Grant discusses the transformative way of thinking about derivatives in calculus and its applications in understanding complex mathematical concepts. Understanding derivatives as transformations rather than mere slopes can revolutionize calculus learning and application.

Grant discusses the application and importance of Taylor series in mathematics and physics, illustrating its utility in simplifying complex functions. Understanding Taylor series allows for effective approximation and deeper insights into complex functions.

Grant discusses higher-order derivatives, focusing on the second derivative, its implications in graph slopes, motion, and acceleration. Understanding second derivatives through graph slopes and motion provides deeper insights into acceleration and function behavior.

Grant discusses the use of integration to find the average value of continuous variables, illustrating with the sin(x) function. Understanding integration and its relationship with derivatives unlocks insights into continuous variables and natural phenomena.

Grant discusses integrals, their relationship with derivatives, and how to use them to solve problems involving variable speeds. Integrals, by measuring areas under curves, simplify calculations and enhance understanding of variable rates.

Grant discusses the concept of limits in calculus, explaining its relation to derivatives and L'Hopital's rule.

Implicit differentiation can feel strange, but thought of the right way it makes a lot of sense. Understanding limits through the epsilon-delta definition enhances foundational calculus concepts and practical applications.

Grant discusses the derivatives of exponential functions, specifically focusing on how the exponential function 2^t can represent population mass and its growth over time. Understanding exponential functions and their derivatives offers profound insights into natural growth processes.

A visual explanation of what the chain rule and product rule are, and why they are true. Grant discusses the concept of derivatives, emphasizing understanding over memorization, and exploring function composition.

A visual explanation of derivative formulas through geometry. Grant explains how to find derivatives for different functions like polynomials, trigonometric, exponential, and illustrates with geometric interpretations. Understanding derivatives through geometric visualizations bridges abstract concepts with practical applications.

What is an "instantaneous rate of change" when change happens across time? Grant explains the concept of derivatives and the logical contradictions involved.

In the first video of a series on the essence of calculus, Grant explores foundational concepts, using visual methods to explain how ideas in calculus, like differentiation and integration, are interconnected and can be conceptually reinvented. Understanding calculus through visualization and fundamental concepts can make anyone feel capable of inventing it.

Grant discusses the application of calculus in machine learning, specifically the back propagation algorithm and its calculations. Back propagation is essential for optimizing neural networks through detailed calculus applications.

A free course offering the core concept of Calculus, with a visuals-first approach aimed at making you feel like you could have discovered the subject yourself.