Science and Mathematics for Engineering

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
SECTION 1: APPLIED MATHEMATICS
1 Basic arithmetic
1.1 Introduction
1.2 Revision of addition and subtraction
1.3 Revision of multiplication and division
1.4 Highest common factors and lowest common multiples
1.5 Order of operation and brackets
2 Fractions, decimals and percentages
2.1 Fractions
2.2 Ratio and proportion
2.3 Decimals
2.4 Percentages
Revision Test 1: Arithmetic, fractions, decimals and percentages
3 Indices, units, prefixes and engineering notation
3.1 Powers and roots
3.2 Laws of indices
3.3 Introduction to engineering units
3.4 SI units
3.5 Common prefixes
3.6 Standard form
3.7 Engineering notation
3.8 Metric conversions
3.9 Metric – US/Imperial conversions
4 Calculations and evaluation of formulae
4.1 Introduction
4.2 Use of calculator
4.3 Evaluation of formulae
Revision Test 2: Indices, units, calculator and evaluation of formulae
5 Basic algebra
5.1 Introduction
5.2 Basic operations
5.3 Laws of indices
5.4 Brackets
5.5 Factorisation
5.6 Laws of precedence
6 Solving simple equations
6.1 Introduction
6.2 Solving equations
6.3 Practical problems involving simple equations
Revision Test 3: Algebra and simple equations
7 Transposing formulae
7.1 Introduction
7.2 Transposing formulae
7.3 Further transposing of formulae
7.4 More difficult transposing of formulae
8 Solving simultaneous equations
8.1 Introduction
8.2 Solving simultaneous equations in two unknowns
8.3 Further solving of simultaneous equations
8.4 Practical problems involving simultaneous equations
9 Logarithms and exponential functions
9.1 Introduction to logarithms
9.2 Laws of logarithms
9.3 Indicial equations
9.4 Graphs of logarithmic functions
9.5 Exponential functions
9.6 Graphs of exponential functions
9.7 Napierian logarithms
9.8 Laws of growth and decay
Revision Test 4: Transposition of formulae, simultaneous equations, logarithms and exponential functions
10 Straight line graphs
10.1 Introduction to graphs
10.2 Axes, scales and co-ordinates
10.3 Straight line graphs
10.4 Gradients, intercepts and equation of a graph
10.5 Practical problems involving straight line graphs
11 Introduction to trigonometry
11.1 Introduction
11.2 The theorem of Pythagoras
11.3 Sines, cosines and tangents
11.4 Evaluating trigonometric ratios of acute angles
11.5 Solving right-angled triangles
11.6 Graphs of trigonometric functions
11.7 Sine and cosine rules
11.8 Area of any triangle
11.9 Worked problems on the solution of triangles and their areas
11.10 Practical situations involving trigonometry
Revision Test 5: Straight line graphs and trigonometry
12 Areas of common shapes
12.1 Introduction
12.2 Common shapes
12.3 Calculating areas of common shapes
12.4 Areas of similar shapes
13 The circle
13.1 Introduction
13.2 Properties of circles
13.3 Radians and degrees
13.4 Arc length and areas of circles and sectors
14 Volumes of common solids
14.1 Introduction
14.2 Calculating volumes and surface areas of common solids
14.3 Summary of volumes and surface areas of common solids
14.4 Calculating more complex volumes and surface areas
14.5 Volumes of similar shapes
Revision Test 6: Areas and volumes
Multiple-choice questions on Applied Mathematics
SECTION II: MECHANICAL APPLICATIONS
15 SI units and density
15.1 SI units
15.2 Density
16 Atomic structure of matter
16.1 Elements, atoms, molecules and compounds
16.2 Mixtures, solutions, suspensions and solubility
16.3 Crystals
16.4 Metals
17 Speed and velocity
17.1 Speed
17.2 Distance/time graph
17.3 Speed/time graph
17.4 Velocity
18 Acceleration
18.1 Introduction to acceleration
18.2 Velocity/time graph
18.3 Free-fall and equation of motion
19 Force, mass and acceleration
19.1 Introduction
19.2 Newton’s laws of motion
19.3 Centripetal acceleration
Revision Test 7: SI units, density, speed and velocity, force, mass and acceleration
20 Forces acting at a point
20.1 Introduction
20.2 Scalar and vector quantities
20.3 Centre of gravity and equilibrium
20.4 Forces
20.5 The resultant of two coplanar forces
20.6 Triangle of forces method
20.7 The parallelogram of forces method
20.8 Resultant of coplanar forces by calculation
20.9 Resultant of more than two coplanar forces
20.10 Coplanar forces in equilibrium
20.11 Resolution of forces
20.12 Summary
21 Work, energy and power
21.1 Introduction
21.2 Work
21.3 Energy
21.4 Power
21.5 Potential and kinetic energy
22 Simply supported beams
22.1 Introduction
22.2 The moment of a force
22.3 Equilibrium and the principle of moments
22.4 Simply supported beams having point loads
Revision Test 8: Forces acting at a point, work, energy and power and simply supported beams
23 Linear and angular motion
23.1 Introduction
23.2 The radian
23.3 Linear and angular velocity
23.4 Linear and angular acceleration
23.5 Further equations of motion
23.6 Relative velocity
24 Friction
24.1 Introduction to friction
24.2 Coefficient of friction
24.3 Applications of friction
25 Simple machines
25.1 Machines
25.2 Force ratio, movement ratio and efficiency
25.3 Pulleys
25.4 The screw-jack
25.5 Gear trains
25.6 Levers
Revision Test 9: Linear and angular motion, friction and simple machines
26 The effects of forces on materials
26.1 Introduction
26.2 Forces
26.3 Tensile force
26.4 Compressive force
26.5 Shear force
26.6 Stress
26.7 Strain
26.8 Elasticity, limit of proportionality and elastic limit
26.9 Hooke’s law
26.10 Ductility, brittleness and malleability
27 Linear momentum and impulse
27.1 Introduction
27.2 Linear momentum
27.3 Impulse and impulsive forces
Revision Test 10: Forces on materials and linear momentum and impulse
28 Torque
28.1 Introduction
28.2 Couple and torque
28.3 Work done and power transmitted by a constant torque
28.4 Kinetic energy and moment of inertia
28.5 Power transmission and efficiency
29 Pressure in fluids
29.1 Pressure
29.2 Fluid pressure
29.3 Atmospheric pressure
29.4 Archimedes’ principle
29.5 Measurement of pressure
29.6 Barometers
29.7 Absolute and gauge pressure
29.8 The manometer
29.9 The Bourdon pressure gauge
29.10 Vacuum gauges
30 Heat energy and transfer
30.1 Introduction
30.2 Heat and temperature
30.3 The measurement of temperature
30.4 Specific heat capacity
30.5 Change of state
30.6 Latent heats of fusion and vaporisation
30.7 A simple refrigerator
30.8 Conduction, convection and radiation
30.9 Vacuum flask
30.10 Use of insulation in conserving fuel
30.11 Thermal efficiency
30.12 Calorific value and combustion
30.13 Heat Exchangers
Revision Test 11: Torque, pressure in fluids, heat energy and transfer
31 Thermal expansion
31.1 Introduction
31.2 Practical applications of thermal expansion
31.3 Expansion and contraction of water
31.4 Coefficient of linear expansion
31.5 Coefficient of superficial expansion
31.6 Coefficient of cubic expansion
32 Ideal gas laws
32.1 Boyle’s law
32.2 Charles’ law
32.3 The pressure or Gay-Lussac’s law
32.4 Dalton’s law of partial pressure
32.5 Characteristic gas equation
32.6 Worked problems on the characteristic gas equation
32.7 Further worked problems on the characteristic gas equation
33 The measurement of temperature
33.1 Introduction
33.2 Liquid-in-glass thermometers
33.3 Thermocouples
33.4 Resistance thermometers
33.5 Thermistors
33.6 Pyrometers
33.7 Temperature-indicating paints and crayons
33.8 Bimetallic thermometers
33.9 Mercury-in-steel thermometer
33.10 Gas thermometers
33.11 Choice of measuring device
Revision Test 12: Thermal expansion, ideal gas laws and temperature measurement
SECTION III: ELECTRICALAPPLICATIONS
34 An introduction to electric circuits
34.1 Introduction
34.2 Standard symbols for electrical components
34.3 Electric current and quantity of electricity
34.4 Potential difference and resistance
34.5 Basic electrical measuring instruments
34.6 Ohm’s law
34.7 Multiples and sub-multiples
34.8 Conductors and insulators
34.9 Electrical power and energy
34.10 Main effects of electric current
34.11 Fuses
35 Resistance variation
35.1 Resistor construction
35.2 Resistance and resistivity
35.3 Temperature coefficient of resistance
35.4 Resistor colour coding and ohmic values
36 Batteries and alternative sources of energy
36.1 Introduction to batteries
36.2 Some chemical effects of electricity
36.3 The simple cell
36.4 Corrosion
36.5 E.m.f. and internal resistance of a cell
36.6 Primary cells
36.7 Secondary cells
36.8 Lithium-ion batteries
36.9 Cell capacity
36.10 Safe disposal of batteries
36.11 Fuel cells
36.12 Alternative and renewable energy sources
36.13 Solar energy
36.14 Glass batteries
37 Series and parallel networks
37.1 Introduction
37.2 Series circuits
37.3 Potential divider
37.4 Parallel networks
37.5 Current division
37.6 Wiring lamps in series and in parallel
Revision Test 13: Electric circuits, resistance variation, batteries and series and parallel networks
38 Kirchhoff’s laws
38.1 Introduction
38.2 Kirchhoff’s current and voltage laws
38.3 Worked problems on Kirchhoff’s laws
39 Magnetism and electromagnetism
39.1 Introduction to magnetism and magnetic circuits
39.2 Magnetic fields
39.3 Electromagnets
39.4 Magnetic flux and flux density
39.5 Force on a current-carrying conductor
39.6 Principle of operation of a simple d.c. motor
39.7 Force on a charge
40 Electromagnetic induction
40.1 Introduction to electromagnetic induction
40.2 Laws of electromagnetic induction
40.3 Self inductance
40.4 Mutual inductance
40.5 The transformer
Revision Test 14: Kirchhoff’s laws, magnetism, electromagnetism and electromagnetic induction
41 Alternating voltages and currents
41.1 Introduction
41.2 The a.c. generator
41.3 Waveforms
41.4 A.c. values
41.5 Electrical safety – insulation and fuses
41.6 Semiconductor diodes
41.7 Rectification
41.8 Smoothing of the rectified output waveform
42 Capacitors and inductors
42.1 Capacitors and capacitance
42.2 The parallel-plate capacitor
42.3 Capacitors connected in parallel and series
42.4 Dielectric strength
42.5 Energy stored in capacitors
42.6 Practical types of capacitor
42.7 Supercapacitors
42.8 Discharging capacitors
42.9 Inductance
42.10 Inductors
42.11 Practical inductors
42.12 Energy stored by inductors
42.13 Inductance of a coil
43 Electrical measuring instruments and measurements
43.1 Introduction
43.2 Electronic instruments
43.3 Multimeters
43.4 Wattmeters
43.5 Instrument ‘loading’ effect
43.6 The oscilloscope
43.7 Virtual test and measuring instruments
43.8 Virtual digital storage oscilloscopes
43.9 Null method of measurement
43.10 Wheatstone bridge
43.11 D.c. potentiometer
44 Global climate change and the future of electricity production
44.1 Introduction
44.2 Global climate change
44.3 Evidence of rapid climate change
44.4 Consequences of global climate change
44.5 How does electric power production affect the global climate?
44.6 Generating electrical power using coal
44.7 Generating electrical power using oil
44.8 Generating electrical power using natural gas
44.9 Generating electrical power using nuclear energy
44.10 Generating electrical power using hydro power
44.11 Generating electrical power using pumped storage
44.12 Generating electrical power using wind
44.13 Generating electrical power using tidal power
44.14 Generating electrical power using biomass
44.15 Generating electrical power using solar energy
44.16 Harnessing the power of wind, tide and sun on an ‘energy island’ – a future possibility?
Revision Test 15: Alternating voltages and currents, capacitors and inductors, measurements and electricity production
SECTION IV: ENGINEERING SYSTEMS
45 Introduction to Engineering systems
45.1 Introduction
45.2 Systems
45.3 Types of systems
45.4 Transducers
45.5 System diagrams
45.6 System control
45.7 Control methods
45.8 System response
45.9 Negative and positive feedback
45.10 Evaluation of system response
List of main Formulae for Science and Mathematics for Engineering
Answers to Practice Exercises
Glossary of terms
Index