| [ |
| { |
| "file_id": "WfEQabCGAqI", |
| "query_id": 3, |
| "timestamp": 1684511496045.0, |
| "annotatedSourceSentencesIndices": [ |
| 196, |
| 197 |
| ], |
| "names": [ |
| "annotator1" |
| ], |
| "text": "Do maths/science/engineering students take this class or some other multivariable calculus course like 18.024?" |
| }, |
| { |
| "file_id": "WfEQabCGAqI", |
| "query_id": 5, |
| "timestamp": 1684511772657.0, |
| "annotatedSourceSentencesIndices": [ |
| 161 |
| ], |
| "names": [ |
| "annotator1" |
| ], |
| "text": "18:09 why the range of r goes from 0 to 1? I think the definition of S in this problem needs further clarification. S should be a paraboloid of z = x^2 + y^2 between z=0 and z=1. It is a little confusing by justing saying \"above the unit disk\". " |
| }, |
| { |
| "file_id": "WfEQabCGAqI", |
| "query_id": 7, |
| "timestamp": 1684511834173.0, |
| "annotatedSourceSentencesIndices": [ |
| 359, |
| 361 |
| ], |
| "names": [ |
| "annotator1" |
| ], |
| "text": "Isn't this theorem called after Ostrogradsky, since he is the first one to prove it?" |
| }, |
| { |
| "file_id": "WfEQabCGAqI", |
| "query_id": 8, |
| "timestamp": 1684512043723.0, |
| "annotatedSourceSentencesIndices": [ |
| 226, |
| 227, |
| 264 |
| ], |
| "names": [ |
| "annotator1" |
| ], |
| "text": "Wait, did he ever account for vector N not being a unit vector? He never required that the N vector represented the area of the delta slanted plane did he?" |
| }, |
| { |
| "file_id": "WfEQabCGAqI", |
| "query_id": 1, |
| "timestamp": 1684192120438.0, |
| "annotatedSourceSentencesIndices": [ |
| 331, |
| 331 |
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| "names": [ |
| "annotator1", |
| "annotator2" |
| ], |
| "text": "I did not understand the last step replacing dA by dxdy. The proof contained slanted plane with an angle alpha to only one axis and not a general slant in both directions. Does this proof apply when we are considering a general slant to both x and y ? Will dA=dS Cos theta still be applicable?" |
| } |
| ] |
