Understanding Engineering Mathematics

• use of inequalities in such topics as linear programming


• manipulation of functions in other maths topics such as calculus


• summation and use of series in approximations and statistics


• iteration in numerical methods


• infinite series expansions for functions


• approximations using the binomial expansion

A note about rigour

An engineer will probably be more concerned about using mathematics, rather than proof
and rigour. However, this chapter contains some topics that do really need careful treatment
even to use them. I have tried to make such things as palatable as possible!

3.1 Review

3.1.1 Definition of a function ➤90 107➤➤

Iff(x)=

x+ 1

x^2 + 2

evaluate (i)f( 0 ) (ii)f(− 1 )

3.1.2 Plotting the graph of a function ➤91 108➤➤

Choosing perpendicularx-,y-axes and suitable scales plot the graph of the functiony=
x^2 − 2 x−3 for integer values ofxin− 2 ≤x≤4. Describe the shape of the function
and discuss the points where it crosses the axes, and the minimum point.

3.1.3 Formulae ➤93 108➤➤

The focal lengthfof a mirror is given by

1

f

=

1

u

+

1

v

whereuis the lens-object distance andvthe lens-image distance. Expressvas a function
ofuandf.

3.1.4 Odd and even functions ➤94 108➤➤

Classify the following functions as odd, even or neither.

(i) 3x^3 −x (ii)

x^2

1 +x^2

(iii)

2 x

x^2 − 1

(iv)

x^2

x+ 1