Concept
Fundamental theorem
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
Also named here as riemann sum — the same set of essays touches all of them, so they are one junction rather than several.
Adding up rectangles until they stop being rectangles
The integral is defined as a limit of sums of rectangles. The definition is exact, the picture is honest about what it costs, and the gap between them is the whole subject.
Area is the undoing of slope
Two operations invented for unrelated reasons — measuring a region and measuring a rate — turn out to be inverse. The picture is two panels sharing one axis, and the claim is that the lower curve's steepness is the upper curve's height.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaLimitRiemann sumAccumulationAntiderivativeContinuityConvergenceDerivativeDirichlet's functionIntegrabilityLebesgue integralMean value theorem