The discussion revolves around the mathematical concepts required to understand the volume of a sphere changing periodically with time. It includes inquiries about the necessary higher mathematics and the role of calculus in this context.
Participants generally agree that calculus is foundational for understanding the problem, but there is no consensus on the necessity of more advanced topics like Bessel functions, as opinions vary on when they are encountered in education.
The discussion does not resolve the specific conditions under which Bessel functions become relevant, nor does it clarify the assumptions about the periodic nature of the volume change.
This discussion may be useful for students or individuals interested in the mathematical foundations of physics, particularly those exploring concepts related to volume changes and calculus.
You'd be surprised how much you can do with just basic calculus.falcon32 said:What kind of higher mathematics do I need to take in order to understand things like the volume of a sphere changing periodically with time? I know the generalized equation for a sphere is x2+y2+z2=r2, but how would time become involved?
Thanks!
falcon32 said:What kind of higher mathematics do I need to take in order to understand things like the volume of a sphere changing periodically with time? I know the generalized equation for a sphere is x2+y2+z2=r2, but how would time become involved?
Thanks!
LCKurtz said:You would just need calculus. An example of volume changing with time would be an inflating balloon.
falcon32 said:hmm ok thanks. what about bessel functions, calc also?
LCKurtz said:Calculus is the basis of all analysis. You normally wouldn't encounter Bessel functions until you take a differential equations, partial differential equations, or an engineering math course, all of which require calculus as a prerequisite.