Bozeman Science
Mathematics - Biology's New Microscope
Paul Andersen (with the help of PatricJMT) explains why mathematics may be biology's next microscope.
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?
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...
3Blue1Brown
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
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
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
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
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
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.
3Blue1Brown
The Brachistochrone, with Steven Strogatz
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
But what is a partial differential equation? | DE2
The heat equation, as an introductory PDE.
3Blue1Brown
Visualizing the chain rule and product rule | Chapter 4, Essence of calculus
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
The Essence of Calculus - Part 1 of 11
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
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.