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Category Archives: Vector Calculus

Vector Calculus: Understanding the Dot Product

22

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

Posted in Math, Vector Calculus | February 27, 2012 by kalid

Understanding Pythagorean Distance and the Gradient

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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

Posted in Math, Vector Calculus | November 4, 2011 by kalid

Vector Calculus: Understanding Circulation and Curl

33

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

Posted in Vector Calculus | February 19, 2007 by kalid

Vector Calculus: Understanding the Gradient

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Vector Calculus: Understanding the Gradient

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

  • Points in the direction of greatest increase of a function (intuition on why)
  • Is
  • … Read article
Posted in Vector Calculus | February 17, 2007 by kalid

Vector Calculus: Understanding Divergence

26

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

Posted in Vector Calculus | September 20, 2006 by kalid

Vector Calculus: Understanding Flux

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Vector Calculus: Understanding Flux

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:

  • Flux is the amount of “something” passing through a surface (electric
  • … Read article
Posted in Vector Calculus | September 16, 2006 by kalid
The mission: share aha! moments in clear, friendly language. I write about topics as I wish they were explained to me. Read more...

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