Manifolds #5 - Tangent Space (Introduction)

Notes are on my GitHub! github.com/rorg314/WHYBmaths 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!

Manifolds #6 - Tangent Space (Detail)

Manifolds #6 - Tangent Space (Detail)

Manifolds #1 - Introducing Manifolds

Manifolds #1 - Introducing Manifolds

What are Tangent Spaces in Differential Geometry?

What are Tangent Spaces in Differential Geometry?

Manifolds #5: Tangent Space (part 1)

Manifolds #5: Tangent Space (part 1)

Lecture 2B: Introduction to Manifolds (Discrete Differential Geometry)

Lecture 2B: Introduction to Manifolds (Discrete Differential Geometry)

Why Vector Bundles

Why Vector Bundles

The Core of Differential Forms

The Core of Differential Forms

Differential Forms | Introduction and the Tangent Space

Differential Forms | Introduction and the Tangent Space

What is a Manifold? - Mikhail Gromov

What is a Manifold? - Mikhail Gromov

Tangent spaces and Riemannian manifolds

Tangent spaces and Riemannian manifolds

Manifolds - Intrinsic Geometry

Manifolds - Intrinsic Geometry

Manifolds 19 | Tangent Space for Submanifolds

Manifolds 19 | Tangent Space for Submanifolds

Why care about differential forms? | Differential forms #1

Why care about differential forms? | Differential forms #1

Manifolds and Tangent Spaces

Manifolds and Tangent Spaces

I Gave ChatGPT a Body

I Gave ChatGPT a Body

Introducing Topology - Topology #1

Introducing Topology - Topology #1

The hidden logic behind #, @, & and §

The hidden logic behind #, @, & and §

The Core of Differential Geometry

The Core of Differential Geometry

Manifolds 21 | Tangent Space (Definition via tangent curves)

Manifolds 21 | Tangent Space (Definition via tangent curves)