14

Analysis for Engineers – Limits,

Sequences, Iteration, Series

and All That

The topics considered in this chapter are often regarded as something of a luxury for
engineers and scientists, who are normally more concerned with using techniques rather
than worrying too much about the underlying theory. However, the ideas are not really
that difficult, and there are in fact many engineering situations where it is necessary
to pay particular attention to things such as continuity and differentiability. Also, even
though some of the techniques may not be of immediate practical use, they are important
in applications of numerical methods in engineering. Thus, before engaging in costly
computational approaches, it is important to check that the problem is mathematically well
defined. Does a ‘solution’ exist? Is it unique? Will the computational scheme converge
to it? How long will it take? What are the error bounds?...etc. These are the sorts of
questions that analysis addresses.

Prerequisites

It will be helpful if you know something about:

• different types of number (5

➤

)

• elementary notion of a limit (231

➤

)

• properties of zero (6

➤

)

• sketching graphs (91

➤

)

• the binomial theorem (71

➤

)

• properties of rational functions (56

➤

)

• slope of a curve (230

➤

)

• inequalities (97

➤

)

• sequences and series (105

➤

)

• the geometric series (105

➤

)

• differentiation (Chapter 8

➤

)

• the modulus sign (96

➤

)

• elementary functions – trig, exponential, etc. (Chapters 4 and 6
  ➤
  )

Objectives

In this chapter you will find:

• more on irrational numbers