# Toronto Math Forum

## APM346-2012 => APM346 Math => Misc Math => Topic started by: James McVittie on September 25, 2012, 08:04:29 PM

Title: Heat Wave Equation Solution Integral
Post by: James McVittie on September 25, 2012, 08:04:29 PM
After we determined the solution to the heat wave equation, we took the integral from negative infinity to some x. The solution was in the form of a Normal Distribution function where in statistics the integral indicates the probability that we randomly choose a value within that interval. I was wondering what are the physical implications of this same integral in the wave equation? Does the area under the solution indicate the energy in the system up to that point or does it have some other meaning?
Title: Re: Heat Wave Equation Solution Integral
Post by: Victor Ivrii on September 26, 2012, 02:28:48 AM
After we determined the solution to the heat wave equation, we took the integral from negative infinity to some x. The solution was in the form of a Normal Distribution function where in statistics the integral indicates the probability that we randomly choose a value within that interval. I was wondering what are the physical implications of this same integral in the wave equation? Does the area under the solution indicate the energy in the system up to that point or does it have some other meaning?

Heat wave equation? WTH are you talking about? There is a wave equation (and its ilk) and the heat equation  (and its ilk) describing either very different processes or the same process under very different assumption. The properties of these equations are really different.

PS Sure more complex phenomena can be described by systems containing both equations but for the purpose of this class ...

Title: Re: Heat Wave Equation Solution Integral
Post by: James McVittie on September 26, 2012, 12:41:27 PM
Sorry I meant the Heat Equation. What does the integral of the solution to that equation represent?
Title: Re: Heat Wave Equation Solution Integral
Post by: Victor Ivrii on September 26, 2012, 12:55:13 PM
Sorry I meant the Heat Equation. What does the integral of the solution to that equation represent?

If we talking about heat equation then it is a total heat energy in $(-\infty,x)$. But for us it mainly a trick to get a a formula for a solution.