Engineering Mathematics

A Programmed Approach, 3th Edition

C. Evans

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781351451000
• Edition: 3
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

The programmed approach, established in the first two editions is maintained in the third and it provides a sound foundation from which the student can build a solid engineering understanding. This edition has been modified to reflect the changes in the syllabuses which students encounter before beginning undergraduate studies. The first two chapters include material that assumes the reader has little previous experience in maths. Written by CHarles Evans who lectures at the University of Portsmouth and has been teaching engineering and applied mathematics for more than 25 years. This text provides one of the essential tools for both undergraduate students and professional engineers.

Basic ideas

1

This opening chapter is designed to lay the foundations of the work which we have to do later. We will therefore describe some notation and examine both arithmetic and algebraic processes.

After completing this chapter you should be able to

□ Approximate calculations to a given number of decimal places and to a given number of significant figures;

□ Apply the rules of elementary algebra correctly;

□ Distinguish between identities and equations;

□ Evaluate binomial coefficients and apply the binomial theorem.

At the end of this chapter we shall solve a practical problem involving the force on a magnetic pole.

1.1 ARITHMETIC

We are all familiar with the basic operations of arithmetic. These are addition and multiplication. The first numbers which we encounter are the ‘whole’ numbers, which we shall call the natural numbers

$1,2,3,4,\mathrm{\dots }$

You will notice that we have not included zero as one of the natural numbers; some people do and some people don’t!

We can add or multiply any two natural numbers together without obtaining results which go beyond this set of numbers.

$\begin{array}{l}\text{12 + 13 = 25}\\ \text{12}\times \text{13 = 156}\end{array}$

Both 25 and 156 are natural numbers too.

When we introduce the operation of subtraction it is necessary to widen the concept of number to include the negative whole numbers and zero. These numbers are known as integers

$\mathrm{\dots }\text{,}-\text{2,}-\text{1, 0, 1, 2, 3,}\mathrm{\dots }$

We observe of course that every natural number is an integer.

Although the integers are sufficient for simple barter of discrete (individually distinct) objects, they are unable to cope with division. The operation of division forces us to ext...