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3Blue1Brown Series

3Blue1Brown is a channel about animating math, in all senses of the word animate.

Genre: Documentary,

Actor:

Creator: Grant Sanderson,

Country:

Type: tv

Season: 4

Episode: N/A

Duration: N/A minutes

Release: 2016-08-06

Rating: 9

1"Vectors, what even are they?"

2016-08-06

Kicking off the linear algebra lessons, let's make sure we're all on the same page about how specifically to think about vectors in this context.

2"Linear combinations, span, and basis vectors"

2016-08-07

The fundamental vector concepts of span, linear combinations, linear dependence, and bases all center on one surprisingly important operation: Scaling several vectors and adding them together.

3"Linear transformations and matrices"

2016-08-07

Matrices can be thought of as transforming space, and understanding how this work is crucial for understanding many other ideas that follow in linear algebra.

4"Matrix multiplication as composition"

2016-08-09

Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.

5"Three-dimensional linear transformations"

2016-08-10

What do 3d linear transformations look like? Having talked about the relationship between matrices and transformations in the last two videos, this one extends those same concepts to three dimensions.

6"The determinant"

2016-08-11

The determinant of a linear transformation measures how much areas/volumes change during the transformation.

7"Inverse matrices, column space and null space"

2016-08-16

How to think about linear systems of equations geometrically. The focus here is on gaining an intuition for the concepts of inverse matrices, column space, rank and null space, but the computation of those constructs is not discussed.

8"Nonsquare matrices as transformations between dimensions"

2016-08-16

Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions.

9"Dot products and duality"

2016-08-24

Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation.

10"Cross products"

2016-09-01

This covers the main geometric intuition behind the 2d and 3d cross products.

11"Cross products in the light of linear transformations"

2016-09-03

For anyone who wants to understand the cross product more deeply, this video shows how it relates to a certain linear transformation via duality. This perspective gives a very elegant explanation of why the traditional computation of a dot product corresponds to its geometric interpretation.

12"Cramer's rule, explained geometrically"

2019-03-17

This rule seems random to many students, but it has a beautiful reason for being true.

13"Change of basis"

2016-09-11

How do you translate back and forth between coordinate systems that use different basis vectors?

14"Eigenvectors and eigenvalues"

2016-09-15

A visual understanding of eigenvectors, eigenvalues, and the usefulness of an eigenbasis.

15"A quick trick for computing eigenvalues"

2021-05-07

How to write the eigenvalues of a 2x2 matrix just by looking at it.

16"Abstract vector spaces"

2016-09-24

This is really the reason linear algebra is so powerful.

1"Essence of calculus"

2017-04-28

In this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.

2"The paradox of the derivative"

2017-04-29

Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work?

3"Derivative formulas through geometry"

2017-04-30

A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition.

4"Visualizing the chain rule and product rule"

2017-05-01

A visual explanation of what the chain rule and product rule are, and why they are true.

5"What's so special about Euler's number e?"

2017-05-02

What is e? And why are exponentials proportional to their own derivatives?

6"Implicit differentiation, what's going on here?"

2017-05-03

Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y).

7"Limits, L'Hopital's rule, and epsilon delta definitions"

2017-05-04

Formal derivatives, the epsilon-delta definition, and why L'Hôpital's rule works.

8"Integration and the fundamental theorem of calculus"

2017-05-05

What is an integral? How do you think about it?

9"What does area have to do with slope?"

2017-05-06

Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video.

10"Higher order derivatives"

2017-05-07

A very quick primer on the second derivative, third derivative, etc.

11"Taylor series"

2017-05-07

Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions.

12"What they won't teach you in calculus"

2018-05-19

A visual for derivatives which generalizes more nicely to topics beyond calculus.

1"But what is a Neural Network?"

2017-10-05

Introduction to neural networks.

2"Gradient descent, how neural networks learn"

2017-10-16

The goal of this video is to introduce the idea of gradient descent and to analyze a specific network.

3"What is backpropagation really doing?"

2017-11-03

What's actually happening to a neural network as it learns?

4"Backpropagation calculus"

2017-11-03

This one is a bit more symbol heavy, and that's actually the point. The goal here is to represent in somewhat more formal terms the intuition for how backpropagation works in part 3 of the series, hopefully providing some connection between that video and other texts/code that you come across later.

1"Overview of differential equations"

2019-03-31

How do you study what cannot be solved?

2"But what is a partial differential equation?"

2019-04-21

The heat equation, as an introductory PDE.

3"Solving the heat equation"

2019-06-16

Boundary conditions, and setup for how Fourier series are useful.

4"But what is a Fourier series?"

2019-06-30

Fourier series, from the heat equation to sines to cycles.