Mcgraw Hill, Dictionary Of Engineering (2003) Episode 1 ppsx

wireway
means of cooling, and feed and take-up spools banded with wire, metal collars, and inserted
for the wire; used to coat wire with resin.
joints, used largely for municipal water supply,
{ wı
¯
r tra
¯
n}
outfall sewers, and mining irrigation. { wu
˙
d
wireway
[
ENG
]
A trough which is lined with
sta
¯
v pı
¯
p}
sheet metal and has hinged covers, designed to
woofer
[
ENG ACOUS
]
A large loudspeaker de-
house electrical conductors or cables.
signed to reproduce low audio frequencies at
{ wı

¯
rwa
¯
}
relatively high power levels; usually used in com-
wire weight gage
[
ENG
]
A river gage in which a
bination with a crossover network and a high-
weight suspended on a wire is lowered to the
frequency loudspeaker called a tweeter.
water surface from a bridge or other overhead
{ wu
˙
fиər}
structure to measure the distance from a point
word concatenation system
[
ENG ACOUS
]
The
of known elevation on the bridge to the water
simplest form of voice response system, which
surface; the distance is usually measured by
retrieves previously spoken versions of words or
counting the number of revolutions of a drum
phrases and carefully forms them into a se-
required to lower the weight, and a counter is

quence without pauses, to approximate normally
provided which reads the water stage directly.
spoken word sequences. { wo
˙
rd kənkatиəna
¯
и
{ wı
¯
r wa
¯
t ga
¯
j}
shən sisиtəm}
wiring
[
ELEC
]
The installation and utilization of
work
[
ELEC
]
See load.
[
IND ENG
]
The physi-
a system of wire for conduction of electricity.

cal or mental effort expended in the performance
Also known as electric wiring.
[
ENG
]
A form-
of a task.
[
MECH
]
The transference of energy
ing process in which the edge of a sheet-metal
that occurs when a force is applied to a body
part is rolled over a wire to produce a tubular
that is moving in such a way that the force has
rim containing the wire. { wı
¯
rиiŋ }
a component in the direction of the body’s
wiring diagram
See circuit diagram. { wı
¯
rиiŋdı
¯
и
motion; it is equal to the line integral of the
əgram }
force over the path taken by the body. { wərk }
wiring harness
[

ELEC
]
An array of insulated
work breakdown structure
[
IND ENG
]
A hierar-
conductors bound together by lacing cord, metal
chy designed to organize, define, and display all
bands, or other binding, in an arrangement suit-
the work that must be performed in order to
able for use only in specific equipment for which
accomplish the objectives of a project. { ¦wərk
the harness was designed; it may include termi-
¦bra
¯
kdau
˙
n strəkиchər}
nations. { wı
¯
rиiŋha
¨
rиnəs}
work cycle
[
IND ENG
]
A sequence of tasks, op-

Wobbe index
[
THERMO
]
A measure of the
erations, and processes, or a pattern of manual
amount of heat released by a gas burner with a
motions, elements, and activities that is re-
constant orifice, equal to the gross calorific value
peated for each unit of work. { wərk sı
¯
иkəl}
of the gas in British thermal units per cubic foot
work design
See job design. { wərk dizı
¯
n}
at standard temperature and pressure divided
worked penetration
[
ENG
]
Penetration of a
by the square root of the specific gravity of the
sample of lubricating grease immediately after
gas. { wa
¨
иbəindeks }
it has been brought to a specified temperature
wobble friction

[
ENG
]
A force that occurs in pre-
and subjected to strokes in a standard grease
stressed concrete when the prestressing tendon
worker. { wərkt penиətra
¯
иshən}
deviates from its specified profile. { wa
¨
bиəl
work element
[
IND ENG
]
In planning amanufac-
frikиshən}
turing process, a single task that cannot be sub-
wobble wheel roller
[
MECH ENG
]
A roller with
divided. { wərk elиəиmənt }
freely suspended pneumatic tires used in soil
work function
See free energy. { wərk fəŋkиshən}
stabilization. { wa
¨

bиəl ¦we
¯
l ro
¯
иlər}
workhead
See headstock. { wərkhed }
Wollaston wire
[
ENG
]
An extremely fine plati-
working area
[
IND ENG
]
A portion of the work-
num wire,produced by enclosing a platinum wire
place in which a worker moves about while fulfill-
in a silver sheath, drawing them together, and
ing work tasks. { wərkиiŋerиe
¯
иə }
using acid to dissolve away the silver; used in
working envelope
[
MECH ENG
]
The surface
electroscopes, microfuses, and hot-wire instru-

bounding the maximum extent and reach of a
ments. { wu
˙
lиəиstən wı
¯
r}
robot’s wrist, excluding the tool tip. Also
wood-carving tools
[
DES ENG
]
The tools nor-
known as working profile. { wərkиiŋenи
mally used in wood carving; they consist of ad-
vəlo
¯
p}
zes, chisels, gouges, files, and rasps, all of which
working life
See work life. { wərkиiŋlı
¯
f}
vary in size and shape. { wu
˙
d ¦ka
¨
rvиiŋtu
¨
lz }
working load

[
ENG
]
The maximum load that
Woodruff key
[
DES ENG
]
A self-aligning ma-
any structural member is designed to support.
chine key made by a side-milling cutter in the
{ wərkиiŋlo
¯
d}
form of a segment of a disk. { wu
˙
иdrəf ke
¯
}
working pressure
[
ENG
]
The allowable op-
wood screw
[
DES ENG
]
A threaded fastener
erating pressure in a pressurized vessel or con-

with a pointed shank, a slotted or recessed head,
duit, usually calculated by ASME (American
and a sharp tapered thread of relatively coarse
Society of Mechanical Engineers) or API (Ameri-
pitch for use only in wood. { wu
˙
d skru
¨
}
can Petroleum Institute) codes. { wərkиiŋ
woodstave pipe
[
DES ENG
]
A pipe made of nar-
row strips of wood placed side by side and preshиər}
618
wrench
working profile
See working envelope. { wərkиiŋ
work stress
[
IND ENG
]
Any external force that
acts on the body of a worker during the perfor-
pro
¯
fı
¯

l}
mance of a task. { wərk stres }
working Q
See loaded Q. { wərkиiŋkyu
¨
}
work task
[
IND ENG
]
A specified amount of
working space-volume
[
MECH ENG
]
The vol-
work, set of responsibilities, or occupation as-
ume enclosed by a robot’s working envelope.
signed to an individual or to a group. { wərk
{ wərkиiŋspa
¯
s va
¨
lиyəm}
task }
working voltage
See voltage rating. { wərkиiŋ
work tolerance
[
IND ENG

]
A time period during
vo
¯
lиtij }
which a worker can effectively perform a task
work-kinetic energy theorem
[
MECH
]
The theo-
without a rest period while maintaining accept-
rem that the change in the kinetic energy of a
able levels of physiological and emotional well-
particle during a displacement is equal to the
being. { wərk ta
¨
lиəиrəns }
work done by the resultant force on the particle
work unit
[
IND ENG
]
An amount of work or the
during this displacement. { wərk kinedиik ¦enи
result of an amount of work that is treated as
ərиje
¯
thirиəm}
an integer (a single piece of information) when

work life
[
CHEM ENG
]
The period of time a resin
work is being characterized quantitatively.
or anadhesive willremain usable afterit is mixed
{ wərk yu
¨
иnət}
with a catalyst and other ingredients. Also
world coordinates
[
CONT SYS
]
A roboticcoordi-
known as pot life; working life. { wərk lı
¯
f}
nate system that is fixed with respect to the
work measurement
[
IND ENG
]
1.
Determina-
Earth. { wərld ko
¯
o
˙

rdиənиəts }
tion of the difficulty of a given task by using both
world modeling
[
CONT SYS
]
Robot program-
physiologic and biomechanical parameters to
ming that allows the system to perform complex
evaluate compatibility of available motions with
tasks, based on stored data. { wərld ma
¨
dиəlи
motions required to perform the task.
2.
See
iŋ }
ergonometrics. { wərk mezhиərиmənt }
worm
[
DES ENG
]
A shank having at least one
work of adhesion
See adhesional work. { wərk əv
complete tooth (thread) around the pitch sur-
adhe
¯
иzhən}
face; the driver of a worm gear. { wərm }

work package
[
IND ENG
]
The amount of work
worm conveyor
See screw conveyor. { wərm
required to complete a given job that falls within
kənva
¯
иər}
the responsibility of a single unit of the organiza-
worm gear
[
DES ENG
]
A gear with teeth cut on
an angle to be driven by a worm; used to connect
tion handling the project. { wərk pakиij }
nonparallel, nonintersecting shafts. { wərm
work physiology
[
IND ENG
]
An aspect of indus-
gir }
trial engineering that takes into account meta-
worm wheel
[
DES ENG

]
A gear wheel with
bolic cost, measurement and prevention of work
curved teeth that meshes with a worm.
strain, and other ergonomic factors in the design
{ wərm we
¯
l}
of tasks and workplaces. { wərk fizиe
¯
a
¨
lиəиje
¯
}
wow
[
ENG ACOUS
]
A low-frequency flutter;
workpiece
[
IND ENG
]
An object that is being
when caused by an off-center hole in a disk re-
manufactured. { wərkpe
¯
s}
cord, occurs once per revolution of the turnta-

workpiece program
[
CONT SYS
]
A program that
ble. { wau
˙
}
directs the machining of a component under nu-
wrap-around grasp
[
IND ENG
]
A basic grasp
merical or computer control. { wərkpe
¯
s pro
¯
whereby an object is held against the palm by
gram }
the fingers wrapped around it, with the thumb
work sampling
[
IND ENG
]
A technique to meas-
opposing the index finger. { rapиərau
˙
nd
ure work activity as related to delays consisting

grasp }
of intermittent observations of actual work and
wrap forming
See stretch forming. { rap fo
˙
rmи
delays. Also known as activity sampling; fre-
iŋ }
quency study; ratio delay study. { wərk samи
wrapper sheet
[
MECH ENG
]
1.
The outer plate
pliŋ }
enclosing the firebox in a fire-tube boiler.
work standardization
[
IND ENG
]
The establish-
2.
The thinner sheet of a boiler drum having two
ment of uniformity of working conditions, tools,
sheets. { rapиər she
¯
t}
equipment, technical procedures, administrative
wrecking ball

See skull cracker. { rekиiŋbo
˙
l}
procedures, workplace arrangements, motion se-
wrecking bar
See ripping bar. { rekиiŋba
¨
r}
quences, materials, quality requirements, and
wrecking strip
[
CIV ENG
]
A small section that
similar factors which affect the performance of
is fitted into a form for poured concrete and is
work. { wərk stanиdərиdəza
¯
иshən}
easily removed before the main panels to facili-
work station
[
IND ENG
]
A workplace that is in-
tate disassembly of the main components of the
cluded in a production system or on a piece of
form. { rekиiŋstrip }
equipment at which an individual worker may
wrench

[
ENG
]
A manual or power tool with
spend only a portion of a working shift. { wərk
adapted or adjustable jaws or sockets either at
sta
¯
иshən}
the endor between the ends of a lever forholding
work station independence
[
CONT SYS
]
Prop-
or turning a bolt, pipe, or other object.
[
MECH
]
erty of a numerical control or robot program
The combination of a couple and a force which
which does not depend on the nature of the work
is parallel to the torque exerted by the couple.
{ rench }station. { wərksta
¯
иshən inиdəpenиdəns }
619
wrench-head bolt
wrench-head bolt
[

DES ENG
]
A bolt with a plates are replaced by charged knife-edges.
2.
An electrometer in which two conducting fi-
square or hexagonal head designed to be
bers are placed side by side, and their separation
gripped between the jaws of a wrench. { rench
upon charging is measured. { ¦wu
˙
lf ilektra
¨
mи
¦hed bo
¯
lt }
ədиər}
wringing fit
[
DES ENG
]
A fit of zero-to-negative
Wulff process
[
CHEM ENG
]
A chemical process
allowance. { riŋиiŋfit }
to make acetylene and ethylene by cracking a
wrist

[
MECH ENG
]
A set of rotary joints to which
hydrocarbon gas (for example, butane) with
the end effector of a robot is attached. Also
high-temperature steam in a regenerative fur-
known as wrist socket. { rist }
nace. { wu
˙
lf pra
¨
иsəs}
wrist pin
See piston pin. { ris pin }
Wurster process
See air-suspension encapsula-
write head
[
ELECTR
]
Device that stores digital
tion. { wərиstər pra
¨
иsəs}
information as coded electrical pulses on a mag-
wye
[
ELEC
]

Polyphase circuit whose phase dif-
netic drum, disk, or tape. { rı
¯
t hed }
ferences are 120Њ and which when drawn resem-
W-truss
[
CIV ENG
]
A truss having upper and
bles the letter Y.
[
ENG
]
A pipe branching off
lower chords joined by web members that form
a straight main run at an angle of 45Њ. Also
a shape resembling the letter W. { dəbиəlyu
¨
known as Y; yoke. { wı
¯
}
trəs}
wye branch
See Y branch. { wı
¯
branch }
Wulf electrometer
[
ENG

]
1.
A variant of the
wye fitting
See Y fitting. { wı
¯
fı
¯
dиiŋ }
wye level
See Y level. { wı
¯
levиəl}string electrometer in which charged metal
620
X
x-radiation for chemical analysis and for magnifi-
X engine
[
MECH ENG
]
An in-line engine with
cation of 100–1000 diameters; it is based on
the cylinder banks so arranged around the crank-
contact or projection microradiography, reflec-
shaft that they resemble the letter X when the
tion x-ray microscopy, or x-ray image spectrogra-
engine is viewed from the end. { eks enиjən}
phy. { eks ra
¯
mı

¯
иkrəsko
¯
p}
X frame
[
DES ENG
]
An automotive frame which
x-ray monochromator
[
ENG
]
An instrument in
either has side rails bent in at the center of the
which x-rays are diffracted from a crystal to pro-
vehicle, making the overall form that of an X, or
duce a beam having a narrow range of wave-
has an X-shaped member which joins the side
lengths. { eks ra
¯
¦ma
¨
nиə¦kro
¯
ma
¯
dиər}
rails with diagonals for added strength and
x-ray telescope

[
ENG
]
An instrument designed
resistance to torsional stresses. { eks fra
¯
m}
to detect x-rays emanating from a source outside
x-ray diffractometer
[
ENG
]
An instrument used
the earth’s atmosphere and to resolve the x-rays
in x-ray analysis to measure the intensities of
into an image; they are carried to high altitudes
the diffracted beams at different angles. { eks
by balloons, rockets, or space vehicles; although
ra
¯
difrakta
¨
mиədиər}
several types of x-ray detector, involving gas
x-ray goniometer
[
ENG
]
A scale designed to
counters, scintillation counters, and collimators,

measure the angle between the incident and re-
have been used, only one, making use of the
fracted beams in x-ray diffraction analysis.
phenomenon of total external reflection of x-rays
{ eks ra
¯
go
¯
иne
¯
a
¨
mиədиər}
from a surface at grazing incidence, is strictly an
x-ray machine
[
ENG
]
The x-ray tube, power sup-
x-ray telescope. { eks ra
¯
telиəsko
¯
p}
ply, and associated equipment required for pro-
x-ray thickness gage
[
ENG
]
A thickness gage

ducing x-ray photographs. { eks ra
¯
məshe
¯
n}
used for measuring and indicating the thickness
x-ray microscope
[
ENG
]
1.
A device in which
of moving cold-rolled sheet steel during the roll-
an ultra-fine-focus x-ray tube or electron gun
ing process without making contact with the
produces an electron beam focused to an ex-
sheet; an x-ray beam directed through the sheet
tremely small image on a transmission-type
is absorbed in proportion to the thickness of the
x-ray target that serves as a vacuum seal; the
material and its atomic number. { eks ra
¯
thikи
magnification is by projection; specimens being
nəs ga
¯
j}
examined can thus be in air, as also can the
XY recorder
[

ENG
]
A recorder that traces on a
photographic film that records the magnified im-
chart the relation of two variables, neither of
which is time. { ¦eks¦wı
¯
riko
˙
rdиər}age.
2.
Any of several instruments which utilize
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Y
subdivided to form two openings, usually at a
yard
[
CIV ENG
]
A facility for building and re-
45Њ angle to the run of the pipe. Also known
pairing ships.
[
MECH
]
A unit of length in com-
as wye fitting. { wı
¯
fidиiŋ }

mon use in the United States and United King-
yield
[
ENG
]
Product of a reaction or process as
dom, equal to 0.9144 meter, or 3 feet. Abbrevi-
in chemical reactions or food processing.
ated yd. { ya
¨
rd }
[
MECH
]
That stress in a material at which plastic
yardage
[
MECH
]
An amount expressed in yards.
deformation occurs. { ye
¯
ld }
{ ya
¨
rdиij }
yield factor
[
IND ENG
]

The ratio of the amount
yard crane
See crane truck. { ya
¨
rd kra
¯
n}
of material that results from an industrial proc-
yard drain
[
CIV ENG
]
A drain for clearing an
ess to the amount of material that went into it.
open area of surface water. { ya
¨
rd dra
¯
n}
{ ye
¯
ld fakиtər}
yard lumber
[
BUILD
]
A category of lumber up
yield point
[
MECH

]
The lowest stress at which
to 5 inches (12.5 centimeters) thick. { ya
¨
rd
strain increases without increase in stress.
ləmиbər}
{ ye
¯
ld po
˙
int }
yard maintenance
[
ENG
]
A category of mainte-
yield rate
[
IND ENG
]
The amount of satisfactory
nance that includes the complete rebuilding of
material available after the completion of a given
parts, subassemblies, or components. { ya
¨
rd
manufacturing process expressed as a percent-
maintиənиəns }
age of the total amount produced. { ye

¯
ld ra
¯
t}
yaw
[
MECH
]
1.
The rotational or oscillatory
yield strength
[
MECH
]
The stress at which a ma-
movement of a ship, aircraft, rocket, or the like
terial exhibits a specified deviation from propor-
about a vertical axis. Also known as yawing.
tionality of stress and strain. { ye
¯
ld streŋkth }
2.
The amount of this movement, that is, the
yield stress
[
MECH
]
The lowest stress at which
angle of yaw.
3.

To rotate or oscillate about a
extension of the tensile test piece increases with-
vertical axis. { yo
˙
}
out increase in load. { ye
¯
ld stres }
yaw acceleration
[
MECH
]
The angular accelera-
yield temperature
[
ENG
]
The temperature at
tion of an aircraft or missile about its normal or
which a fusible plug device melts and is dis-
Z axis. { yo
˙
akselиəra
¯
иshən}
lodged by its holder and thus relieves pressure
yaw axis
[
MECH
]

A vertical axis through an air-
in a pressure vessel; it is caused by the melting
craft, rocket, or similar body, about which the
of the fusible material, which is then forced from
body yaws; it may be a body, wind, or stability
its holder. { ye
¯
ld temиprəиchər}
axis. Also known as yawing axis. { yo
˙
akи
yig device
[
ELECTR
]
A filter, oscillator, paramet-
səs}
ric amplifier, or other device that uses an yttrium-
yawing
See yaw. { yo
˙
иiŋ }
iron-garnet crystal in combination with a vari-
yawing axis
See yaw axis. { yo
˙
иiŋakиsəs}
able magnetic field to achieve wide-band tuning
yaw simulator
[

CONT SYS
]
A test instrument
in microwave circuits. Derived from yttrium-iron-
used to derive and thereby permit study of prob-
garnet device. { yig divı
¯
s}
able aerodynamic behavior in controlled flight
Y level
[
ENG
]
A surveyor’s level with Y-shaped
under specific initial conditions; certain compo-
rests to support the telescope. Also known as
nents of the missile guidance system, such as
wye level. { wı
¯
le
¯
vиəl}
the receiver or servo loop, are connected into
yoke
[
DES ENG
]
A clamp or similar device to
the simulatorcircuitry; also, certain aerodynamic
embrace and hold two other parts.

[
ELECTR
]
parameters of the specific missile mustbe known
See deflection yoke.
[
ENG
]
1.
A bar of wood
and set into the simulator; applicable to the yaw
used to join the necks of draft animals for work-
plane. { yo
˙
simиyəla
¯
dиər}
ing together.
2.
See wye.
[
MECH ENG
]
A slot-
Y branch
[
ENG
]
A Y-shaped branch in a piping
ted crosshead used instead of a connecting rod

system. Also known as wye branch. { wı
¯
in some steam engines. { yo
¯
k}
branch }
York-Scheibel column
See Scheibel extractor.
yd
See yard.
{ yo
˙
rk shı
¯
иbəl ka
¨
lиəm}
Young-Helmholtz laws
[
MECH
]
Two laws de-
Y fitting
[
CIV ENG
]
A pipe fitting with one end
Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
Young’s modulus
scribing the motion of bowed strings; the first sulting strain parallel to the tension. Also

known as modulus of elasticity { yəŋz ma
¨
jиstates that no overtone with a node at the point
of excitation can be present; the second states əиləs}
y parameter
[
ELECTR
]
One of a set of four tran-that when the string is bowed at a distance of
1/n times the string’s length from one of the sistor equivalent-circuit parameters, used espe-
cially with field-effect transistors, that conve-ends, where n is an integer, the string moves
back and forth with two constant velocities, one niently specify performance for small voltage and
current in an equivalent circuit; the equivalentof which has the same direction as that of the
bow and is equal to it, while the other has the circuit is a current source with shunt impedance
at both input and output. { wı
¯
pəramиədиər}opposite direction and is n Ϫ 1 times as large.
{ ¦yəŋ helmho
¯
lts lo
˙
z}
yttrium-iron-garnet device
See yig device. { ¦iиtre
¯
и
əm ¦ı
¯
иərn ¦ga
¨

rиnətdivı
¯
s}
Young’s modulus
[
MECH
]
The ratio of a simple
tension stress applied to a material to the re-
624
Z
same temperature. { ¦ziro
¯
th lo
˙
əv thərиmo
¯
и
zee
[
CIV ENG
]
A metal member whose cross
section has a modified Z shape; the internal dı
¯
namиiks }
angles are slightly less than 90Њ.{ze
¯
}
Ziegler process

[
CHEM ENG
]
A process for the
Zener breakdown
[
ELECTR
]
Nondestructive
low-pressure linear polymerization of ethylene
breakdown in a semiconductor, occurring when
and stereospecific polymerization of propylene;
the electric field across the barrier region be-
the product is a high-density polymer or elasto-
comes high enough to produce a form of field
mer. { ze
¯
иglər pra
¨
иsəs}
emission that suddenly increases the number of
zigzag rule
[
ENG
]
A folding ruler having pivoted
carriers in this region. Also known as Zener
sections that lock when the ruler is opened.
effect. { ze
¯

иnər bra
¯
kdau
˙
n}
{ zigzag ru
¨
l}
Zener diode
[
ELECTR
]
A semiconductor break-
zipper
[
ENG
]
A generic name for slide fasteners
down diode, usually constructed of silicon, in
in which two sets of interlocking teeth of the
which reverse-voltage breakdown is based on the
same design provide sturdy and continuous clo-
Zener effect. { ze
¯
иnər dı
¯
o
¯
d}
sure for adjacent pieces of textile, leather, and

Zener diode voltage regulator
See diode voltage
other materials. { zipиər}
regulator. { ze
¯
иnər dı
¯
o
¯
d vo
¯
lиtij regиyəla
¯
dиər}
zipper conveyor
[
MECH ENG
]
A type of con-
Zener effect
See Zener breakdown.
veyor belt with zipperlike teeth that mesh to form
zero adjuster
[
ENG
]
A device for adjusting the
a closed tube; used to handle fragile materials.
pointer position of an instrument or meter to
{ zipиərkənva

¯
иər}
read zero when the measured quantity is zero.
zirconium oxide-based oxygen transducer
[
ENG
]
{ zirиo
¯
əjəsиtər}
A device in which the concentration of oxygen
zero bevel gear
[
DES ENG
]
A special form of
in a mixture of gases is determined from the
bevel gear having curved teeth witha zero-degree
diffusion voltage across a heated, suitably doped
spiral angle. { zirиo
¯
¦bevиəl gir }
zirconium oxide material placed between this
zero bias
[
ELECTR
]
The condition in which the
mixture and a reference gas. { zər¦ko
¯

nиe
¯
иəm
control grid and cathode of an electron tube
¦a
¨
ksı
¯
d ba
¯
st ¦a
¨
ksиəиjən tranzdu
¨
sиər}
are at the same direct-current voltage. { zirиo
¯
zone
[
MECH ENG
]
1.
In a heating or air-condi-
bı
¯
иəs}
tioning system, one or more spaces whose tem-
zero defects
[
IND ENG

]
A program for improv-
perature is regulated by a single control.
2.
A
ing product quality to the point of perfection,
subdivision of a sprinkler, water-supply, or stand-
so there will be no failures due to defects in
pipe system. { zo
¯
n}
construction. { zirиo
¯
de
¯
feks }
zone control
[
ENG
]
The zoning of a process or
zero gravity
See weightlessness. { zirиo
¯
gravи
building, and the independent heating or tem-
ədиe
¯
}
perature controls for each zone. { zo

¯
nkən
zero level
[
ENG ACOUS
]
Reference level used
tro
¯
l}
for comparing sound or signal intensities; in
zone heat
[
CIV ENG
]
A central heating system
audio-frequency work, a power of 0.006 watt is
arranged to allow different temperatures to be
generally used as zero level; in sound, the thresh-
maintained at the same time in two or more
old of hearing is generally assumed as the zero
areas of a building. { zo
¯
n he
¯
t}
level. { zirиo
¯
levиəl}
zone melting crystallization

[
CHEM ENG
]
A
zero method
See null method. { zirиo
¯
methиəd}
method for purification of crystalline solids; the
zero-order hold
[
CONT SYS
]
A device which
sample, packed in a narrow column, is heated
converts a sampled output into an output which
so that a molten zone passes down through the
is held constant between samples at the last
sample, carrying impurities with it. { zo
¯
n ¦melи
sampled value. { zirиo
¯
¦o
˙
rdиər ho
¯
ld }
tiŋkristиəlиəza
¯

иshən}
zeroth lawof thermodynamics
[
THERMO
]
A law
zone-position indicator
[
ENG
]
Auxiliary radar
that if two systems are separately found to be
set for indicating the general position of an ob-
in thermal equilibrium with a third system, the
ject to another radar set with a narrower field.
first two systems are in thermal equilibrium with
each other, that is, all three systems are at the { zo
¯
npə¦zishиən inиdəka
¯
dиər}
Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
zoning
zoning
[
CIV ENG
]
Designation and reservation
z-transfer function
See pulsed transfer function.

under a master plan of land use for light and
{ ze
¯
tranzиfər fəŋkиshən}
heavy industry, dwellings, offices, and other
Z variometer
See vertical intensity variometer.
buildings; use is enforced by restrictions on
types of buildings in each zone. { zo
¯
nиiŋ }
{ ze
¯
verиe
¯
a
¨
mиədиər}
zoom
[
ENG
]
To enlarge or reduce the size of an
Zyglo method
[
ENG
]
A procedure for visualizing
image in an optical system or electronic dis-
incipient cracks caused by fatigue failure, in

play. { zu
¨
m}
Z parameter
[
ELECTR
]
One of a set of four tran-
which the part is immersed in a special activated
sistor equivalent-circuit parameters; they are
penetrating oil and viewed under black light.
the inverse of the Y parameters. { ze
¯
pəramи
{ zı
¯
иglo
¯
methиəd}
ədиər}
626
Appendix
Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
This page intentionally left blank.
Appendix
Equivalents of commonly used units for the
U.S. Customary System and the metric system
1 inch
ϭ 2.5 centimeters (25 millimeters) 1 centimeter
ϭ 0.4 inch

1 inch ϭ
0.083 foot
1 foot
ϭ 0.3 meter (30 centimeters)
1 meter
ϭ 3.3 feet
1 foot
ϭ 0.33 yard (12 inches)
1 yard
ϭ 0.9 meter
1 meter
ϭ
1.1 yards
1 yard
ϭ 3 feet (36 inches)
1 mile
ϭ 1.6 kilometers
1 kilometer
ϭ 0.62 mile
1 mile
ϭ 5280 feet (1760 yards)
1 acre
ϭ 0.4 hectare
1 hectare
ϭ 2.47 acres
1 acre
ϭ 4047 square meters
1 square meter
ϭ 0.00025 acre
1 gallon

ϭ
3.8 liters
1 liter ϭ 1.06 quarts
ϭ 0.26 gallon
1 quart
ϭ 0.25 gallon (32 ounces; 2 pints)
1 fluid ounce
ϭ 29.6 milliliters
1 milliliter
ϭ 0.034 fluid ounce
1 pint
ϭ 0.125 gallon (16 ounces)
32 fluid ounces
ϭ
946.4 milliliters
1 gallon ϭ
4 quarts (8 pints)
1 quart
ϭ 0.95 liter
1 gram
ϭ 0.035 ounce
1 ounce
ϭ 0.0625 pound
1 ounce
ϭ 28.35 grams
1 kilogram
ϭ 2.2 pounds
1 pound
ϭ 16 ounces
1 pound

ϭ
0.45 kilogram
1 kilogram
ϭ 1.1 ϫ
10
Ϫ3
ton
1 ton
ϭ 2000 pounds
1 ton
ϭ 907.18 kilograms
ЊF ϭ
(1.8 ϫЊC)
ϩ 32
ЊC ϭ
(ЊF Ϫ 32)
Ϭ 1.8
629
Appendix
Conversion factors for the U.S. Customary
System, metric system, and International System
A. Units of length
Units
cm
m
in.
ft
yd
mi
1cm

ϭ
1
0.01
0.3937008
0.03280840
0.01093613
6.213712
ϫ 10
Ϫ6
1m
ϭ
100.
1
39.37008
3.280840
1.093613
6.213712
ϫ 10
Ϫ4
1 in.
ϭ
2.54
0.0254
1
0.08333333
0.02777777 1.578283
ϫ 10
Ϫ5
1ft
ϭ

30.48
0.3048
12.
1
0.3333333
1.893939
ϫ 10
Ϫ4
1yd
ϭ
91.44
0.9144
36.
3.
1
5.681818
ϫ 10
Ϫ4
1mi
ϭ
1.609344
ϫ 10
5
1.609344
ϫ 10
3
6.336
ϫ 10
4
5280.

1760.
1
B. Units of area
Units
cm
2
m
2
in.
2
ft
2
yd
2
mi
2
1cm
2
ϭ 11
0
Ϫ4
0.1550003
1.076391
ϫ
10
Ϫ3
1.195990
ϫ 10
Ϫ4
3.861022

ϫ 10
Ϫ11
1m
2
ϭ 10
4
1
1550.003
10.76391
1.195990
3.861022
ϫ 10
Ϫ7
1 in.
2
ϭ 6.4516
6.4516 ϫ
10
Ϫ4
1
6.944444
ϫ
10
Ϫ3
7.716049
ϫ 10
Ϫ4
2.490977
ϫ 10
Ϫ10

1ft
2
ϭ 929.0304
0.09290304
144.
1
0.1111111
3.587007
ϫ
10
Ϫ8
1yd
2
ϭ 8361.273
0.8361273
1296.
9.
1
3.228306
ϫ
10
Ϫ7
1mi
2
ϭ 2.589988
ϫ 10
10
2.589988
ϫ 10
6

4.014490
ϫ 10
9
2.78784
ϫ 10
7
3.0976
ϫ 10
6
1
630
Appendix
C. Units of volume
Units
m
3
cm
3
liter
in.
3
ft
3
qt
gal
1m
3
ϭ 11
0
6

10
3
6.102374
ϫ 10
4
35.31467
ϫ 10
Ϫ3
1.056688
264.1721
1cm
3
ϭ 10
Ϫ6
11
0
Ϫ3
0.06102374 3.531467
ϫ 10
Ϫ5
1.056688
ϫ 10
Ϫ3
2.641721
ϫ 10
Ϫ4
1 liter
ϭ 10
Ϫ3
1000. 1

61.02374
0.03531467
1.056688
0.2641721
1 in.
3
ϭ 1.638706
ϫ 10
Ϫ5
16.38706 0.01638706 1
5.787037
ϫ 10
Ϫ4
0.01731602
4.329004
ϫ
10
Ϫ3
1ft
3
ϭ 2.831685
ϫ 10
Ϫ2
28316.85 28.31685 1728.
1
2.992208
7.480520
1qt
ϭ 9.463529
ϫ 10

Ϫ4
946.3529 0.9463529 57.75
0.03342014
1
0.25
1 gal (U.S.)
ϭ 3.785412
ϫ 10
Ϫ3
3785.412 3.785412 231.
0.1336806
4.
1
D. Units of mass
Units
g
kg
oz
lb
metric ton
ton
1g
ϭ
11
0
Ϫ3
0.03527396
2.204623
ϫ
10

Ϫ3
10
Ϫ6
1.102311
ϫ 10
Ϫ6
1kg
ϭ
1000.
1
35.27396
2.204623
10
Ϫ3
1.102311
ϫ 10
Ϫ3
1 oz (avdp)
ϭ
28.34952
0.02834952
1
0.0625
2.834952
ϫ
10
Ϫ5
3.125
ϫ 10
Ϫ5

1 lb (avdp)
ϭ
453.5924
0.4535924
16.
1
4.535924
ϫ
10
Ϫ4
5. ϫ
10
Ϫ4
1 metric ton
ϭ
10
8
1000.
35273.96
2204.623
1
1.102311
1 ton
ϭ
907184.7
907.1847
32000.
2000.
0.9071847
1

631
Appendix
Conversion factors for the U.S. Customary
System, metric system, and International System
(cont.)
E. Units of density
Units
g и cm
Ϫ3
g и L
Ϫ1
,kgи
m
Ϫ3
oz и in.
Ϫ3
lb и in.
Ϫ3
lb и ft
Ϫ3
lb и gal
Ϫ1
1gи
cm
Ϫ3
ϭ 1
1000.
0.5780365
0.03612728
62.42795

8.345403
1gи
L
Ϫ1
,kgи
m
Ϫ3
ϭ 10
Ϫ3
1
5.780365
ϫ
10
Ϫ4
3.612728
ϫ 10
Ϫ5
0.06242795 8.345403
ϫ 10
Ϫ3
1ozи
in.
Ϫ3
ϭ 1.729994 1729.994
1
0.0625
108.
14.4375
1lbи
in.

Ϫ3
ϭ 27.67991 27679.91
16.
1
1728.
231.
1lbи
ft
Ϫ3
ϭ 0.01601847 16.01847
9.259259 ϫ
10
Ϫ3
5.787037
ϫ 10
Ϫ4
1
0.1336806
1lbи
gal
Ϫ1
ϭ 0.1198264 119.8264
4.749536 ϫ
10
Ϫ3
4.329004
ϫ 10
Ϫ3
7.480519
1

F. Units of pressure
Units
Pa, N
и m
Ϫ2
dyn и
cm
Ϫ2
bar
atm
kgf
и cm
Ϫ2
mmHg (torr) in. Hg lbf
и in.
Ϫ2
1Pa,1Nи
m
Ϫ2
ϭ 110 10
Ϫ5
9.869233
ϫ 10
Ϫ6
1.019716
ϫ 10
Ϫ5
7.500617
ϫ 10
Ϫ3

2.952999
ϫ 10
Ϫ4
1.450377
ϫ 10
Ϫ4
1 dyn
и cm
Ϫ2
ϭ 0.1 1
10
Ϫ6
9.869233
ϫ 10
Ϫ7
1.019716
ϫ 10
Ϫ6
7.500617
ϫ 10
Ϫ4
2.952999
ϫ 10
Ϫ5
1.450377
ϫ 10
Ϫ5
1 bar
ϭ 10
5

10
6
1
0.9869233 1.019716 750.0617
29.52999 14.50377
1 atm
ϭ 101325 1013250 1.01325 1
1.033227 760.
29.92126 14.69595
1 kgf
и cm
Ϫ2
ϭ 98066.5 980665 0.980665
0.9678411 1
735.5592 28.95903 14.22334
1 mmHg (torr)
ϭ 133.3224 1333.224 1.333224
ϫ
10
3
1.315789
ϫ 10
Ϫ3
1.359510
ϫ 10
Ϫ3
1
0.03937008 0.01933678
1 in. Hg
ϭ 3386.388 33863.88 0.03386388 0.03342105

0.03453155 25.4
1
0.4911541
1 lbf
и in.
Ϫ2
ϭ 6894.757 68947.57 0.06894757
0.06804596 0.07030696 51.71493
2.036021 1
632
Appendix
G. Units of energy
g mass
Units (energy equiv) J
eV cal cal
IT
Btu
IT
kWh hp-h ft-lbf ft
3
и lbf и
in.
Ϫ2
liter-atm
1gmass
ϭ 1
8.987552 5.609589 2.148076 2.146640
8.518555 2.496542 3.347918 6.628878
4.603388 8.870024
(energy equiv)

ϫ 10
13
ϫ 10
32
ϫ 10
3
ϫ 10
13
ϫ 10
10
ϫ 10
7
ϫ 10
7
ϫ 10
13
ϫ 10
11
ϫ 10
11
1J
ϭ 1.112650 1 6.241510 0.2390057
0.2388459 9.478172 2.777777
3.725062 0.7375622 5.121960 9.869233
ϫ 10
Ϫ14
ϫ 10
18
ϫ 10
Ϫ4

ϫ 10
Ϫ7
ϫ 10
Ϫ3
ϫ 10
Ϫ3
1eV
ϭ 1.782662 1.602176 1 3.829293
3.826733 1.518570 4.450490
5.968206 1.181705 8.206283 1.581225
ϫ 10
Ϫ33
ϫ 10
Ϫ19
ϫ 10
Ϫ20
ϫ 10
Ϫ20
ϫ 10
Ϫ22
ϫ 10
Ϫ26
ϫ 10
Ϫ26
ϫ 10
Ϫ19
ϫ 10
Ϫ22
ϫ 10
Ϫ21

1 cal
ϭ 4.655328 4.184 2.611448 1
0.9993312 3.965667 1.1622222
1.558562 3.085960 2.143028 0.04129287
ϫ 10
Ϫ14
ϫ 10
19
ϫ 10
Ϫ3
ϫ 10
Ϫ6
ϫ 10
Ϫ6
ϫ 10
Ϫ2
1 cal
IT
ϭ 4.658443 4.1868 2.613195 1.000669
1
3.968321 1.163 1.559609
3.088025 2.144462 0.04132050
ϫ
10
Ϫ14
ϫ 10
19
ϫ 10
Ϫ3
ϫ 10

Ϫ6
ϫ 10
Ϫ6
ϫ 10
Ϫ2
1 Btu
IT
ϭ 1.173908 1055.056 6.585141 252.1644
251.9958 1
2.930711 3.930148 778.1693 5.403953
10.41259
ϫ
10
Ϫ11
ϫ 10
21
ϫ 10
Ϫ4
ϫ 10
Ϫ4
1kWh
ϭ 4.005540 3600000. 2.246944 860420.7
859845.2 3412.142 1
1.341022 2655224. 18349.06 35529.24
ϫ 10
Ϫ8
ϫ 10
25
1 hp-h
ϭ 2.986931 2384519. 1.675545 641615.6

641186.5 2544.33 0.7456998
1
1980000. 13750. 26494.15
ϫ 10
Ϫ8
ϫ 10
25
1 ft-lbf
ϭ 1.508551 1.355818 8.462351 0.3240483
0.3238315 1.285067 3.766161
5.050505 1 6.944444 0.01338088
ϫ 10
Ϫ14
ϫ 10
18
ϫ 10
Ϫ3
ϫ 10
Ϫ7
ϫ 10
Ϫ7
ϫ 10
Ϫ3
1ft
3
lbf иϭ
2.172313 195.2378 1.218579 46.66295.
46.63174 0.1850497 5.423272 7.272727
144. 1
1.926847

in.
Ϫ2
ϫ 10
Ϫ12
ϫ 10
21
ϫ 10
Ϫ5
ϫ 10
Ϫ5
1 liter-atm
ϭ 1.127393 101.325 6.324210 24.21726
24.20106 0.09603757 2.814583
3.774419 74.73349 0.5189825 1
ϫ 10
Ϫ12
ϫ 10
20
ϫ 10
Ϫ5
ϫ 10
Ϫ5
633
Appendix
Special constants
␲
ϭ 3.14159 26535 89793 23846 2643 . . .
e ϭ 2.71828 18284 59045 23536 0287 . . . ϭ lim
n→ϱ
΂

1 ϩ
1
n
΃
n
ϭ natural base of logarithms
Ί
2 ϭ 1.41421 35623 73095 0488 . . .
Ί
3 ϭ 1.73205 08075 68877 2935 . . .
Ί
5 ϭ 2.23606 79774 99789 6964 . . .
Ί
3
2 ϭ 1.25992 1050 . . .
Ί
3
3 ϭ 1.44224 9570 . . .
Ί
5
2 ϭ 1.14869 8355 . . .
Ί
5
3 ϭ 1.24573 0940 . . .
e
␲
ϭ 23.14069 26327 79269 006 . . .
␲
e
ϭ 22.45915 77183 61045 47342 715 . . .

e
e
ϭ 15.15426 22414 79264 190 . . .
log
10
2 ϭ 0.30102 99956 63981 19521 37389 . . .
log
10
3 ϭ 0.47712 12547 19662 43729 50279 . . .
log
10
e ϭ 0.43429 44819 03251 82765 . . .
log
10
␲
ϭ 0.49714 98726 94133 85435 12683 . . .
log
e
10 ϭ ln 10 ϭ 2.30258 50929 94045 68401 7991 . . .
log
e
2 ϭ ln 2 ϭ 0.69314 71805 59945 30941 7232 . . .
log
e
3 ϭ ln 3 ϭ 1.09861 22886 68109 69139 5245 . . .
␥
ϭ 0.57721 56649 01532 86060 6512 . . . ϭ Euler’s constant
ϭ lim
n→ ϱ
΂

1 ϩ
1
2
ϩ
1
3
ϩ иии ϩ
1
n
Ϫ ln n
΃
e
␥
ϭ 1.78107 24179 90197 9852 . . .
Ί
e ϭ 1.64872 12707 00128 1468 . . .
Ί
␲
ϭ ⌫(
1
–
2
) ϭ 1.77245 38509 05516 02729 8167 . . .
where ⌫ is the gamma function
⌫(
1
–
3
) ϭ 2.67893 85347 07748 . . .
⌫(

1
–
4
) ϭ 3.62560 99082 21908 . . .
1 radian ϭ 180Њ/
␲
ϭ 57.29577 95130 8232 . . .Њ
1Њϭ
␲
/180 radians ϭ 0.01745 32925 19943 29576 92 . . . radians
SOURCE
: Murray R. Spiegel and John Liu, Mathematical Handbook of Formulas and Tables, 2d ed., Schaum’s Outline
Series, McGraw-Hill, 1999.
634
Appendix
Electrical and magnetic units
Quantity Unit and symbol Derivation
S1 base units
Mass kilogram, kg
Time second, s
Length meter, m
Electric current ampere, A
Thermodynamic kelvin, K
temperature
Luminous intensity candela, cd
Amount of substance mole, mol
Derived units
Potential difference, emf vol, V W и A
Ϫ1
ϭ m

2
и kg и s
Ϫ3
и A
Ϫ1
Resistance ohm, ⍀ V и A
Ϫ1
ϭ m
2
и kg и s
Ϫ3
и A
Ϫ2
Electric charge coulomb, C s и A
Capacitance farad, F C и V
Ϫ1
ϭ m
Ϫ2
и kg
Ϫ1
и s
4
и A
2
Conductance siemens, S A и V
Ϫ1
ϭ m
Ϫ2
и kg
Ϫ1

и s
3
и A
2
Magnetic flux weber, Wb V и s ϭ m
2
и kg и s
Ϫ2
и A
Ϫ1
Inductance henry, H Wb и A
Ϫ1
ϭ m
2
и kg и s
Ϫ2
и A
Ϫ2
Magnetic flux density tesla, T Wb и m
Ϫ2
ϭ kg и s
Ϫ2
и A
Ϫ1
Magnetic field strength ampere per meter m
Ϫ1
и A
Current density ampere per square meter m
Ϫ2
и A

Electric field strength volt per meter V и m
Ϫ1
ϭ m и kg и s
Ϫ3
и A
Ϫ1
Permittivity farad per meter F и m
Ϫ1
ϭ m
Ϫ3
и kg
Ϫ1
и s
4
и A
2
Permeability henry per meter H и m
Ϫ1
ϭ m и kg и s
Ϫ2
и A
Ϫ2
Dimensional formulas of common quantities
Dimensional
Quantity Definition formula
Mass Fundamental
M
Length Fundamental
L
Time Fundamental

T
Velocity Distance/time
LT
Ϫ1
Acceleration Velocity/time
LT
Ϫ2
Force Mass ϫ acceleration
MLT
Ϫ2
Momentum Mass ϫ velocity
MLT
Ϫ1
Energy Force ϫ distance
ML
2
T
Ϫ2
Angle Arc/radius 1
Angular velocity Angle/time
T
Ϫ1
Angular acceleration Angular velocity/time
T
Ϫ2
Torque Force ϫ lever arm
ML
2
T
Ϫ2

Angular momentum Momentum ϫ lever arm
ML
2
T
Ϫ1
Moment of inertia Mass ϫ radius squared
ML
2
Area Length squared
L
2
Volume Length cubed
L
3
Density Mass/volume
ML
Ϫ3
Pressure Force/area
ML
Ϫ1
T
Ϫ2
Action Energy ϫ time
ML
2
T
Ϫ1
Viscosity Force per unit area per
ML
Ϫ1

T
Ϫ1
unit velocity gradient
635
Appendix
Internal energy and generalized work
Type of energy Intensive factor Extensive factor Element of work
Mechanical
Expansion Pressure (P) Volume (V) ϪPdV
Stretching Surface tension (
␥
) Area (A)
␥
dA
Extension Tensile stretch (F) Length (l) Fdl
Thermal Temperature (T) Entropy (S) TdS
Chemical Chemical potential (gm) Moles (n)
␮
dn
Electrical Electric potential (E) Charge (Q) EdQ
Gravitational Gravitational field strength (mg) Height (h) mgdh
Polarization
Electrostatic Electric field strength (E) Total electric polar- EdP
ization (P)
Magnetic Magnetic field strength (H) Total magetic polar- HdM
ization (M)
636
Appendix
General rules of integration*
Ύ

adxϭ
ax
Ύ
tan uduϭ
ln sec
u ϭϪln cos
u
Ύ
cot uduϭ
ln sin
u
Ύ
af (x)
dx ϭ a
Ύ
f (x) dx
Ύ
sec uduϭ
ln (sec
u ϩ tan
u) ϭ ln tan
΂
u
2
ϩ
␲
4
΃
Ύ
(u Ϯ

v Ϯ w Ϯ иии)
dx ϭ
Ύ
udxϮ
Ύ
vdxϮ
Ύ
wdxϮ иии
Ύ
csc uduϭ
ln (csc
u Ϫ cot
u) ϭ ln tan
u
2
Ύ
udvϭ
uv Ϫ
Ύ
vdu
[integration by parts]
Ύ
sec
2
uduϭ
tan u
Ύ
f (ax)
dx ϭ
1

a
Ύ
f (u) du
Ύ
csc
2
uduϭϪ
cot u
Ύ
tan
2
uduϭ
tan u Ϫ
u
Ύ
cot
2
uduϭϪ
cot u Ϫ
u
Ύ
F{ f(x)}
dx ϭ
Ύ
F(u)
dx
du
du ϭ
Ύ
F(u)

f Ј(x)
du
where u ϭ
f (x)
Ύ
sin
2
uduϭ
u
2
Ϫ
sin 2u
4
ϭ
1
2
(u Ϫ sin
u cos u)
Ύ
u
n
du ϭ
u
nϩ1
n ϩ 1
,
n Ϫ1 [for
n ϭϪ
1]
Ύ

cos
2
uduϭ
u
2
ϩ
sin 2u
4
ϭ
1
2
(u ϩ sin
u cos u)
Ύ
du
u
ϭ ln u
if u Ͼ 0orln(
Ϫu)ifu
Ͻ 0
Ύ
sec u
tan uduϭ
sec u
ϭ
ln ȊuȊ
Ύ
csc u
cot uduϭϪ
csc u

Ύ
e
u
du ϭ
e
u
Ύ
sinh uduϭ
cosh
u
Ύ
a
u
du ϭ
Ύ
e
u ln
a
du ϭ
e
u ln
a
ln a
ϭ
a
u
ln a
, a
Ͼ 0, a 
1

Ύ
cosh
uduϭ sinh
u
Ύ
sin uduϭϪ
cos
u
Ύ
tanh
uduϭ ln cosh
u
Ύ
coth
uduϭ ln sinh
u
Ύ
cos uduϭ
sin u
637
Appendix
General rules of integration* (cont.)
Ύ
sech
uduϭ sin
Ϫ1
(tanh
u)or2tan
Ϫ1
e

u
Ύ
du
u
2
Ϫ a
2
ϭ
1
2a
ln
΂
u Ϫ a
u ϩ a
΃
ϭϪ
1
a
coth
Ϫ1
u
a
u
2
Ͼ a
2
Ύ
csch
uduϭ ln tanh
u

2
or Ϫcoth
Ϫ1
e
u
Ύ
du
a
2
Ϫ u
2
ϭ
1
2a
ln
΂
a ϩ u
a Ϫ u
΃
ϭ
1
a
tanh
Ϫ1
u
a
u
2
Ͻ a
2

Ύ
sech
2
uduϭ
tanh u
Ύ
du
Ί
a
2
Ϫ u
2
ϭ sin
Ϫ1
u
a
Ύ
csch
2
uduϭϪ
coth u
Ύ
du
Ί
u
2
ϩ a
2
ϭ ln(u
ϩ

Ί
u
2
ϩ a
2
) or sinh
Ϫ1
u
a
Ύ
tanh
2
uduϭ
u Ϫ tanh
u
Ύ
du
Ί
u
2
Ϫ a
2
ϭ ln(u
ϩ
Ί
u
2
Ϫ a
2
)

Ύ
coth
2
uduϭ
u Ϫ coth
u
Ύ
du
u
Ί
u
2
Ϫ a
2
ϭ
1
a
sec
Ϫ1
Ϳ
u
a
Ϳ
Ύ
sinh
2
uduϭ
sinh 2u
4
Ϫ

u
2
ϭ
1
2
(sinh u cosh
u Ϫ u)
Ύ
du
u
Ί
u
2
ϩ a
2
ϭϪ
1
a
ln
΂
a ϩ
Ί
u
2
ϩ a
2
u
΃
Ύ
cosh

2
uduϭ
sinh 2u
4
ϩ
u
2
ϭ
1
2
(sinh u cosh
u ϩ u)
Ύ
du
u
Ί
a
2
Ϫ u
2
ϭϪ
1
a
ln
΂
a ϩ
Ί
a
2
Ϫ u

2
u
΃
Ύ
sech
u tanh uduϭϪ
sech
u
Ύ
f
(n)
gdxϭ
f
(nϪ1)
g Ϫ f
(nϪ2)
gЈ ϩ
f
(nϪ3)
gЉ Ϫ иии
(Ϫ1)
n
Ύ
fg
(n)
dx
Ύ
csch
u coth uduϭϪ
csch

u
This is called generalized integration by parts.
Ύ
du
u
2
ϩ a
2
ϭ
1
a
tan
Ϫ1
u
a
*Here,
u, v, w
are functions of
x;
a, b, p,
q, n any constants, restricted if indicated;
e
ϭ 2.71828 . . . is the natural base of logarithms;
ln
u denotes the natural logarithm of
u where it is
assumed that
u Ͼ
0 [in general, to extend formulas to cases
where u

Ͻ 0 as well, replace ln
u by ln
ȊuȊ]; all angles are in radians; all constants
of integration are omitted but implied.
SOURCE
: Murray R. Spiegel and John Liu,
Mathematical Handbook of Formulas and Tables,
2d ed., Schaum’s Outline Series, McGraw-Hill,
1999.
638
Appendix
Schematic electronic symblols*
*From S. Gibilisco, The Illustrated Dictionary of Electronics, 8th ed., McGraw-Hill, 2001.
639
Appendix
640
Appendix
641
Appendix
642