Vector Fields and Tensors Differential Geometry Part 4

[bebeheuy]

I am very happy to see the vidoe after you give this Vector fields and the concept of parallel transport of a vector are introduced. Cartesian tensors are defined using the concept of tensor product which "glues" two vectors together

[AntoMelta]

I Really Like The Video From Your Vector fields and the concept of parallel transport of a vector are introduced

[willamricard]

Your Video Is Very Useful Sharing Vector fields and the concept of parallel transport of a vector are introduced. Cartesian tensors are defined using the concept of tensor product which "glues" two vectors together.

[imegatrone]

after i watched this video, my insight is very open because the video is very good to give information Vector Fields and Tensors Differential Geometry Part 4

[Gigantum1000]

HI and thanks a lot for this very easy way of teaching Tensors

[omicron8251]

Wondering if that's the tangent space, what's a cotangent space? (i.e.)Tn*Mn.

[Mathview]

@omicron8251 Yes, excellent question. Occasionally, I use the term tangent space loosely to indicate any local linear space at a point in a manifold. The actual meaning should be clear in the context. Officially, the local linear space of differentials in the neighborhood of a point p in a Riemann manifold is called the cotangent space at p. It is the dual of the local vector space of inverse differentials say.. (d/dx, d/dy, d/dz) at p. The metric tensor converts from one to another.

[lordborda]

Great!

[SarahStarmer]

I am so glad you made these videos. I kept coming accross the words covarient and contravarient and tensor and it made me feel very ignorant especialy when I looked them up in wickapedia and still didn't understand what they ment.

So thank you so much you have been very helpful.

[Mathview]

Very smart question. Tensors as discussed here can be shown to form a natural linear space (vector space.) Tensors of the same rank can be added or subtracted element by element. Tensors can be multiplied by a scalar again element by element. There is a zero tensor. So yes. More info in the playlist titled Mathematical Spaces and in the video Rotation Operators part3. 

[Darkkaz118]

Does other vector properties still stand if these vectors are a tensor? Namely, if I multiply a tensor by a constant k, will the tensor be amplified by a factor of k, just like a vector?

And by the way, great vids., they are really helping me! :-)

[Mathview]

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[Sconz32]

I just used this to prove the existence of god.

[Mathview]

Completed two new videos continuing the discussion of Vectors and Tensors (Sept 20 2010.) One covers topics of Tensor Algebra and Wedge Product, Exterior Product Spaces, and Differential Forms explained simply. The other is on converting Geometry into Algebra using Tensors. We know mathematics can convert Geometry into Analysis using Analytic Geometry and Calculus. We can also convert Geometry into Algebra using Tensor Products, and create new kinds of Vector Spaces. Comments welcome.

[thebestsuperdoctor]

This a greate way to learn tensor math. In the future I would like see the functional tensor and directional derivative definition of tensor videos. What also would be good is work each coordinate system with its metric tensor. Then a detailed general relativity ending with the Keluza-Klein tensorial matrix which could workout entry by entry in each coordinate system.

[FanOfJanis]

As a youth, I was majoring in theoretical astrophysics at the U. of Chicago and was tutored by S. Chandrasekhar personally, because I sought him out ... as a 17-year-old freshman. Got side-tracked from it all with family responsibilties and all. No, In late-middle-age, I STILL love this stuff! Thank you, Mathview, for making an old-timer's day!  Peace ... FoJ

[danieljimenez1989]

@FanOfJanis I'm soooo jealous!!!!

what was your experience with professor Chandrasekhar?

[IQ20000Berta]

So easy for the kids nowadays to learn math. The are experts in vector and tensor math in 10 minutes. Great video.

[tfennimore]

superb, clear explanation! thanks... now I want to know what interpretation to give to the four components of a (second-order) tensor...

[domtheodore]

very clear explanation. you made tensors slightly less scary.

[gre36789]

When I was an undergrad I was not taught tensors in this fashion. Why is dyadic notation not taught? I think it would make somethings easier. You could derive the tensor of inertia a lot quicker this way.

[Rafabomb]

It can be very kool if you can give some exercise page with solutions to see if one has grasped the main ideas...

[web2wl00p]

very nice way of introducing the topic!!! good job! thx for sharing :-)

[penguino29]

Thanks for the tutorial. You have explained it very clearly and I've learnt something that I thought I could never understand in this short 10 mins. Much appreciated.

[omerfarooq1900]

very good video but it is short I want to learn more Thanks for this

[mohsin987]

thanks a lot 4 ur efforts

[erAshwanisoni]

it was very informatice and good video. keep it up

[fin63rm4n]

kool. hope to see more in the furure

[leon522amanda]

fine and insteresting, thanks

[gzajicek20]

I am a physician by training, who decided to explore what is there in advanced math and physics that might be relevant to medicine. Your lectures opened my eyes. You expose important ideas in a simple and lucid way. Thanks

[johann022086]

Thanks, I'm excited to see these videos. Continue that good work!

[johann022086]

very nice thanks. but where is the video next to this? Is it this: "How do I get the arc length from the metric tensors".

[Mathview]

Thank you, you are observant. My original intention was put differential forms after this part. But I decided that it would be better at the beginning of a new series on Curved Spaces and Riemannian Manifolds.

I hope to get those videos started in the next week or so. It seems there is interest in this subject, and I am really enjoying it. Thanks for the views.

[xslaya22x]

Someone finally gives me some tangibility in the tensor department. Keep this series up, it's very helpful!

[addercap]

This is a great series of videos. You explain very well.