3Blue1Brown
Visualizing quaternions (4d numbers) with stereographic projection
How to visualize quaternions, a 4d number system, in our 3d world
3Blue1Brown
Eigenvectors and eigenvalues | Essence of linear algebra, chapter 14
Eigenvalues and eigenvectors are one of the most important ideas in linear algebra, but what on earth are they?
3Blue1Brown
Cramer's rule, explained geometrically | Essence of linear algebra, chapter 12
What Cramer's rule is, and a geometric reason it's true
3Blue1Brown
Abstract vector spaces | Essence of linear algebra, chapter 11
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
3Blue1Brown
But what is a Fourier series? From heat flow to circle drawings | DE4
Fourier series, from the heat equation to sines to cycles.
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A quick trick for computing eigenvalues | Essence of linear algebra, chapter 15
A quick way to compute eigenvalues of a 2x2 matrix
3Blue1Brown
Alice, Bob, and the average shadow of a cube
A story of problem-solving styles, with the central example of finding the average area for the shadow of a cube.
3Blue1Brown
Eigenvectors and eigenvalues: Essence of Linear Algebra - Part 14 of 15
Eigenvalues and eigenvectors are one of the most important ideas in linear algebra, but what on earth are they?
3Blue1Brown
Integration and the fundamental theorem of calculus | Essence of calculus, chapter 8
What is integration? Why is it computed as the opposite of differentiation? What is the fundamental theorem of calculus?
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Cross products in the light of linear transformations | Essence of linear algebra chapter 11
The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.
3Blue1Brown
Euler's formula with introductory group theory
Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.
3Blue1Brown
The more general uncertainty principle, beyond quantum
The general uncertainty principle, about the concentration of a wave vs the concentration of its fourier transform, applied to two non-quantum examples before showing what it means for the Heisenberg uncertainty principle.
3Blue1Brown
Derivative formulas through geometry | Essence of calculus, chapter 3
Introduction to the derivatives of polynomial terms and trigonometric functions thought about geometrically and intuitively. The goal is for these formulas to feel like something the student could have discovered, rather than something...
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How (and why) to raise e to the power of a matrix | DE6
Exponentiating matrices, and the kinds of linear differential equations this solves.
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Group theory, abstraction, and the 196,883-dimensional monster
An introduction to group theory, and the monster group.
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What's so special about Euler's number e? Essence of Calculus - Part 5 of 11
What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.
3Blue1Brown
Visualizing quaternions (4d numbers) with stereographic projection - Part 1 of 2
How to visualize quaternions, a 4d number system, in our 3d world
3Blue1Brown
Feynman's Lost Lecture
This video recounts a lecture by Richard Feynman giving an elementary demonstration of why planets orbit in ellipses. See the excellent book by Judith and David Goodstein, "Feynman's lost lecture”, for the full story behind this lecture,...
3Blue1Brown
What are quaternions, and how do you visualize them? A story of four dimensions.
How to think about this 4d number system in our 3d space.
3Blue1Brown
Some light quantum mechanics (with MinutePhysics)
An introduction to the quantum behavior of light, specifically the polarization of light. The emphasis is on how many ideas that seem "quantumly weird" are actually just wave mechanics, applicable in a lot of classical physics.
3Blue1Brown
Three-dimensional linear transformations: Essence of Linear Algebra - Part 5 of 15
How to think of 3x3 matrices as transforming 3d space
3Blue1Brown
The more general uncertainty principle, beyond quantum
The general uncertainty principle, about the concentration of a wave vs the concentration of its fourier transform, applied to two non-quantum examples before showing what it means for the Heisenberg uncertainty principle.
3Blue1Brown
The Essence of Calculus, Chapter 1
An overview of what calculus is all about, with an emphasis on making it seem like something students could discover for themselves. The central example is that of rediscovering the formula for a circle's area, and how this is an...
3Blue1Brown
Quaternions and 3d rotation, explained interactively - Part 2 of 2
An introduction to an interactive experience on why quaternions describe 3d rotations