Although the "supergeometric" series f(z) = z - z2 + z4 - z8 + ... converges much faster inside the unit disk than an ordinary geometric series, it has very complex behavior at the boundary. The image on the left shows the magnitude of f(z), and might lead us to believe not much is going on near z = 1; for example, that the limit z -> 1 exists. On the right we have zoomed in on z = 1 by four orders of magnitude and see evidence that something regular is going on, even while the limit z -> 1 does not exist. We finish the mini-course by working out the complete leading order behavior as we approach the boundary on the real axis.
Message from Andy Ruina
Homework
- Assignment 1, Due 2/27
- Assignment 2, Due 3/6
Possibly a resource, when doing integrals.
Text
- There is no required text but Advanced Mathematical Methods for Scientists and Engineers, by Bender & Orszag, is highly recommended.
Grading
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To receive credit for this part of Basic Training you need to receive passing scores on two of the three assignments.
Lecturer
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Veit Elser, 426 PSB, office hours: Mondays 2-3:30 pm
Grader
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Colin Clement, 425A PSB
Movies
