I'm studying for a complex analysis qualifying exam, and I'm working on a question about harmonic functions:
42.
Is it still a harmonic function, thus extended ?-talk ) 16 : 46, 9 June 2009 ( UTC)
43.
Harmonic function is generally disregarded in a sequence, or, at least, it is far less important than the sequential motion.
44.
The solution is not unique, since addition of any harmonic function to " w " will not affect the equation.
45.
His research in partial differential equations, applied mathematics and classical analysis, particularly on harmonic functions, gained him a wide recognition.
46.
The following year he produced " The Geometry of Harmonic Functions ", which won the Carl B . Allendoerfer Award for 1995.
47.
The quantity u _ { xx } measures how far off the temperature is from satisfying the mean value property of harmonic functions.
48.
A similar argument shows that the average of a harmonic function on the boundary of a disk equals its value at the centre.
49.
The association of a bounded harmonic function to an ( essentially ) bounded function on the boundary is one-to-one.
50.
The " first golden age " of minimal surfaces began . representation formulas, firmly linking minimal surfaces to complex analysis and harmonic functions.
