I see the dot product as directional multiplication. But multiplication goes beyond repeated counting… Read article: it’s applying the essence of one item to another.
Normal multiplication combines growth rates: “3 x 4″ can mean “Take your 3x growth and make
The Pythagorean Theorem shows how strange our concept of distance is. Using the rule a2 + b2 = c2… Read article, we can trade some “a” to get more “b”.
Starting with
means “A 13-inch pizza equals a
Circulation… Read article is the amount of force that pushes along a closed boundary or path. It's the total "push" you get when going along a path, such as a circle.
A vector field is usually the source of the circulation. If
The gradient is a fancy word for derivative, or the rate of change of a function. It’s a vector (a direction to move) that
Physical Intuition
Divergence (div) is “flux density”—the amount of flux… Read article entering or leaving a point. Think of it as the rate of flux expansion (positive divergence) or flux contraction (negative divergence). If you measure flux in bananas (and c’mon, who
Once you understand flux intuitively, you don’t need to memorize equations. The formulas become “obvious” dare I say. However, it took a lot of effort to truly understand that:
