3Blue1Brown
What does area have to do with slope? | Chapter 9, Essence of calculus
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
Derivatives of exponentials | Chapter 5, Essence of calculus
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 the chain rule and product rule: Essence of Calculus - Part 4 of 11
The product rule and chain rule in calculus can feel like they were pulled out of thin air, but is there an intuitive way to think about them?
3Blue1Brown
Taylor series: Essence of Calculus - Part 11 of 11
Taylor series are extremely useful in engineering and math, but what are they? This video shows why they're useful, and how to make sense of the formula.
3Blue1Brown
Change of basis: Essence of Linear Algebra - Part 13 of 15
What is a change of basis, and how do you do it?
3Blue1Brown
Change of basis | Essence of linear algebra, chapter 13
What is a change of basis, and how do you do it?
3Blue1Brown
Euler's formula with introductory group theory - Part 1 of 4
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
Thinking outside the 10-dimensional box
A method for thinking about high-dimensional spheres, introduced in the context of a classic example involving a high-dimensional sphere inside a high-dimensional box.
3Blue1Brown
Why do colliding blocks compute pi?
A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi
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
Fractals are typically not self-similar
What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".
3Blue1Brown
How colliding blocks act like a beam of light...to compute pi: Colliding Blocks - Part 3 of 3
The third and final part of the block collision sequence.
3Blue1Brown
Fractals are typically not self-similar
What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".
3Blue1Brown
Visualizing the chain rule and product rule | Essence of calculus, chapter 4
The product rule and chain rule in calculus can feel like they were pulled out of thin air, but is there an intuitive way to think about them?
3Blue1Brown
So why do colliding blocks compute pi?
A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi
3Blue1Brown
So why do colliding blocks compute pi? Colliding Blocks - Part 2 of 3
A solution to the puzzle involving two blocks, sliding fricionlessly, where the number of collisions mysteriously computes pi
3Blue1Brown
Solving the heat equation: Differential Equations - Part 3 of 5
Solving the heat equation.
Bozeman Science
AP Biology Practice 2 - Using Mathematics Appropriately
Paul Andersen explains how to use mathematics appropriately. He begins by emphasizing the important role that mathematics plays in the life sciences today and in that the future. He describes important mathematical equations in each of...
3Blue1Brown
What does area have to do with slope? | Essence of calculus, chapter 9
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
But what is the Fourier Transform? A visual introduction.
An animated introduction to the Fourier Transform, winding graphs around circles.
3Blue1Brown
Dot products and duality | Essence of linear algebra, chapter 7
What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.
3Blue1Brown
The Brachistochrone, with Steven Strogatz: Brachistochrone - Part 1 of 2
A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.
3Blue1Brown
The paradox of the derivative | Essence of calculus, chapter 2
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.