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A function in Euclidean space has a property described by this adjective if it satisfies Laplace’s equation. For 10 points each:
[10m] Give this adjective that also names a divergent series defined as the sum over n of 1 over n.
ANSWER: harmonic [accept harmonic function; accept harmonic series]
[10h] For a holomorphic function, the real and imaginary parts are both harmonic because they satisfy this pair of doubly-eponymous partial differential equations, which are a necessary and sufficient condition for a complex function to be complex differentiable.
ANSWER: Cauchy–Riemann equations [reject partial answers]
[10e] Cauchy also names a theorem regarding this operation in complex analysis, which states that this operation applied to any closed contour is zero. By the fundamental theorem of calculus, this operation is the inverse of differentiation.
ANSWER: integration [accept word forms: accept performing an integral; accept Cauchy’s integral theorem; accept contour integral]
<UBC B, Other Science>

EditionsHeardPPBEasy %Medium %Hard %
212216.07100%50%11%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Cambridge AImperial B001010E
Cambridge COxford1001020ME
Cambridge DImperial C10101030MHE
Cambridge EBirmingham001010E
CardiffWarwick1001020ME
LSEBristol001010E
SouthamptonImperial D001010E

Summary

TournamentEditionExact Match?HeardPPBEasy %Medium %Hard %
UK (North)UKY520.00100%60%40%
UK (South)UKY715.71100%43%14%
Northern CaliforniaUSY420.00100%100%0%
Southern CaliforniaUSY717.14100%57%14%
Eastern Canada (1)USY415.00100%50%0%
Eastern Canada (2)USY914.44100%22%22%
FloridaUSY412.50100%25%0%
Great LakesUSY1117.27100%64%9%
Lower Mid-AtlanticUSY914.44100%44%0%
Upper Mid-AtlanticUSY1217.50100%58%17%
MidwestUSY914.44100%33%11%
NorthUSY415.00100%50%0%
NortheastUSY1217.50100%58%17%
PacificUSY813.75100%38%0%
SoutheastUSY1217.50100%67%8%
Upstate NYUSY512.00100%20%0%