Download ebooks file Mathematics pocket book for engineers and scientists 5th edition john bird all
Visit to download the full and correct content document: https://ebookmass.com/product/mathematics-pocket-book-for-engineers-and-scientist s-5th-edition-john-bird/
More products digital (pdf, epub, mobi) instant download maybe you interests ...
Statistics for Engineers and Scientists 5th Edition
Why is knowledge of science and mathematics important in engineering?
A career in any engineering field will require both basic and advanced mathematics and science. Without mathematics and science to determine principles, calculate dimensions and limits, explore variations, prove concepts, and so on, there would be no mobile telephones, televisions, stereo systems, video games, microwave ovens, computers, or virtually anything electronic. There would be no bridges, tunnels, roads, skyscrapers, automobiles, ships, planes, rockets or most things mechanical. There would be no metals beyond the common ones, such as iron and copper, no plastics, no synthetics. In fact, society would most certainly be less advanced without the use of mathematics and science throughout the centuries and into the future.
Electrical engineers require mathematics and science to design, develop, test, or supervise the manufacturing and installation of electrical equipment, components, or systems for commercial, industrial, military, or scientific use.
Mechanical engineers require mathematics and science to perform engineering duties in planning and designing tools, engines, machines, and other mechanically functioning equipment; they oversee installation, operation, maintenance, and repair of such equipment as centralised heat, gas, water, and steam systems.
Aerospace engineers require mathematics and science to perform a variety of engineering work in designing, constructing, and testing aircraft, missiles, and spacecraft; they conduct basic and applied research to evaluate adaptability of materials and equipment to aircraft design and manufacture and recommend improvements in testing equipment and techniques.
Nuclear engineers require mathematics and science to conduct research on nuclear engineering problems or apply principles and theory of nuclear science to problems concerned with release, control, and utilisation of nuclear energy and nuclear waste disposal.
Petroleum engineers require mathematics and science to devise methods to improve oil and gas well production and determine the need for new or modified tool designs; they oversee drilling and offer technical advice to achieve economical and satisfactory progress.
Industrial engineers require mathematics and science to design, develop, test, and evaluate integrated systems for managing industrial production processes, including human work factors, quality control, inventory control, logistics and material flow, cost analysis, and production coordination.
Environmental engineers require mathematics and science to design, plan, or perform engineering duties in the prevention, control, and remediation of environmental health hazards, using various engineering disciplines; their work may include waste treatment, site remediation, or pollution control technology.
Civil engineers require mathematics and science in all levels in civil engineering – structural engineering, hydraulics and geotechnical engineering are all fields that employ mathematical tools such as differential equations, tensor analysis, field theory, numerical methods and operations research.
Architects require knowledge of algebra, geometry, trigonometry and calculus. They use mathematics for several reasons, leaving aside the necessary use of mathematics in the engineering of buildings. Architects use geometry because it defines the spatial form of a building, and they use mathematics to design forms that are considered beautiful or harmonious. The front cover of this text shows a modern London architecture and the financial district, all of which at some stage required in its design a knowledge of mathematics.
Knowledge of mathematics and science is clearly needed by each of the disciplines listed above.
It is intended that this text – Mathematics Pocket Book for Engineers and Scientists – will provide a step by step, helpful reference, to essential mathematics topics needed by engineers and scientists.
Mathematics Pocket Book for Engineers and Scientists
Fifth Edition
John Bird
Fifth edition published 2020 by Routledge
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN and by Routledge
The right of John Bird to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers.
Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.
First edition published as Newnes Mathematics for Engineers Pocket Book by Newnes 1983 Fourth edition published as Engineering Mathematics Pocket Book by Routledge 2008
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data
A catalog record has been requested for this book
ISBN: 978-0-367-26653-0 (hbk)
ISBN: 978-0-367-26652-3 (pbk)
ISBN: 978-0-429-29440-2 (ebk)
Typeset in Frutiger 45 Light by Servis FIlmsetting Ltd, Stockport, Cheshire.
Mathematics Pocket Book for Engineers and Scientists
John Bird is the former Head of Applied Electronics in the Faculty of Technology at Highbury College, Portsmouth, UK. More recently, he has combined freelance lecturing at the University of Portsmouth, with examiner responsibilities for Advanced Mathematics with City and Guilds and examining for International Baccalaureate. He has over 45 years’ experience of successfully teaching, lecturing, instructing, training, educating and planning trainee engineers study programmes. He is the author of 140 textbooks on engineering, science and mathematical subjects, with worldwide sales of over one million copies. He is a chartered engineer, a chartered mathematician, a chartered scientist and a Fellow of three professional institutions. He is currently lecturing at the Defence College of Marine Engineering in the Defence College of Technical Training at H.M.S. Sultan, Gosport, Hampshire, UK, one of the largest technical training establishments in Europe.
Section
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Section
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter 118 Integration using trigonometric and hyperbolic substitutions
Chapter 119 Integration using partial fractions
Chapter 120 The t = tan
Chapter 121 Integration by parts
Chapter 123 Double and triple integrals
Chapter 124 Numerical integration
Chapter 125 Area under and between curves
Chapter 126 Mean or average values
Chapter 127 Root mean square values
Chapter 128 Volumes of solids of revolution
Chapter 129 Centroids
Chapter 130 Theorem of Pappus
Chapter 131 Second moments of area
Section 13 Differential equations
Chapter 132 The solution of equations of the form
Chapter 133 The solution of equations of the form dy dx f(y)
Chapter 134 The solution of equations of the form dy
Chapter 135 Homogeneous
Chapter 137 Numerical methods for first order differential equations (1) – Euler’s method
Chapter 138 Numerical methods for first order differential equations (2) – Euler-Cauchy method
Chapter 139 Numerical methods for first order differential equations (3) – Runge-Kutta method
Chapter 140 Second order differential equations of the form
Chapter 141 Second order differential equations of the form
Chapter 142 Power series methods of solving ordinary differential equations (1) – Leibniz theorem
Chapter 143 Power series methods of solving ordinary differential equations (2) – Leibniz-Maclaurin method
Chapter 144 Power series methods of solving ordinary differential equations (3) – Frobenius method
Chapter 145 Power series methods of solving ordinary differential equations (4) – Bessel’s equation
Chapter 146 Power series methods of solving ordinary differential equations (5) – Legendre’s equation and Legendre’s polynomials
Chapter 147 Power series methods of solving ordinary differential equations (6) – Rodrigue’s formula
Chapter
Chapter 187 Wilcoxon signed-rank test 537
Chapter 188 The Mann-Whitney test 540
Index 547
Preface
Mathematics Pocket Book for Engineers and Scientists 5th Edition is intended to provide students, technicians, scientists and engineers with a readily available reference to the essential engineering mathematics formulae, definitions, tables and general information needed during their work situation and/or studies – a handy book to have on the bookshelf to delve into as the need arises.
In this 5th edition, the text has been re-designed to make information easier to access. The importance of why each mathematical topic is needed in engineering and science is explained at the beginning of each section. Essential theory, formulae, definitions, laws and procedures are stated clearly at the beginning of each chapter, and then it is demonstrated how to use such information in practice.
The text is divided, for convenience of reference, into seventeen main sections embracing engineering conversions, constants and symbols, some algebra topics, some number topics, areas and volumes, geometry and trigonometry, graphs, complex numbers, vectors, matrices and determinants, Boolean algebra and logic circuits, differential and integral calculus and their applications, differential equations, Laplace transforms, z-transforms, Fourier series and statistics and probability. To aid understanding, over 675 application examples have been included, together with some 300 line diagrams.
The text assumes little previous knowledge and is suitable for a wide range of disciplines and/or courses of study. It will be particularly useful as a reference for those in industry involved in engineering and science and/or for students studying mathematics within Engineering and Science Degree courses, as well as for National and Higher National Technician Certificates and Diplomas, GCSE and A levels.
JOHN BIRD BSc(Hons), CEng, CSi, CMath, FIET, FIMA, FCollP Royal Naval Defence College of Marine Engineering, HMS Sultan,formerly University of Portsmouth and Highbury College, Portsmouth
Engineering conversions, constants and symbols Section 1
Why are engineering conversions, constants and symbols important?
In engineering there are many different quantities to get used to, and hence many units to become familiar with. For example, force is measured in Newtons, electric current is measured in amperes and pressure is measured in Pascals. Sometimes the units of these quantities are either very large or very small and hence prefixes are used. For example, 1000 Pascals may be written as 103 Pa which is written as 1 kPa in prefix form, the k being accepted as a symbol to represent 1000 or 103. Studying, or working, in an engineering and science discipline, you very quickly become familiar with the standard units of measurement, the prefixes used and engineering notation. An electronic calculator is extremely helpful with engineering notation.
Unit conversion is very important because the rest of the world other than three countries uses the metric system. So, converting units is important in science and engineering because it uses the metric system.
Without the ability to measure, it would be difficult for scientists to conduct experiments or form theories. Not only is measurement important in science and engineering, it is also essential in farming, construction, manufacturing, commerce, and numerous other occupations and activities.
Measurement provides a standard for everyday things and processes. Examples include weight, temperature, length, currency and time, and all play a very important role in our lives.
Chapter 1 General conversions and Greek alphabet
Length (metric)
General conversions
kilometre (km) 1000 metres (m)
metre (m) 100 centimetres (cm) 1 metre (m) 1000 millimetres (mm)
British gallon 4 qt 4.545 l 1.201 US gallon 1 US gallon 3.785 l
1 kilogram (kg) 1000 g 2.2046 pounds (lb) 1 lb 16 oz 453.6 g 1 tonne (t) 1000 kg 0.9842 ton
1 km/h 0.2778 m/s 0.6214 m.p.h. 1 m.p.h. 1.609 km/h 0.4470 m/s 1 rad/s 9.5493 rev/min 1 knot 1 nautical mile per hour 1.852 km/h 1.15 m.p.h.
1 km/h 0.540 knots 1 m.p.h. 0.870 knots
measure 1 rad 57.296°
Letter Name
Alpha
Epsilon
Zeta
Eta
Iota
Mu
Omicron
Greek alphabet
Chapter 2 Basic SI units, derived units and common prefixes
Basic SI units
Quantity
Unit
Length metre, m
Mass kilogram, kg
Time second, s
Electric current ampere, A
Thermodynamic temperature kelvin, K
Luminous intensity candela, cd
Amount of substance mole, mol
Plane angle
SI supplementary units
radian, rad
Solid angle steradian, sr
Derived units
Quantity Unit
Electric capacitance farad, F
Electric charge coulomb, C
Electric conductance siemens, S
Electric potential difference volts, V
Electrical resistance ohm,
Energy joule, J
Force Newton, N
Frequency hertz, Hz
Illuminance lux, lx
Inductance henry, H
Luminous flux lumen, lm
Magnetic flux weber, Wb
Magnetic flux density tesla, T
Power watt, W
Pressure pascal, Pa
Some other derived units not having special names
Quantity Unit
Acceleration metre per second squared, m/s2
Angular velocity radian per second, rad/s
Area square metre, m2
Current density ampere per metre squared, A/m2
Density kilogram per cubic metre, kg/m3
Dynamic viscosity pascal second, Pa s
Electric charge density coulomb per cubic metre, C/m3
Electric field strength volt per metre, V/m
Energy density joule per cubic metre, J/m3
Heat capacity joule per Kelvin, J/K
Quantity Unit
Heat flux density watt per square metre, W/m3
Kinematic viscosity square metre per second, m2/s
Luminance candela per square metre, cd/m2
Magnetic field strength ampere per metre, A/m
Moment of force newton metre, Nm
Permeability henry per metre, H/m
Permittivity farad per metre, F/m
Specific volume cubic metre per kilogram, m3/kg
Surface tension newton per metre, N/m
Thermal conductivity watt per metre Kelvin, W/(mK)
Velocity metre per second, m/s2
Volume cubic metre, m3
Common prefixes
Prefix Name Meaning
Y yotta multiply by 1024
Z zeta multiply by 1021
E exa multiply by 1018
P peta multiply by 1015
T tera multiply by 1012
G giga multiply by 109
M mega multiply by 106
k kilo multiply by 103
m milli multiply by 10 3
micro multiply by 10 6
n nano multiply by 10 9
p pico multiply by 10 12
f femto multiply by 10 15
a atto multiply by 10 18
z zepto multiply by 10 21
y yocto multiply by 10 24
Chapter 3 Some physical and mathematical constants
Below are listed some physical and mathematical constants, each stated correct to 4 decimal places, where appropriate.
Astronomical constants
Chapter 4 Recommended mathematical symbols
equal to
not equal to
identically equal to
corresponds to
approximately equal to
approaches
proportional to
infinity
smaller than
larger than
smaller than or equal to
larger than or equal to
much smaller than
much larger than
plus
minus plus or minus
minus or plus
a multiplied by b
or a b or a ? b a divided by ba b or a/borab 1
magnitude of a
a raised to power n
square root of a
n’th root of a aora or a n 1 n 1/n
mean value of a a
factorial of a a! sum
function of x f(x)
limit to which f(x) tends as x approaches a → lim f( x) xa finite increment of x Dx variation of x x
differential coefficient of f(x) with respect to x ′ df dx or df/dyorf (x)
differential coefficient of order n of f(x) df dx or df/dxorf (x) n n n2 n
partial differential coefficient of f(x, y, …) w.r.t. x when y, … are held constant
total differential of f df indefinite integral of f(x) with respect to x
definite integral of f(x) from x a to x b
f(x,y,...) x or f x or f y x
f( x) dx
f( x) dx a b
logarithm to the base a of x loga x common logarithm of x lg x or log10 x exponential of x ex or exp x natural logarithm of x ln x or loge x sine of x sin x cosine of x cos x tangent of x tan x secant of x sec x cosecant of x cosec x cotangent of x cot x inverse sine of x sin 1 x or arcsin x inverse cosine of x cos 1 x or arccos x inverse tangent of x tan 1 x or arctan x inverse secant of x sec 1 x or arcsec x inverse cosecant of x cosec 1 x or arccosec x inverse cotangent of x cot 1 x or arccot x hyperbolic sine of x sinh x hyperbolic cosine of x cosh x hyperbolic tangent of x tanh x hyperbolic secant of x sech x hyperbolic cosecant of x cosech x
hyperbolic cotangent of x coth x
inverse hyperbolic sine of x sinh 1 x or arsinh x
inverse hyperbolic cosine of x cosh 1 x or arcosh x
inverse hyperbolic tangent of x tanh 1 x or artanh x
inverse hyperbolic secant of x sech 1 x or arsech x
inverse hyperbolic cosecant of x cosech 1 x or arcosech x
inverse hyperbolic cotangent of x coth 1 x or arcoth x
complex operator i, j modulus of z |z| argument of z arg z complex conjugate of z z* transpose of matrix A AT determinant of matrix A |A|
vector A or A → magnitude of vector A |A|
scalar product of vectors A and B A • B vector product of vectors A and B A B
Chapter
5 Symbols for physical quantities
(a) Space and time
angle (plane angle)
solid angle
height
thickness d, radius r diameter d distance along path s, L rectangular co-ordinates x, y, z cylindrical co-ordinates r, φ, z
spherical co-ordinates r, θ, φ area A volume V time t
angular speed, d dt
angular acceleration, d dt
du dt acceleration, a acceleration of free fall
speed of light in a vacuum
Mach number Ma
(b) Periodic and related phenomena
period
frequency
rotational frequency
(c) Mechanics
second moment of area
second polar moment of area
torque; moment of couple
strain
shear strain
Young’s modulus
shear modulus
bulk modulus
Poisson ratio
energy
potential energy
kinetic energy
E, W
Ep, V,
Ek, T, K
power P
gravitational constant G
Reynold’s number Re
(d) Thermodynamics
thermodynamic temperature T, common temperature
linear expansivity
cubic expansivity
, heat; quantity of heat
q work; quantity of work
w heat flow rate
thermal conductivity
heat capacity
specific heat capacity
internal energy
enthalpy
Helmholtz function A, F
Planck function
specific entropy
specific internal energy u, e specific enthalpy h specific Helmholz function a, f
(e) Electricity and magnetism
Electric charge; quantity of electricity
electric current
charge density
surface charge density
electric field strength
electric potential
electric potential difference
electromotive force
electric displacement
electric flux
capacitance
permittivity
permittivity of a vacuum
relative permittivity
electric current density
magnetic field strength
magnetomotive force
magnetic flux
magnetic flux density
self inductance
mutual inductance M coupling coefficient k leakage coefficient
permeability
permeability of a vacuum
0 relative permeability
r magnetic moment m resistance R resistivity conductivity , reluctance Rm, S permeance number of turns N number of phases m number of pairs of poles p loss angle
phase displacement
impedance Z reactance X
resistance R quality factor Q admittance Y susceptance B conductance G power, active P power, reactive Q power, apparent S
(f) Light and related electromagnetic radiations
radiant energy Q, Qe radiant flux, radiant power , e, P radiant intensity I, Ie radiance L, Le radiant exitance M, Me irradiance E, Ee emissivity e quantity of light Q, Qv luminous flux , v luminous intensity I, Iv luminance L, Lv luminous exitance M, Mv illuminance E, Ev light exposure H luminous efficacy K absorption factor, absorptance
reflexion factor, reflectance
transmission factor, transmittance
linear extinction coefficient
linear absorption coefficient
refractive index
refraction
angle of optical rotation
(g) Acoustics
R
speed of sound c speed of longitudinal waves cl speed of transverse waves
group speed
sound energy flux
sound intensity
ct
cg
P
I, J
reflexion coefficient
acoustic absorption coefficient , a
transmission coefficient
dissipation coefficient
loudness level
(h) Physical chemistry
atomic weight
molecular weight
LN
Ar
Mr amount of substance
molar mass
molar volume
molar internal energy
molar enthalpy
molar heat capacity
molar entropy
molar Helmholtz function
molar Gibbs function
(molar) gas constant
compression factor
mole fraction of substance B
n
M
Vm
Um
Hm
Cm
Sm
Am
Gm
R
Z
xB
mass fraction of substance B wB
volume fraction of substance B
φB
molality of solute B mB
amount of substance concentration of solute B cB
chemical potential of substance B
absolute activity of substance B
B
B
partial pressure of substance B in a gas mixture pB fugacity of substance B in a gas mixture fB
relative activity of substance B
B
activity coefficient (mole fraction basis) fB
activity coefficient (molality basis)
B
activity coefficient (concentration basis) yB
osmotic coefficient
φ, g
osmotic pressure
surface concentration
electromotive force
E
Faraday constant F charge number of ion i zi
ionic strength I velocity of ion i vi
electric mobility of ion i
electrolytic conductivity
molar conductance of electrolyte
transport number of ion i
molar conductance of ion i
overpotential
exchange current density
electrokinetic potential
intensity of light
transmittance
absorbance
(linear) absorption coefficient
molar (linear) absorption coefficient
angle of optical rotation
specific optical rotatory power
molar optical rotatory power
molar refraction
stoiciometric coefficient of molecules B
extent of reaction
affinity of a reaction
equilibrium constant
degree of dissociation
rate of reaction
rate constant of a reaction
activation energy of a reaction
(i) Molecular physics
Avogadro constant L, NA number of molecules
number density of molecules
molecular mass
molecular velocity
molecular position
molecular momentum
average velocity
average speed
most probable speed
mean free path
molecular attraction energy
interaction energy between molecules i and j
distribution function of speeds
Boltzmann function
generalized co-ordinate
generalized momentum
volume in phase space
Boltzmann constant
partition function
grand partition function
statistical weight
symmetrical number
dipole moment of molecule
quadrupole moment of molecule polarizability of molecule
Planck constant h characteristic temperature
Debye temperature D
Einstein temperature
E
rotational temperature r
vibrational temperature v
Stefan-Boltzmann constant
first radiation constant c1
second radiation constant c2
rotational quantum number J, K
vibrational quantum number v
(j) Atomic and nuclear physics
nucleon number; mass number A atomic number; proton number Z neutron number N (rest) mass of atom ma unified atomic mass constant mu (rest) mass of electron me (rest) mass of proton mp (rest) mass of neutron mn elementary charge (of protons) e
