pi/2?

When can de l'Hospital rule be applied?

Edited October 16, 2016 by Oversleep

[Silverblade5 he/him]

Just now, Oversleep said:

@Silverblade5 it's because you can't apply de l'Hospital here. What is the limit of sin(x) as x approaches pi/2? What is the limit of cos(x) as x approaches pi/2?

Using direct substitution, the limit of sin would be 1. The limit of cos would be 0.

[Eki]

1 minute ago, Silverblade5 said:

Using direct substitution, the limit of sin would be 1. The limit of cos would be 0.

Like Oversleep says, that means the rule can't be used. It's only for when both limits are 0 (or +- infinity, but that's less useful).

https://en.wikipedia.org/wiki/L'Hôpital's_rule

[Silverblade5 he/him]

Just now, Eki said:

Like Oversleep says, that means the rule can't be used. It's only for when both limits are 0 (or +- infinity, but that's less useful).

https://en.wikipedia.org/wiki/L'Hôpital's_rule

Oh, ok. Thanks.

[Chaos he/him]

Another subtle thing with L'Hopital's rule is that if you have a 0/0 (or infinity/infinity form) and you differentiate the top and bottom, and you find that the limit does not exist, that doesn't mean the original limit does not exist. 

[Darkness Ascendant he/him]

I just realised I accidently stumbled here.

Bye.

[Mestiv he/him]

I had no idea science has gone so far already:

 

[Spoolofwhool]

The Schwarzschild radius is pretty interesting, and that of an average human is about 1.20 femtoangstrom, assuming my math is right.