Manifolds #5 - Tangent Space (Introduction)

Показать описание

In this video I give an overview of the concepts involved in constructing the tangent space. I briefly introduce the notion of a vector as a derivative, acting on smooth functions at a point to produce the tangent vector at that point.

For more detail on this construction see the next video!

If you like my videos and want to consider supporting the channel I am now accepting donations in DOGE and BTC (other cryptos on request) See my channel description for the addresses!

Рекомендации по теме

Комментарии

Hello, I am from India. I follow your all videos. Can you suggest me a basic book on smooth manifold. I am first learner.

abhijitmahata

I like how you fast-forward though the stuff that would make me bored to make it easier to focus on the concepts you explain in a way that more-naturally flows instead of getting distracted by the time it takes to draw something!

joem

Excellent video, your dog Lula is the real tangent hero ! Happy you have such a bond!

TheTimtimtimtam

found your video to get and idea about tangent space for numerical optimization course for my masters, wanted to thank you for your clear easy to follow teaching and yeah :3, will save it to my playlist so i can tell other students about it :), thanks again and wish you all the best
greetings from Egyptian studying in Germany

mostafaelborgy

I really like the material! And the dog!

hellokingston-zg

I'm doing my masters in mathematical physics and your videos help soo much!

janerex

Thank you! This has been very useful in my Geometric Data Analysis class.

spitfirerulz

Commenting for support and to come back to this once I've covered my fundamentals :D

chingalingaling

I really like your videos. Please keep it up and cuddle your puppy for me

trigger-red-airsoft

Thumbs up, you deserve it. And doggy too

toxxikanshul

>implying you can teach mathematics

joke, this was a brilliant video dude x

blackbirdipsissimus

Hello, I've been binge watching this series and I must say ur method of teaching has helped me a lot. I'm writing my high school essay on spherical and cylindrical coordinate systems and watched this topology series for more insight. If possible, could you recommend books or any other source I could use to write my essay?

mahatbh

@ 5:10 The phi(lambda) in the x, y-plane is NOT the same function as the phi(lambda) on the manifold M!
@ 7:51 In 2D we had a tangent-LINE to a curve, in 3D we had a tangent-PLANE to a surface and now in 4D we have some tangent-SPACE to some "volume" called a manifold. Never forget The Bigger Picture ;-)

jacobvandijk

Yess i needed this intuition! thanks a lot!! ps: what is the name of those star-like thingies hanging from your blackboard?

fvs

How do you know that the tangents of all curves at the point lie in one plane?

loxoloop

Great stuff, mate. I just can't figure where you've introduced the vector space in this playlist?

lubiekanapke

Isn't C-infinity(M) a collection of functions? I don't understand how it is the "tangent" space of the manifold

educationtarunramkanuri

Good going. Plz solved some research problem

lokeshkumar

i coudnt understand the word durative u used for tangent vector.. explain plzzz

harshagarwal

Thanks for great explanations. Is this a hobby of yours? Are you a student or a teacher? I am a hobbyist

drlangattxdotnet

Manifolds #5 - Tangent Space (Introduction)

Manifolds #5 - Tangent Space (Introduction)

Manifolds #5: Tangent Space (part 1)

Intro to Manifolds Part 5: Mappings and Tangents

Lecture 5: Tangent Spaces (International Winter School on Gravity and Light 2015)

Lecture 5 Definition of the tangent manifold

Differential Forms: PART 1A: TANGENT SPACES (INTUITIVELY)

Tutorial 5: Tangent Spaces (International Winter School on Gravity and Light 2015)

Manifolds 4.1 : Introduction to the Tangent Space

Daniel Beltita - Leaf spaces in Lie theory

Analysis II Lecture 12 Part 1 the tangent space

Tangent spaces and Riemannian manifolds

TSBP: Tangent Space Belief Propagation for Manifold Learning

Manifolds #6 - Tangent Space (Detail)

21.2 The tangent space to a manifold

Tangent Space

Aspects of the Tangent Space derivation

Manifold 4.2 : Differentials of Smooth Maps and Dimension of the Tangent Space

Tangent space

Analysis II Lecture 12 Part 2 tangent space using curves

Manifolds and Tangent Spaces

Lecture 4 Trying to define the tangent space

Finding Tangent Space to Cylinder

What is a Manifold? Lesson 9: The Tangent Space-Definition

Manifolds, Tangent Spaces, and Coordinate Basis | Tensor Intuition