Increments and Differentials

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Increments and Differentials

Differentials of y (dy)

They give an estimate of the real change on the value of a quantity (or variable).

dy ≈ Δy dy = f ’ (x) * dx

Infinitely small quantities.

Increments vs Differentials

Differentials

The information comes from the tangent line.

dy ≈ Δy dx = Δx dy = f ’(x) * dx dx = x2 – x1 f ’(x) * dx ≈ y2 – y1

Give an estimate of the real change among two values.

Increments

The information comes from the actual situation (f(x)).

y2 = Δy + y1 x2 = Δx + x1 Δy = y2 – y1 Δx = x2 – x1

Give the real change between two quantities.

Increment (Δy)

Can be positive or negative (decrement).

To calculate an increment you need to obtain the difference between the final and the initial value:

Δy = y2 – y1 Δx = x2 – x1

To denote an increment we use upper case delta: Δ

Used to show a change in the value of a variable.

Δy: change on the variable y

Δt: change in time

ΔT: change in Temperature

Δy: change in the volume of an object

Δp: price

When a changing quantity passes from an initial value to another value, it is said that it had an increment.