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# Monthly Archives: August 2009

## Global harmonic miracle

That harmonic functions would satisfy the mean value property for infinitesimally small circles is intuitively somewhat clear. But that this property should persist on circles of arbitrary radius is quite miraculous. To recall, if is harmonic on a domain and … Continue reading

Posted in Complex Variables
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## Qual-type problem

Problem: Let be entire and suppose that for all : Show that . Solution: For let On one hand, using the fact that we get that as , for each . And on the other hand, direct integration shows that … Continue reading

Posted in Complex Variables
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## Syllabus clarity

Another funny story heard at lunch. The professor says: “On Monday we’ll have a quiz and it will be 10% of your final grade”. A student gets 9 out of 10 on the quiz and stops coming to class. At … Continue reading

Posted in Curiosity
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