Page **37** of **44**

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 4:32 pm**

by **Cuchulainn**

I just rebooted my machine to windows 7. I am getting the same issue with PowerPoint with the formatting. The same as I posted for LibreOffice.

I am able to export to pdf through File -> Save As -> Select PDF -> Save

Back to Linux.

OK. We are making the word file now and exporting to pdf.

Un moment svp.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 4:40 pm**

by **ppauper**

How do you know you are talking to an engineer? they call [$]\mathbb{\nabla}[$] "nabla"

I used to know engineering students who called it "triangle"

The only person I've ever known to call it "nabla" out loud was a visiting professor from Israel (I think he was on sabbatical) from whom I took a course in grad school.

I was brought up to put 1 line under a vector and 2 lines under a matrix, but it seems these days, people either put them both in bold (so you can't tell the difference between a vector and a matrix) or sometimes not even that

wiki: curl
The alternative terminology rotor, rotation or rotational and alternative notations **rot F** and ∇ × **F** are often used (the former especially in many European countries, the latter, using the del (or nabla) operator and the cross product, is more used in other countries) for **curl F**. In a context where the cross product is denoted with the wedge symbol, ∇ ∧ **F** would be used.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 5:07 pm**

by **Cuchulainn**

Workaround: here is readable Word style.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 5:26 pm**

by **Cuchulainn**

History of nabla. Seems it was invented by William Rowan Hamilton but it had no name.

https://en.wikipedia.org/wiki/Nabla_symbol
I used to do APL and it also had a nabla.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 5:36 pm**

by **katastrofa**

How do you know you are talking to an engineer? they call [$]\mathbb{\nabla}[$] "nabla"

I think the French call Curl "rot"?? The Germans certainly do.

More correct is to say in french (not the French), the Curl is "rot" for "rotationnel". The rotational is also noted as [$] \mathbb{\nabla} \wedge V[$], [$] \mathbb{\nabla} \times V [$], [$] \vec{\mathbb{\nabla}} \wedge \vec{V}[$] or [$] \vec{\mathbb{\nabla}} \times \vec{V}[$]. They are all correct.

While the notation for vectors is arbitrary, it's not correct to say that curl/rotation and exterior derivative are the same. Rotation is a 3D case of exterior derivative.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 6:40 pm**

by **FaridMoussaoui**

Rotational (Curl, rot in french) can be defined in any dimension by using n-forms. The rotational is not a vector but a bi-vector (a tensor). In 3D, there is a bijection between bi-vectors and vectors.

In a space with n dimensions, the dimension of the space of bi-vectors is [$]\binom{n}{2}[$]. A fortunate coincidance is for n = 3, [$]\binom{3}{2}[$] = 3.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 7:11 pm**

by **Cuchulainn**

*I was brought up to put 1 line under a vector and 2 lines under a matrix, but it seems these days, people either put them both in bold (so you can't tell the difference between a vector and a matrix) or sometimes not even that.*

In Schaum Vector analysis they use bold upper case Romans for vector field and unbold lower-case Greeks for scalar fields.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 7:26 pm**

by **Cuchulainn**

How do you know you are talking to an engineer? they call [$]\mathbb{\nabla}[$] "nabla"

I think the French call Curl "rot"?? The Germans certainly do.

More correct is to say in french (not the French), the Curl is "rot" for "rotationnel". The rotational is also noted as [$] \mathbb{\nabla} \wedge V[$], [$] \mathbb{\nabla} \times V [$], [$] \vec{\mathbb{\nabla}} \wedge \vec{V}[$] or [$] \vec{\mathbb{\nabla}} \times \vec{V}[$]. They are all correct.

While the notation for vectors is arbitrary, it's not correct to say that curl/rotation and exterior derivative are the same. Rotation is a 3D case of exterior derivative.

Exact!. The wedge product [$]\wedge[$] is used in context of general n-dimensional vector space and multilinear algebra but with 3d PDEs in electromagnetics and MHD [$]\times[$] is standard.

Its use does not add any extra value; in fact is non-standard and confusing. It's almost pure maths notation. I'm with Maxwell and Hamilton on this one.

https://en.wikipedia.org/wiki/Magnetohydrodynamics
It's a bit like saying that [$]5\times2[$] is the dot product of two instances of a vectorSpace<int> of size 1.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 10th, 2019, 11:46 pm**

by **katastrofa**

Rotational (Curl, rot in french) can be defined in any dimension by using n-forms. The rotational is not a vector but a bi-vector (a tensor). In 3D, there is a bijection between bi-vectors and vectors.

In a space with n dimensions, the dimension of the space of bi-vectors is [$]\binom{n}{2}[$]. A fortunate coincidance is for n = 3, [$]\binom{3}{2}[$] = 3.

Following Cuchulainn's remarks, rotation - also denoted as curl(V) or rot(V) - is the nomenclature of vector calculus (in R3 Euclidean space). You used the notation for a cross product (R3) and exterior derivative. Of course one can generalise it to higher dimensions, but then it's not called a rotation (because it's getting a bit more complicated). I just think it's good to stick to the general rules, when you teach someone maths...

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 11th, 2019, 12:10 am**

by **Collector**

"I just think it's good to stick to the general rules" so biceps curl only?

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 11th, 2019, 12:14 am**

by **katastrofa**

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 11th, 2019, 10:54 am**

by **Cuchulainn**

Rotational (Curl, rot in french) can be defined in any dimension by using n-forms. The rotational is not a vector but a bi-vector (a tensor). In 3D, there is a bijection between bi-vectors and vectors.

In a space with n dimensions, the dimension of the space of bi-vectors is [$]\binom{n}{2}[$]. A fortunate coincidance is for n = 3, [$]\binom{3}{2}[$] = 3.

Can we extend the equations from 3 to n dimensions? Or results in n dimensions that are readily specialised to 3 dimensions? (Deduction versus induction).

To be honest, using wedge notation in applications where curl and X is standard will confuse a lot of people. Is is the Bourbaki influence?

// The book by Rietoord uses 'Rot'.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 11th, 2019, 12:06 pm**

by **FaridMoussaoui**

May be Poincaré & Cartan. I have to find out my "differential geometry" course but any idea where there are now. I learnt mathematics in french, so it was somehow influencial.

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 11th, 2019, 12:12 pm**

by **katastrofa**

I thought that "rotation" in French was "croissant".

### Re: "Unified Revolution" new book by Espen Haug

Posted: **January 11th, 2019, 1:20 pm**

by **Cuchulainn**

Last week someone showed me some lecture notes for FDM; the indexes used were m and n and by this you conclude it was written by a British mathematician. Americans use n,i and j while Russians use n,j and k.

m and n are too close together for comfort.