Bonus
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>
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 2 | 122 | 16.07 | 100% | 50% | 11% |
Conversion
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| UK (North) | UK | Y | 5 | 20.00 | 100% | 60% | 40% |
| UK (South) | UK | Y | 7 | 15.71 | 100% | 43% | 14% |
| Northern California | US | Y | 4 | 20.00 | 100% | 100% | 0% |
| Southern California | US | Y | 7 | 17.14 | 100% | 57% | 14% |
| Eastern Canada (1) | US | Y | 4 | 15.00 | 100% | 50% | 0% |
| Eastern Canada (2) | US | Y | 9 | 14.44 | 100% | 22% | 22% |
| Florida | US | Y | 4 | 12.50 | 100% | 25% | 0% |
| Great Lakes | US | Y | 11 | 17.27 | 100% | 64% | 9% |
| Lower Mid-Atlantic | US | Y | 9 | 14.44 | 100% | 44% | 0% |
| Upper Mid-Atlantic | US | Y | 12 | 17.50 | 100% | 58% | 17% |
| Midwest | US | Y | 9 | 14.44 | 100% | 33% | 11% |
| North | US | Y | 4 | 15.00 | 100% | 50% | 0% |
| Northeast | US | Y | 12 | 17.50 | 100% | 58% | 17% |
| Pacific | US | Y | 8 | 13.75 | 100% | 38% | 0% |
| Southeast | US | Y | 12 | 17.50 | 100% | 67% | 8% |
| Upstate NY | US | Y | 5 | 12.00 | 100% | 20% | 0% |