How to visualize quaternions, a 4d number system, in our 3d world

What Cramer's rule is, and a geometric reason it's true

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

How to think about this 4d number system in our 3d space.

How to visualize quaternions, a 4d number system, in our 3d world

The third and final part of the block collision sequence.

The third and final part of the block collision sequence.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

This rule seems random to many students, but it has a beautiful reason for being true.

Divergence, curl, and their relation to fluid flow and electromagnetism

The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.

What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.

Intuitions for divergence and curl, and where they come up in physics.

Divergence, curl, and their relation to fluid flow and electromagnetism

This content provides a step-by-step solution for calculating the torque on a particle about the origin, given its position vector and an applied force vector, using unit-vector notation. It then demonstrates how to find the angle...

This video demonstrates how to calculate the work done by a force and the power generated as an object moves through a given displacement over time. It provides a clear, step-by-step solution to a physics problem involving vectors.

We've looked at a few simple examples of first-order differential equations and how to solve them. Now let's take a look at exact first-order differential equations.

JAX is a Python library similar to NumPy for scientific computing and linear algebra, but designed to run on accelerators like Cuda-based GPUs and Google's TPUs.

In this video, you will apply what you have learned about classes through a practical exercise. You will be given a problem statement and will learn how to design and implement a class to solve the problem. This exercise will help you...

This video demonstrates the multiplication of a parallel matrix in the naive or basic way.

In this episode, the team explores the fascinating interplay between moving electric charges and magnetic fields, unveiling the reciprocal relationship where moving magnetic poles generate electric fields. Delving into electromagnetic...

In this next episode, Mr. P guides us through the culmination of electromagnetic knowledge – Maxwell's equations. After a quick recap of Gauss's law and its magnetic counterpart, the class dives into Faraday's law of induction, unveiling...