The Chemistry Maths Book, Second Edition

Only real coefficients are discussed here; the case of complex coefficients is shown

in Section 8.4 to involve no new principles.

EXAMPLE 2.13Write out in full:

(1)

(2)

(3)

0 Exercises 36–39

Degree n 1 = 11 : linear function

f(x) 1 = 1 a

0

1 + 1 a

1

x (2.11)

This is the simplest type of function, and is better known in the form

y 1 = 1 mx 1 + 1 c (2.12)

The graph of the function is a straight line. It has slope m, and intercepts the vertical

y-axis (whenx 1 = 10 ) at the pointy 1 = 1 c, as shown in Figure 2.6.

If we take any two points on the line, with coordinates (x

1

,y

1

) and (x

2

,y

2

), then

y

1

1 = 1 mx

1

1 + 1 c

y

2

1 = 1 mx

2

1 + 1 c

() () () ()−=−+−+−=−+

=

∑

xxxxxxx

i

234234

2

4

x

n

xxxx

x

xx x

n

21 1135 35

0

3

11234

1

23 4

−−

=

= + + + =++ +

∑∑

ix x x x x x x x

i

=× +× +× +× =+ +

=

∑

0123 23

01 2 3 23

0

3

2.5 Polynomials 41

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...

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..

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.

..

...

.

−c/m

x

1

x

2

(x

1

,y

1

)

(x

2

,y

2

)

y

2

−y

1

x

2

−x

1

y

2

y

1

y

x

c

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Figure 2.6