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## Main Question or Discussion Point

This is not only a question strictly about mathematics, but in science or any other quantitative field in which there is an integration - or a summation that is like a discrete integration.

[ A ] the parameter that is considered the input variable for the integration/summati - i.e., the

[ B ] the parameter that is the function being integrated/summed -

[ C ] the integration/summation result - { ∫ f( x ) dx } OR { Σ [ f( x ) Δx ] }

Obviously the fact that one is a summation while the other is integration (which itself is simply the limit of the summation being an infinite number of discrete quantities) should make no difference in the abstract terminology. Also, speaking only for physics here, there are a number of different such summation relationships ...

Mechanical Energy = Σ [ Force(Distance) * Δ Distance ]

Momentum = Σ [ Force(Time) * Δ Time ]

Elastic Energy = Σ [ Stiffness(Deformation) * Δ Deformation ] = Σ [ Elasticity(Strain) * Δ Strain ]

Thermomechanical Energy = Σ [ Pressure(Volume) * Δ Volume ]

Heat = Σ [ Temperature(Entropy) * Δ Entropy

Energy = Σ [ Power( Time ) * Δ Time ]

Voltage = Σ [ ElectricalField( Distance ) * Δ Distance ]

ElectricalCharge = Σ [ Current(Time) * Δ Time ]

Flux = Σ [ Field( 2-D coordinates on surface ) * Δ Area ]

... to name a few. Likewise, the function here is the derivative of the integration result with respect to the differential parameter. It seems that there must be a nice set of elegant terms to describe any such relationship; the best I can come up are ...

[ A ] the displacement function

[ B ] the forcing function

[ C ] the accumulation

... which obviously is inconsistent. I think the term for [ C ] sounds pretty good, but I can't come up with a term that is as generic as "accumulation" to describe [ A } & [ B ]. Surely some great commentator on mathematics has come up with such a set of nice terms.

[ A ] the parameter that is considered the input variable for the integration/summati - i.e., the

*x*of*dx*[ B ] the parameter that is the function being integrated/summed -

*f( x )*[ C ] the integration/summation result - { ∫ f( x ) dx } OR { Σ [ f( x ) Δx ] }

Obviously the fact that one is a summation while the other is integration (which itself is simply the limit of the summation being an infinite number of discrete quantities) should make no difference in the abstract terminology. Also, speaking only for physics here, there are a number of different such summation relationships ...

Mechanical Energy = Σ [ Force(Distance) * Δ Distance ]

Momentum = Σ [ Force(Time) * Δ Time ]

Elastic Energy = Σ [ Stiffness(Deformation) * Δ Deformation ] = Σ [ Elasticity(Strain) * Δ Strain ]

Thermomechanical Energy = Σ [ Pressure(Volume) * Δ Volume ]

Heat = Σ [ Temperature(Entropy) * Δ Entropy

Energy = Σ [ Power( Time ) * Δ Time ]

Voltage = Σ [ ElectricalField( Distance ) * Δ Distance ]

ElectricalCharge = Σ [ Current(Time) * Δ Time ]

Flux = Σ [ Field( 2-D coordinates on surface ) * Δ Area ]

... to name a few. Likewise, the function here is the derivative of the integration result with respect to the differential parameter. It seems that there must be a nice set of elegant terms to describe any such relationship; the best I can come up are ...

[ A ] the displacement function

[ B ] the forcing function

[ C ] the accumulation

... which obviously is inconsistent. I think the term for [ C ] sounds pretty good, but I can't come up with a term that is as generic as "accumulation" to describe [ A } & [ B ]. Surely some great commentator on mathematics has come up with such a set of nice terms.