
Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 09:25 AM
micromass

1 
30,178 
If the direction of the gradient of f in a point P is the direction of most/minor gradient, so a direction of the curl...

Apr1014 09:58 AM
chogg

1 
722 
I'm just learning this theory and the maths is really trivial but the theory is slightly confusing me.
I...

Apr914 08:08 PM
HallsofIvy

1 
668 
Hello,
I'm reading the book Geometrical methods of mathematial physics by Brian Schutz. In chapter 3, on Lie...

Apr914 10:55 AM
George Jones

7 
837 
Hi,
I would like to understand the leftinvariant vector field of the additive group of real number. The left...

Apr814 03:42 AM
AlbertEi

2 
659 
If the gradient of f is equal to differential of f wrt s: \vec{\nabla}f=\frac{df}{d\vec{s}} so, what is the curl of f...

Apr514 04:33 PM
Mark44

7 
825 
Every conservative vector field is irrotational? Every irrotational vector field is conservative?
Every solenoidal...

Apr414 01:55 PM
Matterwave

4 
731 
According to Isham (Differential Geometry for Physics) at page 115 he claims:
"If X is a complete vector field then...

Apr414 02:50 AM
center o bass

2 
666 
What do you think, might be generalized the helix in the manner that I propose in the attached material?

Apr314 03:45 AM
micromass

5 
674 
As I understand it, Felix Klein sought to classify geometries with respect to what groups G that respected the...

Mar3114 12:02 AM
homeomorphic

1 
766 
Let's say that ##\vec{f}## is an exact oneform, so we have that ##\vec{f}=\vec{\nabla}f##, and ##\vec{F}## is an...

Mar3014 10:41 AM
chogg

3 
744 
Vector, by definition, have 2 or 3 scalar components (generally), but the curl of a vector field f(x,y) in 2D have...

Mar2914 01:35 PM
chogg

5 
896 
I am reading up on principal bundles and currently I'm trying to get to grips with the definition of a connection on...

Mar2814 01:55 PM
homeomorphic

8 
963 
The ##\vec{\nabla} \cdot \vec{\nabla} = \nabla^2## so, ##\vec{\nabla} \times \vec{\nabla} = \vec{0}## ? I think that...

Mar2814 04:01 AM
arildno

6 
1,015 
A Lie Subgroup is defined as follows:
A Lie subgroup of a Lie group G is (i) an abstract subgroup H that is (ii) an...

Mar2714 05:17 AM
micromass

3 
744 
If given an oneform like: ##\omega = u dx + v dy##, dω is ##d\omega = \left ( \frac{\partial v}{\partial x} ...

Mar2414 04:09 PM
Ben Niehoff

1 
785 
I found what might be the worst written book on Lie Groups. Ever. Until I find one I like better, I'm going to see if...

Mar2314 11:17 AM
Mandelbroth

1 
787 
In some books, when discussing the relation between partial/directional derivatives and tangent vectors, one makes a...

Mar2214 02:25 PM
Mandelbroth

4 
894 
I've been trying to prove that the closed unit ball is a manifold with boudnary, using the stereographic projection...

Mar2214 12:25 PM
kostas230

2 
675 
Hello,
I am looking into finding geodesic distances for an ellipsoid. I will designate two points then find the...

Mar1614 01:00 PM
jsbxd9

0 
896 
Suppose we measure and plot the polarization of the Cosmic Background Radiation on a spherical plot. Could the data at...

Mar1414 08:53 PM
Spinnor

0 
688 
I have a curved surface which I know the (x,y and z) coordinates for 5 separate points on it and I was wondering how...

Mar1414 06:57 PM
Chestermiller

5 
826 
We call originary curve the curve for that at baseline the Frenet trihedron TNB coincides with the cartesian trihedron...

Mar1114 04:32 AM
micromass

5 
861 
There are two theorems from multivariable calculus that is very important for manifold theory.
The first is the...

Mar914 11:52 AM
micromass

1 
751 
Any Kähler form (?) can be written in local coordinates as \omega = \frac{i}{2} \sum h_{ij} dz^i \wedge d z^j with...

Mar814 08:19 AM
nonequilibrium

14 
846 
''..Cauchy stress tensor in every material point in the body satisfy the equilibrium equations.''
...

Mar714 01:51 PM
nejibanana

1 
658 
I don't know very much about differential geometry but from the things I know I think that the metric is somehow the...

Mar714 01:29 AM
maajdl

3 
619 
I am struggling to make sense out some things. Hopefully someone can help or at least offer some different point of...

Mar314 05:42 PM
Demon117

6 
1,071 
I'd like to understand why i cannot seem to be able to define unit polar basis vectors. Let me explain:
We have...

Mar314 09:44 AM
Chestermiller

1 
599 
Suppose that we have a Riemannian manifold (M,g) with a lower dimensional Riemannian submanifold (N,h) and a map F: M...

Mar314 04:17 AM
center o bass

0 
538 
In wolframpage there is follows definition for shape operator in a given point by vector v:
...

Mar214 11:25 AM
Mark44

6 
951 
Thank you for taking time to read my post, I hope I am putting into the correct area of the physics forum.
I am...

Mar214 05:29 AM
pbayer123

1 
630 
First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution...

Feb2814 10:33 PM
Chestermiller

3 
644 
When I derive dθ/ds I get the curvature k of a curve. But exist too the torsion τ of a curve and I think that exist...

Feb2714 10:25 PM
Abel Cavaşi

3 
697 
In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the...

Feb2714 06:30 AM
Chestermiller

1 
593 
I hope I am able to formulate this question properly as I am not extremely versed in differential geometry.
I have...

Feb2614 08:40 PM
Chestermiller

15 
1,304 
I noticed that in wiki there is the follows conversion:
...

Feb2614 04:03 PM
Jhenrique

0 
569 
The following definitions are correct?
We associate to a circular helix a complex numbers called complex...

Feb2214 12:45 PM
Abel Cavaşi

2 
669 
Hellow everybody!
If ##d\vec{r}## can be written in terms of curvilinear coordinates as ##d\vec{r} = h_1 dq_1...

Feb2114 08:10 PM
joshmccraney

5 
1,134 
It is known that the vector in polar coordinate system can be expressed as \mathbf{r}=r\hat{r}. In this formula, we...

Feb1914 06:01 AM
vanhees71

3 
754 
How would one prove Stokes' Theorem? I'm 15. I learned about Stokes' Theorem recently and I have a decent understand...

Feb1914 12:19 AM
mathwonk

5 
1,110 