SCADA Training Manual

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Basic Engineering Mathematics

Basic Engineering Mathematics

Introduction

   Basic Engineering Mathematics 5th Edition provides a lead into Engineering Mathematics 6th Edition. Each topic considered in the text is presented in a way that assumes in the reader little previous knowledge of that topic. Each chapter begins with a brief outline of essential theory, definitions, formulae, laws and procedures; however, these are kept to a minimum as problem solving is extensively used to establish and exemplify the theory. It is intended that readers will gain real understanding through seeing problems solved and then solving similar problems themselves.

Direct proportion

    Two quantities are in direct proportion when they increase or decrease in the same ratio. For example, if 12 cans of lager have a mass of 4 kg, then 24 cans of lager will have a mass of 8 kg; i.e., if the quantity of cans doubles then so does the mass. This is direct proportion

ELECTRIC POWER GENERATION, TRANSMISSION, and DISTRIBUTION

Here are three laws in engineering which involve direct proportion:

(a) Hooke’s law states that, within the elastic limit of a material, the strain ε produced is directly proportional to the stress σ producing it, i.e. ε ∝ σ (note than ‘∝’ means ‘is proportional to’).

(b) Charles’s law states that, for a given mass of gas at constant pressure, the volume V is directly proportional to its thermodynamic temperature T , i.e. V ∝ T 

(c) Ohm’s law states that the current I flowing through a fixed resistance is directly proportional to the applied voltage V , i.e. I ∝ V .

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Table of Content

1 Basic arithmetic

2 Fractions

3 Decimals

4 Using a calculator

5 Percentages

6 Ratio and proportion

7 Powers, roots and laws of indices

8 Units, prefixes and engineering notation

9 Basic algebra

10 Further algebra

11 Solving simple equations

12 Transposing formulae

13 Solving simultaneous equations

14 Solving quadratic equations

15 Logarithms

16 Exponential functions

17 Straight line graphs

18 Graphs reducing non-linear laws to linear form

19 Graphical solution of equations

20 Angles and triangles

21 Introduction to trigonometry

22 Trigonometric waveforms

23 Non-right-angled triangles and some practical applications

24 Cartesian and polar co-ordinates

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