engineering mathematics pocket book fourth edition pdf

Engineering Mathematics
Pocket Book
Fourth Edition

John Bird


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Engineering Mathematics
Pocket Book
Fourth edition

John Bird BSc(Hons), CEng, CSci, CMath,
FIMA, FIET, MIEE, FIIE, FCollT

AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD
PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Newnes is an imprint of Elsevier


Newnes is an imprint of Elsevier
Linace House, Jordan Hill, Oxford OX2 8DP, UK
30 Corporate Drive, Suite 400, Burlington, MA 01803, USA
First published as the Newnes Mathematics for Engineers Pocket Book 1983
Reprinted 1988, 1990 (twice), 1991, 1992, 1993
Second edition 1997
Third edition as the Newnes Engineering Mathematics Pocket Book 2001
Fourth edition as the Engineering Mathematics Pocket Book 2008

Copyright © 2008 John Bird, Published by Elsevier Ltd. All rights reserved
The right of John Bird to be identified as the author of this work has been asserted
in accordance with the Copyright, Designs and Patents Act 1988
No part of this publication may be reproduced, stored in a retrieval system or
transmitted in any form or by any means electronic, mechanical, photocopying,
recording or otherwise without the prior written permission of the publisher
Permission may be sought directly from Elsevier’s Science & Technology Rights
Department in Oxford, UK: phone (ϩ44) (0) 1865 843830; fax (ϩ44) (0) 1865
853333; email: Alternatively you can submit your request
online by visiting the Elsevier website at http:elsevier.com/locate/permissions,
and selecting Obtaining permission to use Elsevier material
Notice
No responsibility is assumed by the publisher for any injury and/or damage to persons
or property as a matter of products liability, negligence or otherwise, or from any
use or operation of any methods, products, instructions or ideas contained in the
material herein.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing in Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN: 978-0-7506-8153-7

For information on all Newnes publications
visit our web site at
Typeset by Charon Tec Ltd., A Macmillan Company.
(www.macmillansolutions.com)

Printed and bound in United Kingdom
08 09 10 11 12

10 9 8 7 6 5 4 3 2 1


Contents
Preface

xi

1
1.1
1.2
1.3
1.4
1.5
1.6

Engineering Conversions, Constants and Symbols
General conversions
Greek alphabet
Basic SI units, derived units and common prefixes
Some physical and mathematical constants
Recommended mathematical symbols
Symbols for physical quantities

1
1
2
3
5
7

10

2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10

Some Algebra Topics
Polynomial division
The factor theorem
The remainder theorem
Continued fractions
Solution of quadratic equations by formula
Logarithms
Exponential functions
Napierian logarithms
Hyperbolic functions
Partial fractions

20
20
21
23

24
25
28
31
32
36
41

3
3.1
3.2
3.3
3.4
3.5
3.6
3.7

Some Number Topics
Arithmetic progressions
Geometric progressions
The binomial series
Maclaurin’s theorem
Limiting values
Solving equations by iterative methods
Computer numbering systems

46
46
47
49

54
57
58
65

4
4.1
4.2
4.3
4.4

Areas and Volumes
Area of plane figures
Circles
Volumes and surface areas of regular solids
Volumes and surface areas of frusta of pyramids and cones

73
73
77
82
88


vi

Contents

4.5
4.6

4.7

The frustum and zone of a sphere
Areas and volumes of irregular figures and solids
The mean or average value of a waveform

92
95
101

5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14

105
105
106
108

109
110
112
113
116
119
124
125
127
134

5.15

Geometry and Trigonometry
Types and properties of angles
Properties of triangles
Introduction to trigonometry
Trigonometric ratios of acute angles
Evaluating trigonometric ratios
Fractional and surd forms of trigonometric ratios
Solution of right-angled triangles
Cartesian and polar co-ordinates
Sine and cosine rules and areas of any triangle
Graphs of trigonometric functions
Angles of any magnitude
Sine and cosine waveforms
Trigonometric identities and equations
The relationship between trigonometric and hyperbolic
functions
Compound angles

6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9

Graphs
The straight line graph
Determination of law
Logarithmic scales
Graphical solution of simultaneous equations
Quadratic graphs
Graphical solution of cubic equations
Polar curves
The ellipse and hyperbola
Graphical functions

149
149
152
158
163
164
170

171
178
180

7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8

Vectors
Scalars and vectors
Vector addition
Resolution of vectors
Vector subtraction
Relative velocity
Combination of two periodic functions
The scalar product of two vectors
Vector products

188
188
189
191
192
195

197
200
203

8
8.1
8.2

Complex Numbers
General formulae
Cartesian form

206
206
206

139
141


Contents

vii

8.3
8.4
8.5
8.6

Polar form

Applications of complex numbers
De Moivre’s theorem
Exponential form

209
211
213
215

9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8

Matrices and Determinants
Addition, subtraction and multiplication of matrices
The determinant and inverse of a 2 by 2 matrix
The determinant of a 3 by 3 matrix
The inverse of a 3 by 3 matrix
Solution of simultaneous equations by matrices
Solution of simultaneous equations by determinants
Solution of simultaneous equations using Cramer’s rule
Solution of simultaneous equations using Gaussian
elimination

217
217
218
220
221
223
226
230

10
10.1
10.2
10.3
10.4
10.5
10.6
10.7

Boolean Algebra and Logic Circuits
Boolean algebra and switching circuits
Simplifying Boolean expressions
Laws and rules of Boolean algebra
De Morgan’s laws
Karnaugh maps
Logic circuits and gates
Universal logic gates

234
234
238

239
241
242
248
253

11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
11.12
11.13
11.14
11.15
11.16
11.17
11.18
11.19
11.20

Differential Calculus and its Applications
Common standard derivatives

Products and quotients
Function of a function
Successive differentiation
Differentiation of hyperbolic functions
Rates of change using differentiation
Velocity and acceleration
Turning points
Tangents and normals
Small changes using differentiation
Parametric equations
Differentiating implicit functions
Differentiation of logarithmic functions
Differentiation of inverse trigonometric functions
Differentiation of inverse hyperbolic functions
Partial differentiation
Total differential
Rates of change using partial differentiation
Small changes using partial differentiation
Maxima, minima and saddle points of functions of
two variables

258
258
259
261
262
263
264
265
267

270
272
273
276
279
281
284
289
292
293
294

232

295


viii

Contents

12
12.1
12.2
12.3
12.4

Integral Calculus and its Applications
Standard integrals
Non-standard integrals

Integration using algebraic substitutions
Integration using trigonometric and hyperbolic
substitutions
Integration using partial fractions
θ
The t ϭ tan substitution
2
Integration by parts
Reduction formulae
Numerical integration
Area under and between curves
Mean or average values
Root mean square values
Volumes of solids of revolution
Centroids
Theorem of Pappus
Second moments of area

303
303
307
307

Differential Equations
dy
The solution of equations of the form
ϭ f(x)
dx
dy
13.2 The solution of equations of the form

ϭ f(y)
dx
dy
ϭ f(x).f(y)
13.3 The solution of equations of the form
dx
13.4 Homogeneous first order differential equations
13.5 Linear first order differential equations
13.6 Second order differential equations of the form
d2y
dy
a 2 ϩb
ϩ cy ϭ 0
dx
dx
13.7 Second order differential equations of the form
d2y
dy
a 2 ϩb
ϩ cy ϭ f(x)
dx
dx
13.8 Numerical methods for first order differential equations
13.9 Power series methods of solving ordinary differential
equations
13.10 Solution of partial differential equations

366
366

12.5
12.6
12.7
12.8
12.9
12.10
12.11
12.12
12.13
12.14
12.15
12.16
13
13.1

14
14.1
14.2

Statistics and Probability
Presentation of ungrouped data
Presentation of grouped data

310
317
319
323
326
331
336

343
345
347
350
354
359

367
368
371
373
375

379
385
394
405
416
416
420


Contents

ix

14.3
14.4
14.5
14.6

14.7
14.8
14.9
14.10
14.11
14.12
14.13
14.14
14.15

Measures of central tendency
Quartiles, deciles and percentiles
Probability
The binomial distribution
The Poisson distribution
The normal distribution
Linear correlation
Linear regression
Sampling and estimation theories
Chi-square values
The sign test
Wilcoxon signed-rank test
The Mann-Whitney test

424
429
431
434
435
437

443
445
447
454
457
460
464

15
15.1
15.2
15.3
15.4
15.5

Laplace Transforms
Standard Laplace transforms
Initial and final value theorems
Inverse Laplace transforms
Solving differential equations using Laplace transforms
Solving simultaneous differential equations using
Laplace transforms

472
472
477
480
483

Fourier Series

Fourier series for periodic functions of period 2π
Fourier series for a non-periodic function over range 2π
Even and odd functions
Half range Fourier series
Expansion of a periodic function of period L
Half-range Fourier series for functions defined over range L
The complex or exponential form of a Fourier series
A numerical method of harmonic analysis
Complex waveform considerations

492
492
496
498
501
504
508
511
518
522

16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8

16.9
Index

487

525


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Preface
Engineering Mathematics Pocket Book 4th 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 studies and/or work situation – a handy book to have on the
bookshelf to delve into as the need arises.
In this 4th edition, the text has been re-designed to make information easier to access. Essential theory, formulae, definitions, laws and
procedures are stated clearly at the beginning of each section, and
then it is demonstrated how to use such information in practice.
The text is divided, for convenience of reference, into sixteen main
chapters embracing engineering conversions, constants and symbols, some algebra topics, some number topics, areas and volumes,
geometry and trigonometry, graphs, vectors, complex numbers,
matrices and determinants, Boolean algebra and logic circuits, differential and integral calculus and their applications, differential equations, statistics and probability, Laplace transforms and Fourier series.
To aid understanding, over 500 application examples have been
included, together with over 300 line diagrams.
The text assumes little previous knowledge and is suitable for a
wide range of courses of study. It will be particularly useful for students studying mathematics within National and Higher National
Technician Certificates and Diplomas, GCSE and A levels, for

Engineering Degree courses, and as a reference for those in the
engineering industry.
John Bird
Royal Naval School of Marine Engineering,
HMS Sultan, formerly University of Portsmouth
and Highbury College, Portsmouth


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1

Engineering Conversions,
Constants and Symbols

1.1 General conversions
Length (metric)

1 kilometre (km) ϭ 1000 metres (m)
1 metre (m) ϭ 100 centimetres (cm)
1 metre (m) ϭ 1000 millimetres (mm)
1 cm ϭ 10Ϫ2 m
1 mm ϭ 10Ϫ3 m
1 micron (μ) ϭ 10Ϫ6 m
1 angstrom (A) ϭ 10Ϫ10 m

Length (imperial)

1 inch (in) ϭ 2.540 cm or 1 cm ϭ 0.3937 in

1 foot (ft) ϭ 30.48 cm
1 mile (mi) ϭ 1.609 km or 1 km ϭ 0.6214 mi
1 cm ϭ 0.3937 in
1 m ϭ 39.37 in ϭ 3.2808 ft ϭ 1.0936 yd
1 km ϭ 0.6214 mile
1 nautical mile ϭ 1.15 mile

Area (metric)

1 m2 ϭ 106 mm2
1 mm2 ϭ 10Ϫ6 m2
1 m2 ϭ 104 cm2
1 cm2 ϭ 10Ϫ4 m2
1 hectare (ha) ϭ 104 m2

Area (imperial)

1 m2 ϭ 10.764 ft2 ϭ 1.1960 yd2
1 ft2 ϭ 929 cm2
1 mile2 ϭ 640 acres
1 acre ϭ 43560 ft2 ϭ 4840 yd2
1 ha ϭ 2.4711 acre ϭ 11960 yd2 ϭ 107639 ft2

Volume

1 litre (l) ϭ 1000 cm3
1 litre ϭ 1.057 quart (qt) ϭ 1.7598 pint (pt) ϭ
0.21997 gal
1 m3 ϭ 1000 l

2

Engineering Mathematics Pocket Book

1 British gallon ϭ 4 qt ϭ 4.545 l ϭ 1.201 US
gallon
1 US gallon ϭ 3.785 l
Mass

1 kilogram (kg) ϭ 1000 g ϭ 2.2046 pounds (lb)
1 lb ϭ 16 oz ϭ 453.6 g
1 tonne (t) ϭ 1000 kg ϭ 0.9842 ton

Speed

1 km/h ϭ 0.2778 m/s ϭ 0.6214 m.p.h.
1 m.p.h. ϭ 1.609 km/h ϭ 0.4470 m/s
1 rad/s ϭ 9.5493 rev/min
1 knot ϭ 1 nautical mile per hour ϭ
1.852 km/h ϭ 1.15 m.p.h.
1 km/h ϭ 0.540 knots
1 m.p.h. ϭ 0.870 knots

Angular measure

1 rad ϭ 57.296°

1.2 Greek alphabet
Letter Name

Upper Case

Lower Case

Alpha

A

α

Beta

B

β

Gamma

Γ

γ
δ

Delta

Δ

Epsilon

E

ε

Zeta

Z

ζ

Eta

H

η

Theta

θ

θ

Iota

l

ι

Kappa

K

κ

Lambda

Λ

λ

Mu

M

μ

Nu

N

ν

Xi

Ξ

ξ


Engineering Conversions, Constants and Symbols

Omicron

O

o

Pi

Π

π

Rho

P

ρ

Sigma

Σ

σ

Tau

T

τ

Upsilon

Y

υ

Phi

Φ

φ

Chi

X

χ

Psi

Ψ

␺

Omega

Ω

ω

1.3 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

SI supplementary units

Plane angle

radian, rad

Solid angle

steradian, sr

3


4

Engineering Mathematics Pocket Book

Derived units
Quantity

Unit

Electric capacitance
Electric charge

Electric conductance
Electric potential difference
Electrical resistance
Energy
Force
Frequency
Illuminance
Inductance
Luminous flux
Magnetic flux
Magnetic flux density
Power
Pressure

farad, F
coulomb, C
siemens, S
volts, V
ohm, Ω
joule, J
Newton, N
hertz, Hz
lux, lx
henry, H
lumen, lm
weber, Wb
tesla, T
watt, W
pascal, Pa

Some other derived units not having special names
Quantity

Unit

Acceleration
Angular velocity
Area
Current density
Density
Dynamic viscosity
Electric charge density
Electric field strength
Energy density
Heat capacity
Heat flux density
Kinematic viscosity
Luminance

metre per second squared, m/s2
radian per second, rad/s
square metre, m2
ampere per metre squared, A/m2
kilogram per cubic metre, kg/m3
pascal second, Pa s
coulomb per cubic metre, C/m3
volt per metre, V/m
joule per cubic metre, J/m3
joule per Kelvin, J/K
watt per square metre, W/m3

square metre per second, m2/s
candela per square metre, cd/m2


Engineering Conversions, Constants and Symbols

Magnetic field strength
Moment of force
Permeability
Permittivity
Specific volume
Surface tension
Thermal conductivity
Velocity
Volume

5

ampere per metre, A/m
newton metre, Nm
henry per metre, H/m
farad per metre, F/m
cubic metre per kilogram, m3/kg
newton per metre, N/m
watt per metre Kelvin, W/(mK)
metre per second, m/s2
cubic metre, m3

Common prefixes
Prefix

Name

Meaning

Y
Z
E
P
T
G
M
k
m
μ
n
p
f
a
z
y

yotta
zeta
exa
peta
tera
giga
mega
kilo

milli
micro
nano
pico
femto
atto
zepto
yocto

multiply by 1024
multiply by 1021
multiply by 1018
multiply by 1015
multiply by 1012
multiply by 109
multiply by 106
multiply by 103
multiply by 10Ϫ3
multiply by 10Ϫ6
multiply by 10Ϫ9
multiply by 10Ϫ12
multiply by 10Ϫ15
multiply by 10Ϫ18
multiply by 10Ϫ21
multiply by 10Ϫ24

1.4 Some physical and mathematical constants
Below are listed some physical and mathematical constants, each
stated correct to 4 decimal places, where appropriate.

6

Engineering Mathematics Pocket Book

Quantity

Symbol

Value

Speed of light in a
vacuum
Permeability of free
space
Permittivity of free
space
Elementary charge
Planck constant

c

2.9979 ϫ 108 m/s

μ0

4π ϫ 10Ϫ7 H/m

ε0

8.8542 ϫ 10Ϫ12 F/m

e
h

1.6022 ϫ 10Ϫ19 C
6.6261 ϫ 10Ϫ34 J s

ϭ
Fine structure constant
Coulomb force
constant
Gravitational constant
Atomic mass unit
Rest mass of electron
Rest mass of proton
Rest mass of neutron
Bohr radius
Compton wavelength
of electron
Avogadro constant
Boltzmann constant
Stefan-Boltzmann
constant
Bohr constant
Nuclear magnetron
Triple point
temperature
Molar gas constant
Micron

Characteristic
impedance of vacuum

αϭ

h
2π
e2
4πε0 c

1.0546 ϫ 10Ϫ34 J s
7.2974 ϫ 10Ϫ3

ke
G
u
me
mp
mn
a0
λC

8.9875 ϫ 109 Nm2/C2
6.6726 ϫ 10Ϫ11 m3/kg s2
1.6605 ϫ 10Ϫ27 kg
9.1094 ϫ 10Ϫ31 kg
1.6726 ϫ 10Ϫ27 kg
1.6749 ϫ 10Ϫ27 kg
5.2918 ϫ 10Ϫ11 m
2.4263 ϫ 10Ϫ12 m

NA
k
σ

6.0221 ϫ 1023/mol
1.3807 ϫ 10Ϫ23 J/K
5.6705 ϫ 10Ϫ8 W /m2K4

μB
μN
Tt

9.2740 ϫ 10Ϫ24 J/T
5.0506 ϫ 10Ϫ27 J/T
273.16 K

R
μm
Zo

8.3145 J/K mol
10Ϫ6 m
376.7303 Ω


Engineering Conversions, Constants and Symbols

7

Astronomical constants
Mass of earth
Radius of earth
Gravity of earth’s surface
Mass of sun
Radius of sun
Solar effective temperature
Luminosity of sun
Astronomical unit
Parsec
Jansky
Tropical year
Standard atmosphere

5.976 ϫ 1024 kg
6.378 ϫ 106 m
9.8067 m/s2
1.989 ϫ 1030 kg
6.9599 ϫ 108 m
5800 K
3.826 ϫ 1026 W
1.496 ϫ 1011 m
3.086 ϫ 1016 m
10Ϫ26 W/m2HZ
3.1557 ϫ 107 s
101325 Pa

mE
RE
g

M
R
Te
L
AU
pc
Jy
atm

Mathematical constants
Pi (Archimedes’ constant)
Exponential constant
Apery’s constant
Catalan’s constant
Euler’s constant
Feigenbaum’s constant
Feigenbaum’s constant
Gibb’s constant
Golden mean
Khintchine’s constant

π
e
ζ (3)
G
γ
α
δ
G
φ

K

3.1416
2.7183
1.2021
0.9160
0.5772
2.5029
4.6692
1.8519
1.6180
2.6855

1.5 Recommended mathematical symbols
equal to
not equal to
identically equal to
corresponds to
approximately equal to
approaches
proportional to

ϭ
϶
ϵ
‫־‬
Ϸ
→
ϰ

8

Engineering Mathematics Pocket Book

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

ϱ
Ͻ
Ͼ
Յ
Ն
ϽϽ
ϾϾ
ϩ
Ϫ
Ϯ
ϯ
ab or a ϫ b or a и b

a divided by b

a
or a/b or abϪ1
b

magnitude of a
a raised to power n

|a|
an
1

square root of a

a or a 2
1

n’th root of a

n

mean value of a

a

factorial of a
sum
function of x

limit to which f(x) tends as
x approaches a
finite increment of x
variation of x

a!
Σ
f(x)

⌬x
δx

differential coefficient of f(x) with
respect to x

df
or df/dy or fЈ(x)
dx

differential coefficient of order n of f(x)

dnf
or dnf/dx 2 or fn (x)
dxn

a or an or a1/n

lim f( x )

x→a

Engineering Conversions, Constants and Symbols

partial differential coefficient of
f(x, y, …) w.r.t. x when y, … are held
constant
total differential of f
indefinite integral of f(x) with
respect to x

9

⎛ ∂f ⎞
∂f(x,y,...)
or ⎜⎜ ⎟⎟⎟ or fx
⎜⎝ ∂x ⎠
∂x
y
df

∫

f( x )dx

definite integral of f(x) from
x ϭ a to x ϭ b

∫a

logarithm to the base a of x
common logarithm of x
exponential of x
natural logarithm of x
sine of x
cosine of x
tangent of x
secant of x
cosecant of x
cotangent of x
inverse sine of x
inverse cosine of x
inverse tangent of x
inverse secant of x
inverse cosecant of x
inverse cotangent of x
hyperbolic sine of x
hyperbolic cosine of x
hyperbolic tangent of x
hyperbolic secant of x
hyperbolic cosecant of x
hyperbolic cotangent of x
inverse hyperbolic sine of x
inverse hyperbolic cosine of x
inverse hyperbolic tangent of x
inverse hyperbolic secant of x
inverse hyperbolic cosecant of x
inverse hyperbolic cotangent of x

loga X

lg x or log10 x
ex or exp x
ln x or loge x
sin x
cos x
tan x
sec x
cosec x
cot x
sinϪ1 x or arcsin x
cosϪ1 x or arccos x
tanϪ1 x or arctan x
secϪ1 x or arcsec x
cosecϪ1 x or arccosec x
cotϪ1 x or arccot x
sinh x
cosh x
tanh x
sech x
cosech x
coth x
sinhϪ1 x or arsinh x
coshϪ1 x or arcosh x
tanhϪ1 x or artanh x
sechϪ1 x or arsech x
cosechϪ1 x or arcosech x
cothϪ1 x or arcoth x

b

f( x )dx


10

Engineering Mathematics Pocket Book

complex operator
modulus of z
argument of z
complex conjugate of z
transpose of matrix A
determinant of matrix A

i, j
|z|
arg z
z*
AT
|A|

vector
magnitude of vector A
scalar product of vectors A and B
vector product of vectors A and B

A or A
|A|
A•B
A؋B

1.6 Symbols for physical quantities
(a) Space and time
angle (plane angle)
solid angle
length
breadth
height
thickness
radius
diameter
distance along path
rectangular co-ordinates
cylindrical co-ordinates
spherical co-ordinates
area
volume
time

angular speed,

dθ
dt

angular acceleration,
speed,

ds
dt

α, β, γ, θ, φ, etc.
Ω, ω
l
b
h
d, δ
r
d
s, L
x, y, z
r, φ, z
r,θ, φ
A
V
t
ω

d
dt

α
u, v, w


Engineering Conversions, Constants and Symbols

acceleration,

du
dt

acceleration of free fall
speed of light in a vacuum
Mach number

a
g
c
Ma

(b) Periodic and related phenomena
period
frequency
rotational frequency
circular frequency
wavelength
damping coefficient
attenuation coefficient
phase coefficient
propagation coefficient

T
f
n
ω
λ
δ
α
β
γ

(c) Mechanics
mass
density
relative density
specific volume
momentum
moment of inertia
second moment of area
second polar moment of area
force
bending moment
torque; moment of couple
pressure
normal stress
shear stress
linear strain
shear strain
volume strain
Young’s modulus
shear modulus
bulk modulus

m
ρ
d
v
p
I, J
Ia

Ip
F
M
T
p, P
σ
τ
ε, e
γ
θ
E
G
K

11


12

Engineering Mathematics Pocket Book

Poisson ratio
compressibility
section modulus
coefficient of friction
viscosity
fluidity
kinematic viscosity
diffusion coefficient
surface tension

angle of contact
work
energy
potential energy
kinetic energy
power
gravitational constant
Reynold’s number

μ, ν
κ
Z, W
μ
η
φ
ν
D
γ, σ
θ
W
E, W
Ep, V, Φ
Ek, T, K
P
G
Re

(d) Thermodynamics
thermodynamic temperature
common temperature

linear expansivity
cubic expansivity
heat; quantity of heat
work; quantity of work
heat flow rate
thermal conductivity
heat capacity
specific heat capacity
entropy
internal energy
enthalpy
Helmholtz function
Planck function
specific entropy
specific internal energy
specific enthalpy
specific Helmholz function

T, Θ
t, θ
α, λ
α, γ
Q, q
W, w
Φ, q
λ, k
C
c
S
U, E

H
A, F
Y
s
u, e
h
a, f