Category Archives: Equations

Q: Is there such a thing as half a derivative?

Posted on May 26, 2015 by The Physicist

The original question was: Another one of those questions of the type “does this make sense”.  You have first derivatives and second derivatives.  f'(x), f”(x) or sometimes dy/dx and d^2y/dx^2. Is there any sensible definition of a something like a “half” … Continue reading →

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

Q: How do I know my windmill is on straight?

Posted on January 26, 2015 by The Physicist

The original question was: I got quite the challenge from my father in law. The problem is well defined, but I’m having difficulties finding a meaningful answer. The reason why he asked me is because I’m an engineering student and … Continue reading →

Posted in -- By the Physicist, Engineering, Equations, Geometry, Math | 4 Comments

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

Posted on August 3, 2014 by The Physicist

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 →

Posted in -- By the Physicist, Equations, Math | 4 Comments

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

Posted on June 6, 2014 by The Physicist

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 | 10 Comments

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

Posted on April 12, 2014 by The Physicist

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 →

Posted in -- By the Physicist, Equations, Math | 10 Comments

Q: What does “E=mc2” mean?

Posted on April 7, 2014 by The Physicist

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 | 25 Comments