Erwin Kreyszig Advanced Engineering Mathematics.pdf

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Systems of Units. Some Important Conversion Factors
The most important systems of units are shown in the table below. The mks system is also known as
the
International System of Units
(abbreviated
SI),
and the abbreviations sec (instead of s),
gm (instead of g), and nt (instead of N) are also used.
System of units
cgs system
mks system
Engineering system
Length
centimeter (cm)
meter (m)
foot (ft)
Mass
gram (g)
kilogram (kg)
slug
Time
second (s)
second (s)
second (s)
Force
dyne
newton (nt)
pound (lb)
1 inch (in.)
1 yard (yd)
2.540000 cm
3 ft
91.440000 cm
6080 ft
1.853184 km
1 foot (ft)
12 in.
30.480000 cm
5280 ft
1.609344 km
1 statute mile (mi)
1 nautical mile
1 acre
4840 yd
2
4046.8564 m
2
231/128 in.
3
1 mi
2
640 acres
2.5899881 km
2
1 fluid ounce
1 U.S. gallon
1/128 U.S. gallon
4 quarts (liq)
29.573730 cm
3
3785.4118 cm
3
4546.087 cm
3
8 pints (liq)
128 fl oz
1 British Imperial and Canadian gallon
1 slug
14.59390 kg
4.448444 nt
1.200949 U.S. gallons
1 pound (lb)
1 newton (nt)
1054.35 joules
1 joule
10
5
dynes
1 British thermal unit (Btu)
1 calorie (cal)
4.1840 joules
10
7
ergs
1 kilowatt-hour (kWh)
1 horsepower (hp)
1 kilowatt (kW)
°F
°C
•
1.8
3414.4 Btu
3.6
•
10
6
joules
178.298 cal/sec
0.74570 kW
2542.48 Btu/h
1000 watts
3414.43 Btu/h
238.662 cal/s
1°
60
3600
0.017453293 radian
32
For further details see, for example, D. Halliday, R. Resnick, and J. Walker,
Fundamentals of Physics.
9th ed., Hoboken,
N. J: Wiley, 2011. See also AN American National Standard, ASTM/IEEE Standard Metric Practice, Institute of Electrical and
Electronics Engineers, Inc. (IEEE), 445 Hoes Lane, Piscataway, N. J. 08854, website at www.ieee.org.
Differentiation
(cu)
(u
(uv)
u
( )
v
du
dx
v)
u
v
u
v
v
du dy
•
dy dx
2
Integration
uv dx
x
n
dx
1
x dx
e
ax
dx
sin
x dx
uv
x
n
1
n
1
ln
x
1
ax
ae
cos
x
sin
x
c
c
c
tan
x
cot
x
c
c
c
c
c
c
c
c
c
c
c
u
v
dx
(by parts)
c
(n
1)
cu
u
(c constant)
v
uv
uv
(Chain rule)
cos
x dx
tan
x dx
ln cos
x
ln sin
x
ln sec
x
ln csc
x
(x )
(e )
(e )
(a
x
)
(sin
x)
(cos
x)
(tan
x)
(cot
x)
(sinh
x)
(cosh
x)
ax
x
n
nx
e
x
n
1
cot
x dx
sec
x dx
ae
ax
a
x
ln
a
cos
x
sin
x
sec
2
x
csc
x
cosh
x
sinh
x
1
x
log
a
e
x
1
1
x
2
1
1
1
1
x
2
1
1
x
2
2
csc
x dx
dx
x
2
a
dx
a
2
dx
x
2
dx
x
2
2
1
x
arctan
a
a
x
2
a
2
a
2
_
x
1
2
arcsin
x
a
x
a
x
a
arcsinh
arccosh
sin
2
x dx
cos
2
x dx
tan
2
x dx
cot
2
x dx
_
sin 2x
1
4
(ln
x)
_
x
1
2
_
sin 2x
1
4
(log
a
x)
tan
x
cot
x
x
ln
x
x
x
x
c
c
c
(arcsin
x)
ln
x dx
(arccos
x)
e
ax
sin
bx dx
x
2
a
2
e
ax
b
2
(a sin
bx
b
cos
bx)
c
(arctan
x)
(arccot
x)
e
ax
cos
bx dx
e
ax
a
2
b
2
(a cos
bx
b
sin
bx)
c

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