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The essence of calculus

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What might it feel like to invent calculus?
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In this first video of the series, we see how unraveling the nuances of a simple geometry question can lead to integrals, derivatives, and the fundamental theorem of calculus.

Thanks to these viewers for their contributions to translations
Dutch: @LFWarsen, Lauri Warsen
Hebrew: Imri, Omer Tuchfeld
Hindi: Vinayak
Hungarian: homok43
Italian: @Deye27, @hi-anji, alberto alessi
Korean: Hana Seo
Portuguese: redkk123
Spanish: @agustin-j
Vietnamese: @ngvutuan2811, ngvutuan

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Music by Vincent Rubinetti.
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The essence of calculus

Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus

The paradox of the derivative | Chapter 2, Essence of calculus

Taylor series | Chapter 11, Essence of calculus

Derivative formulas through geometry | Chapter 3, Essence of calculus

What does area have to do with slope? | Chapter 9, Essence of calculus

What's so special about Euler's number e? | Chapter 5, Essence of calculus

The hardest problem on the hardest test

Limits, L'Hôpital's rule, and epsilon delta definitions | Chapter 7, Essence of calculus

Researchers thought this was a bug (Borwein integrals)

Why π is in the normal distribution (beyond integral tricks)

Higher order derivatives | Chapter 10, Essence of calculus

Implicit differentiation, what's going on here? | Chapter 6, Essence of calculus

Differential equations, a tourist's guide | DE1

Divergence and curl: The language of Maxwell's equations, fluid flow, and more

Visualizing the chain rule and product rule | Chapter 4, Essence of calculus

But what is a partial differential equation? | DE2

e^(iπ) in 3.14 minutes, using dynamics | DE5

Why is pi here? And why is it squared? A geometric answer to the Basel problem

But what is the Riemann zeta function? Visualizing analytic continuation

Grant Sanderson (3Blue1Brown) - Past, Present, & Future of Mathematics

But why is a sphere's surface area four times its shadow?

Why greatest Mathematicians are not trying to prove Riemann Hypothesis? || #short #terencetao #maths

A tale of two problem solvers (Average cube shadows)

But what is the Central Limit Theorem?

Solving the heat equation | DE3

Who cares about topology? (Inscribed rectangle problem)

Euler's formula with introductory group theory

How (and why) to raise e to the power of a matrix | DE6

But what is the Fourier Transform? A visual introduction.

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