The discussion centers on the relationship between harmonic functions, which are solutions to the Laplace partial differential equation, and harmonic oscillators, typically found in physics. Participants explore the meaning of "harmonic" in both mathematical and physical contexts.
Participants do not reach a consensus on the relationship between harmonic functions and periodic functions, with some asserting distinctions while others seek clarification on the definitions and connections.
The discussion highlights potential limitations in understanding the definitions of harmonic and periodic functions, as well as the need for clarity in distinguishing between mathematical and physical contexts.
Ok.. So are all the solutions of the Laplace equation (in complex analysis) periodic? By definition, they are harmonic. So is a harmonic function and a periodic function the same thing?mathman said:Harmonic in both physics and math usually refer to things which are periodic. In math it is usually used in descriptions involving sines and cosines. In physics it is usually used in discussing pendulums and such things.