3Blue1Brown Series (2016)

Vectors, what even are they?

Linear combinations, span, and basis vectors

Linear transformations and matrices

Matrix multiplication as composition

Three-dimensional linear transformations

The determinant

Inverse matrices, column space and null space

Nonsquare matrices as transformations between dimensions

Dot products and duality

Cross products

Cross products in the light of linear transformations

Cramer's rule, explained geometrically

Change of basis

Eigenvectors and eigenvalues

A quick trick for computing eigenvalues

Abstract vector spaces

Essence of calculus

The paradox of the derivative

Derivative formulas through geometry

Visualizing the chain rule and product rule

What's so special about euler's number e?

Implicit differentiation, what's going on here?

Limits, l'hopital's rule, and epsilon delta definitions

Integration and the fundamental theorem of calculus

What does area have to do with slope?

Higher order derivatives

Taylor series

What they won't teach you in calculus

But what is a neural network?

Gradient descent, how neural networks learn

What is backpropagation really doing?

Backpropagation calculus

Overview of differential equations

But what is a partial differential equation?

Solving the heat equation

But what is a fourier series?

Understanding e to the i pi in 3.14 minutes

How (and why) to raise e to the power of a matrix