/sci/ - Science & Math

How do we take the derivative of a tensor with respect to another tensor?

when would hyperbolic trig functions be used in engineering? why?

>>6039992
wow you might actually be serious

>>6040001
I'm trying to keep calm because of how smart you are, but would you please provide me with an answer?

>>6040011

I would quite like you to answer the question to OP.

>>6040011
I'm not OP but here's a link I found from Google:
http://cosmoquest.org/forum/showthread.php?109266-What-is-the-point-of-hyperbolic-trig-functions
Aside from that I seem to recall hyperbolic functions showing up as solutions of a heat or wave equation. Then again, just about every possible function does...

>>6040024
ah, thank you. I'm curious as to why we have to cover an entire unit over it in my Calc 2 class. Everybody I ask never seems to know an obvious application that uses it daily. I guess being introduced to it and knowing what it is can be important. Having said that, my adv. algebra class my freshman year in uni skipped conic sections because the professor didn't think it was practical. Same professor this year, and we're being drilled hyperbolic trig functions.

Where did the calculus expert go?

>>6039973
By defining a local connection on the tensor bundle.

>>6039992
Hyperbolic trig functions often arise in the theory of differential equations and integrals. They are of utmost importance in many approaches to the unsolved problem of triple integrals. HTF's allow mathematicians to dismiss the inconsistent notion of complex numbers by using split-complex numbers instead. <span class="math">e^{jx}=\cosh(x)+j\sinh(x)[/spoiler] is more powerful than Euler's identity and accounts better for the geometry of non-cubic spacetime.

>>6040051
I was busy solving a quadratic equation.

>>6040071
>PhD in calculus
>j^2 = -1

Story of my group labs.

>>6039970
how do you prove the fundamental theorems of calculus using Henstock–Kurzweil integral (not the Riemann classical one) ?

>>6040243
Use the same proof by virtue of the fact that it only involves the property <span class="math">\int_a^b = \int_a^c + \int_c^b[/spoiler] which holds true for HK integral as well as R integral.

>>6039970
what is the most effective means by which to develop greater mathematical maturity, problem solving ability and skill in proof writing.

>>6040071
nigga if I'm understanding you correctly, you got a PhD in Triple Integrals?

how do i compute the subdifferential of the frobenius norm on NxN matrices?

Have you evaluated a quadruple integral before?

What is tripple integral?

If you do an integral and then you differentiate it and then you integrate it again and differentiate it again and integrate it a third time, is that the same as doing a triple integral?

>>6041350
>/sci/

>>6040782
OK, so either you have a proof of these theorems I didn't heard of, either you don't understand what HK integration is.

How do I solve for x?

>>6039970

Hello!

What's your favorite theorem in calculus? :)

Best!

>>6041019

Hello!

Not OP. I don't know if I understand the question. I just looked up what a subdifferential is, and it looks like it's just a set of bounds on the possible values on the various limits of difference quotients. What would be the generalization to higher dimensions?

Also, for you, is the Frobenius norm just $tr(AA*)$?

Best!

>>6039970
Given a proper geometric cofiber of the integral sheaf calculus on a standard moduli space of bifunctorially normed topoi schemes, can one always use Euler's construction of the derived stack to compute a Serre basis, or is that approach limited to the case where the generic tensor magma is nilpotent?

>>6043696

Hello!

Did you use one of those online generators? :)

Best!

I am a CS grad and I am gonna study math this year. I can choose between following elective subjects:

Basics of EE for MechEng
Mechanics for Physics
Physics for EE
Quantum Theory I
Systems and Signals (basically LTI system theory)

What do I choose OP?

I want to discuss y=x^x and its limits as x approaches 0.

How use calculus for finding GLOBAL maxima/minima in nonlinear programs?

>>6043696
lol

>>6043719
I'm not a calculus expert in any sense, but calculus, being the study of local phenomena, can't make meaningful statements about the global phenomena of a function.
Unless you impose some sort of boundary condition and continuity condition in the interior of your domain, the maxima/minima could be anywhere and you won't be able to detect it using calculus methods.

>>6043709
anyone?

>>6039970
What is the limit of the volume of an (n - s) dimensional sphere of diameter s, where s -> 0, n -> infinity, and n & s are discrete and real?
What is the limit of the volume of an (n - s) dimensional sphere of diameter s, where s -> 1, n -> infinity, and n & s are discrete and real?

>>6043786
nailed it

How much is calculus used in digital image processing,and what are the things that are mostly used?

What's your point of view on non-standard analysis?

>>6039970
PhD in "calculus"??

Let me guess, are you an American? Calculus is something I use everyday, what specifically did you do your PhD in?

>>6043870
>Not understanding that it's a joke
>2012+1
ishygddt

>>6043893
autists are strong in /sci/ today

>>6043825
fourier analysis, so lots of integrals. you have to understand sinusoidals and how they can be represented in complex form. expect derivatives as well

>>6043703
Nah, just made it up on the spot. The online generators I know of sound too formulaic.

>>6043893
It could be legit in theory
http://www.damtp.cam.ac.uk/research/apde/

>>6043756
>study of local phenomena

Hey OP, why is calculus so useless?