Category Archives: Equations

Q: Since it involves limits, is calculus always an approximation?

Physicist: Nope!  Calculus is exact.  For those of you unfamiliar with calculus, what follows is day 1. In order to find the slope of a curve at a particular point requires limits, which always feel a little incomplete.  When taking … Continue reading

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Q: Where do the rules for “significant figures” come from?

Physicist: When you’re doing math with numbers that aren’t known exactly, it’s necessary to keep track of both the number itself and the amount of error that number carries.  Sometimes this is made very explicit.  You may for example see … Continue reading

Posted in -- By the Physicist, Conventions, Equations, Math | 1 Comment

Q: How do you define the derivatives of the Heaviside, Sign, Absolute Value, and Delta functions? How do they relate to one another?

Physicist: These are four standard reference functions.  In the same way that there are named mathematical constants, like π or e, there are named mathematical functions.  These are among the more famous (after the spotlight hogging trig functions). The absolute value … Continue reading

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Q: What does “E=mc2” mean?

Physicist: This famous equation is a little more subtle than it appears.  It does provide a relationship between energy and matter, but importantly it does not say that they’re equivalent. First, it’s worth considering what energy actually is.  Rather than … Continue reading

Posted in -- By the Physicist, Equations, Philosophical, Physics, Relativity | 10 Comments

Q: Can resonance be used to destroy anything? Is the “brown note” possible?

Physicist: Nope! “Resonance” is a “driven harmonic oscillation“, where the driving force pushes and pulls at, or near, the “resonant frequency” of whatever it is that doing the resonating.  There are two big issues involved with destroying stuff using sound, … Continue reading

Posted in -- By the Physicist, Equations, Math, Physics | 23 Comments

Q: What is a Fourier transform? What is it used for?

Physicist: Almost every imaginable signal can be broken down into a combination of simple waves.  This fact is the central philosophy behind Fourier transforms (Fourier was very French, so his name is pronounced a little wonky: “4 E yay”). Fourier … Continue reading

Posted in -- By the Physicist, Equations, Math | 13 Comments