Understanding Engineering Mathematics

temperatureTby theideal gas law:

P=

nRT

V

wherenRis a constant dependent on the gas. IfTis fixed then we can regard this formula
as expressingPas a functionf,say,ofV:

P=f(V)

IfVis fixed thenPcan be regarded as a (different) function,g,ofT:

P=g(T)

IfV andTcan vary then we can regardP as afunction,F,of the two variablesT
andV(we study such functions in Chapter 16):

P=F(T,V)

So the termfunctionis really a precise formulation of the idea of a formula.
In the above examples it may, for example, be thatPandTare known and it is required
to findV. We do this by rearranging ortransposingthe formula to giveVas a function
ofPandT– in this case:

V=

nRT

P

We s a y t h i s i smakingV the subject of the formula.

Solution to review question 3.1.3

Given that

1

f

=

1

u

+

1

v

then if we knowuandf we can obtainvas follows:

1

v

=

1

f

−

1

u

=

u−f

uf

So

v=

uf

u−f

makingvthe subject of the formula.

3.2.4 Odd and even functions

➤

88 108➤

Aneven functionis one which is unchanged when the sign of its argument changes,

f(−x)=f(x)