3Blue1Brown
Differential equations, studying the unsolvable | DE1
What is a differential equation, the pendulum equation, and some basic numerical methods
3Blue1Brown
What they won't teach you in calculus
A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.
3Blue1Brown
Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus
How to think about implicit differentiation in terms of functions with multiple inputs, and tiny nudges to those inputs.
TED Talks
Greg Lynn: Organic algorithms in architecture
Greg Lynn talks about the mathematical roots of architecture -- and how calculus and digital tools allow modern designers to move beyond the traditional building forms. A glorious church in Queens (and a titanium tea set) illustrate his...
3Blue1Brown
Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus
What is integration? Why is it computed as the opposite of differentiation? What is the fundamental theorem of calculus?
3Blue1Brown
Snell's law proof using springs: Brachistochrone - Part 2 of 2
A clever mechanical proof of Snell's law.
3Blue1Brown
What's so special about Euler's number e? | Essence of calculus, chapter 5
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
Taylor series | Chapter 10, Essence of calculus
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
The paradox of the derivative: Essence of Calculus - Part 2 of 11
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.
3Blue1Brown
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...
SciShow
Alan Turing: Great Minds
Hank introduces us to that great mathematical mind, Alan Turing, who, as an openly gay man in the early 20th century faced brutal prejudice that eventually led to his suicide, despite being a genius war hero who helped the Allies defeat...
3Blue1Brown
Integration and the fundamental theorem of calculus: Essence of Calculus - Part 8 of 11
What is integration? Why is it computed as the opposite of differentiation? What is the fundamental theorem of calculus?
3Blue1Brown
Higher order derivatives | Footnote, Essence of calculus
What is the second derivative? Third derivative? How do you think about these?
TED Talks
Arthur Benjamin: Teach statistics before calculus!
Someone always asks the math teacher, "Am I going to use calculus in real life?" And for most of us, says Arthur Benjamin, the answer is no. He offers a bold proposal on how to make math education relevant in the digital age.
3Blue1Brown
Higher order derivatives: Essence of Calculus - Part 10 of 11
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Derivative formulas through geometry | Chapter 3, Essence of calculus
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...
3Blue1Brown
Limits, L'Hôpital's rule, and epsilon delta definitions | Essence of calculus, chapter 7
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
3Blue1Brown
The other way to visualize derivatives
A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.
3Blue1Brown
But WHY is a sphere's surface area four times its shadow?
Two proofs for the surface area of a sphere
Crash Course
Derivatives: Crash Course Physics
CALCULUS! Today we take our first steps into the language of Physics; mathematics. Every branch of science has its own way to describe the things that it investigates. And, with Physics, that's math. In this episode, Shini talks us...
3Blue1Brown
Derivative formulas through geometry: Essence of Calculus - Part 3 of 11
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...
3Blue1Brown
What they won't teach you in calculus
A visual for derivatives which generalizes more nicely to topics beyond calculus.
3Blue1Brown
What does area have to do with slope? Essence of Calculus - Part 9 of 11
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?