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Basic Engineering Mathematics
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| 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
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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