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Applied Mathematics: Advanced Engineering

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Question:

Discuss about the Applied Mathematics for Advanced Engineering.

 

Answer:

Differentials:

Differential can be considered as a small difference in the success value of quantities. In the current case Volume of the orange fruit (V) is the parameter discussed and V is the change of the volume during the process of peeling.

Differential change of volume:

Peeling an orange changes its volume by ΔV, which mean that the original volume V of the orange will be changed by ΔV after doing the peeling of the fruit. ΔV is the essentially the volume of the thin outer cover of the orange fruit, which is actually removed during the peeling operation. Suppose V is the volume of the fruit, then after the peeling process the new volume(V’)  will be V-ΔV.

To put in equation form,

V’-V = ΔV.

Inferences: Differential does not refer anything towards the rate at which the process is achieved or alternatively there is no discussion towards the rate at which the peeling is done for orange. The time function is totally not present in differentials at this stage.

 

References:

Kreyszig, E. (2010). Advanced engineering mathematics. John Wiley & Sons.

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