E1 - Essence of calculus

Aired: April 28, 2017

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.

E2 - The paradox of the derivative

Aired: April 29, 2017

Derivatives center on the idea of change in an instant, but change happens across time while an instant consists of just one moment. How does that work?

E3 - Derivative formulas through geometry

Aired: April 30, 2017

A few derivative formulas, such as the power rule and the derivative of sine, demonstrated with geometric intuition.

E4 - Visualizing the chain rule and product rule

Aired: May 01, 2017

A visual explanation of what the chain rule and product rule are, and why they are true.

E5 - What's so special about Euler's number e?

Aired: May 02, 2017

What is e? And why are exponentials proportional to their own derivatives?

E6 - Implicit differentiation, what's going on here?

Aired: May 03, 2017

Implicit differentiation can feel weird, but what's going on makes much more sense once you view each side of the equation as a two-variable function, f(x, y).

E7 - Limits, L'Hopital's rule, and epsilon delta definitions

Aired: May 04, 2017

Formal derivatives, the epsilon-delta definition, and why L'Hôpital's rule works.

E8 - Integration and the fundamental theorem of calculus

Aired: May 05, 2017

What is an integral? How do you think about it?

E9 - What does area have to do with slope?

Aired: May 06, 2017

Integrals are used to find the average of a continuous variable, and this can offer a perspective on why integrals and derivatives are inverses, distinct from the one shown in the last video.

E10 - Higher order derivatives

Aired: May 07, 2017

A very quick primer on the second derivative, third derivative, etc.

E11 - Taylor series

Aired: May 07, 2017

Taylor polynomials are incredibly powerful for approximations, and Taylor series can give new ways to express functions.

E12 - What they won't teach you in calculus

Aired: May 19, 2018

A visual for derivatives which generalizes more nicely to topics beyond calculus.