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[
{
"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": [
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],
"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,
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264
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"names": [
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"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": [
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"names": [
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],
"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?"
}
] |