/sci/ - Science & Math » Thread #12824232

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Anonymous Fri 12 Mar 20:39:31 2021 No.12824232 View Reply Original Report

Quoted By: >>12824340 >>12824427 >>12825677

Is vector calculus only used for electromagnetism? I'm talking about integration and it's theorems, I know the differential part of the course is used in mechanics, thermodynamics, economics and what not.

Anonymous

Anonymous Fri 12 Mar 2021 20:49:47 No.12824262 Report

Quoted By: >>12824478

realistically anywhere where there are vectors it could have meaning.

Anonymous

Anonymous Fri 12 Mar 2021 21:13:42 No.12824340 Report

Quoted By: >>12824478

>>12824232
It's used everywhere where there is calculus and linear algebra.

Anonymous

Anonymous Fri 12 Mar 2021 21:19:22 No.12824349 Report

Quoted By: >>12824478

Lol. It's easier to ask where vector calculus isn't used, pseud.

Anonymous

Anonymous Fri 12 Mar 2021 21:46:55 No.12824427 Report

Quoted By: >>12824478

>>12824232
>Is vector calculus only used for electromagnetism? I'm talking about integration and it's theorems,
Pretty much just for physics, yes.

Anonymous

Anonymous Fri 12 Mar 2021 22:00:02 No.12824478 Report

Quoted By: >>12824624 >>12825567

>>12824262
Ah, so it should also be useful in fluid mechanics. I thought that was mostly PDE and complex variable, but then again I've never studied fluid mechanics.
>>12824340
Sorry, I meant applications of vector calculus, I'm sure it's used in math like differential geometry and such, but do you know of any area where Stokes' theorem has an application other than electromagnetism (and maybe fluid mechanics)?
>>12824349
>I'm talking about integration and it's theorems
>>12824427
I really think that's the only time integral theorems have been useful. Maybe I just haven't studied enough physics.

Anonymous

Anonymous Fri 12 Mar 2021 22:37:48 No.12824624 Report

Quoted By:

>>12824478
General relativity is based on differential geometry

Anonymous

Anonymous Fri 12 Mar 2021 22:50:45 No.12824665 Report

Quoted By:

It is also used from some specific implementations in games. Some procedural surfaces are generated based on vector calculus. Not many game developers understand vector calculus so most of the time they just fuck around and use commonsense and normal linear algebra a calculus to do things.

Anonymous

Anonymous Sat 13 Mar 2021 03:38:07 No.12825567 Report

Quoted By:

>>12824478
>any area where Stokes' theorem has an application
literally any time you want to find a relation between flux and circulation. this is often in fluid mechanics and aerodynamics.

Anonymous

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Anonymous Sat 13 Mar 2021 04:26:26 No.12825677 Report

Quoted By:

>>12824232
In (Civil/Mechanical/Aerospace) Structural Engineering it's used to calculate stresses and deformations caused by loads in Surfaces such as:
Concrete Slabs, Domes, Shells, Walls, Ship Hulls, Aircraft Airframes, Tents, Decks, etc

Using the equations of Plate theory:
> https://en.wikipedia.org/wiki/Plate_theory
that doesn't involve just Vector Calculus but also Differential Geometry (Tensor Calculus).

Here some example of such Equations:

stress-strain relations for Isotropic quasistatic Kirchhoff-Love plates

$ \begin{bmatrix}\sigma_{11} \\ \sigma_{22} \\ \sigma_{12} \end{bmatrix} = \cfrac{E}{1-\nu^2} \begin{bmatrix} 1 & \nu & 0 \\ \nu & 1 & 0 \\ 0 & 0 & 1-\nu \end{bmatrix} \begin{bmatrix}\varepsilon_{11} \\ \varepsilon_{22} \\ \varepsilon_{12} \end{bmatrix} \,.$

Torque (Moments) of Isotropic quasistatic Kirchhoff-Love plates

$ \begin{bmatrix}M_{11} \\ M_{22} \\ M_{12} \end{bmatrix} = -\cfrac{2h^3E}{3(1-\nu^2)}~\begin{bmatrix} 1 & \nu & 0 \\ \nu & 1 & 0 \\ 0 & 0 & {1-\nu} \end{bmatrix} \begin{bmatrix} w^0_{,11} \\ w^0_{,22} \\ w^0_{,12} \end{bmatrix}$

Reissner–Stein static theory for isotropic cantilever plates

$ \begin{align} & bD \frac{\mathrm{d}^4w_x}{\mathrm{d}x^4} = q_1(x) - n_1(x)\cfrac{d^2 w_x}{d x^2} - \cfrac{d n_1}{d x}\,\cfrac{d w_x}{d x} - \frac{1}{2}\cfrac{d n_2}{d x}\,\cfrac{d \theta_x}{d x} - \frac{n_2(x)}{2}\cfrac{d^2 \theta_x}{d x^2} \\ &\frac{b^3D}{12}\,\frac{\mathrm{d}^4\theta_x}{\mathrm{d}x^4} - 2bD(1-\nu)\cfrac{d^2 \theta_x}{d x^2} = q_2(x) - n_3(x)\cfrac{d^2 \theta_x}{d x^2} - \cfrac{d n_3}{d x}\,\cfrac{d \theta_x}{d x} - \frac{n_2(x)}{2}\,\cfrac{d^2 w_x}{d x^2} - \frac{1}{2}\cfrac{d n_2}{d x}\,\cfrac{d w_x}{d x} \end{align}$

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