# Simon differentiating 3tan(2x)

To solve the problem, Simon chooses not to look up what the derivative of a tangent is but work everything out from scratch. He generally doesn’t like rote learning but prefers to gain deep understanding of how and why.

# Impressions on Newton’s mechanics.

“Are you impressed?” – Simon asks, laughingly, and I can see it must be a pun. We are in bed, reading up on Newton’s laws of motion that talk of forces being “impressed” upon bodies.

Simon continues: “Newton’s mechanics says that the speed limit is infinite, which says that matter doesn’t exist, which says that Physics doesn’t exist, which says that Newton’s mechanics doesn’t exist. Newton’s mechanics contradicts itself!”

The book we are reading (17 Equations that Changed the World by Ian Stewart) goes on to describe how in Newton’s laws, calculus peeps out from behind the curtains and how the second law of motion specifies the relation between a body’s position, and the forces that act on it, in the form of a differential equation: second derivative of position = force/mass. To find the position, the book says, we have to solve this equation, defusing the position from its second derivative. “Do you get it?” – I ask, “Because I don’t think I do”. — “I’ll need a piece of paper for this”, – Simon quickly comes back dragging his oversized sketchbook. Then he quickly writes down the differential equation (where the x is the position) to explain to me what the second derivative is. And then he solves it:

# Geometric Definition of e

The idea comes from a video by Mathologer. Simon sketches a geometric definition of the Euler’s number (e) using integrals. He messed up a little with the integral notation, but corrected it later (after we stopped filming). Please see the photos below:

Simon seems to be setting first gentle steps in Calculus, once again thanks to Daniel Shiffman.

In the videos below, Simon talks about minimizing and maximizing functions, the power rule, the chain rule and partial derivatives. Simon’s videos are his resumes of Daniel Shiffman’s Calculus Intelligence and Learning course tutorial 3.5 and a few other related tutorials. “Intelligence and Learning” course is a Spring 2017 course that Daniel Shiffman taught at the ITP, the Interactive Telecommunications Program, a graduate programme at NYU’s Tisch School of the Arts.

On Saturday morning Simon also chose to do Calculus with his math teacher (via Khan Academy), instead of Algebra and polynomial expressions that they were actually doing for the past weeks.

Daniel Shiffman’s videos on Calculus:
Power Rule: https://youtu.be/IKb_3FJtA1U