The Essence of Calculus
In this video, we see how unraveling the nuances of a simple geometry question can lead to the essence of calculus.
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The Paradox of the Derivative
What is an "instantaneous rate of change" when change happens across time? Is it the paradox of the derivative? Here is a beautiful explanation.
Derivative Formulas Through Geometry
After introducing the derivative in the last lesson, the next step is to learn how to compute the derivative formulas through geometry.
Visualizing the Chain Rule and Product Rule
Our goal now is to understand how to take derivatives of more complicated combinations by visualizing the chain rule and product rule.
What’s So Special About Euler’s Number e?
What is Euler's number e? Why are exponentials proportional to their derivatives? We will see why e^x is arguably the most important exponential.
Implicit Differentiation, What’s Going on Here?
Calculus students find it particularly weird to see implicit differentiation for the first time when they are learning calculus.
Limits, L’Hôpital’s Rule, and Epsilon-Delta Definition
In this lesson, you will understand what it means for one value to approach another, the epsilon-delta definition, and why L'Hôpital's rule works.
Integration and the Fundamental Theorem of Calculus
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.
What Does Area Have to Do with Slope?
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
Higher Order Derivatives
What is the second derivative? Third derivative? What do you think about these? This lecture is a quick primer on higher order derivatives.
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