Advanced Engineering Mathematics 10th Edition
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Page 2
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
Length
Mass
Time
Force
cgs system
centimeter (cm)
gram (g)
second (s)
dyne
mks system
meter (m)
kilogram (kg)
second (s)
newton (nt)
Engineering system
foot (ft)
slug
second (s)
pound (lb)
1 inch (in.)
2.540000 cm
1 foot (ft)
1 yard (yd)
3 ft
1 statute mile (mi)
5280 ft
1 mi2
2.5899881 km2
1 nautical mile
1 acre
91.440000 cm
6080 ft
4840 yd2
4046.8564 m2
1/128 U.S. gallon
1 U.S. gallon
4 quarts (liq)
231/128 in.3
8 pints (liq)
1 British Imperial and Canadian gallon
1.609344 km
640 acres
29.573730 cm3
3785.4118 cm3
128 fl oz
4546.087 cm3
1.200949 U.S. gallons
14.59390 kg
1 pound (lb)
4.448444 nt
1 British thermal unit (Btu)
1 calorie (cal)
°C • 1.8
1054.35 joules
1 joule
3414.4 Btu
105 dynes
107 ergs
3.6 • 106 joules
2542.48 Btu/h
1 horsepower (hp)
1 kilowatt (kW)
1 newton (nt)
4.1840 joules
178.298 cal/sec
1 kilowatt-hour (kWh)
°F
30.480000 cm
1.853184 km
1 fluid ounce
1 slug
12 in.
1000 watts
32
3414.43 Btu/h
0.74570 kW
238.662 cal/s
1°
60
3600
0.017453293 radian
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.
fendpaper.qxd
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Page 3
Differentiation
(cu)
(u
cu
(c constant)
v)
(uv)
uv
uv
uv
x n ln x
v
du dx (x n)
nxn
(e x)
(n
1)
c
sin x dx
du dy
•
dy dx
c
1
1 ax ae eax dx
2
u v dx (by parts)
n1
1
x
11/4/10
12:05 PM
Page 2
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
Length
Mass
Time
Force
cgs system
centimeter (cm)
gram (g)
second (s)
dyne
mks system
meter (m)
kilogram (kg)
second (s)
newton (nt)
Engineering system
foot (ft)
slug
second (s)
pound (lb)
1 inch (in.)
2.540000 cm
1 foot (ft)
1 yard (yd)
3 ft
1 statute mile (mi)
5280 ft
1 mi2
2.5899881 km2
1 nautical mile
1 acre
91.440000 cm
6080 ft
4840 yd2
4046.8564 m2
1/128 U.S. gallon
1 U.S. gallon
4 quarts (liq)
231/128 in.3
8 pints (liq)
1 British Imperial and Canadian gallon
1.609344 km
640 acres
29.573730 cm3
3785.4118 cm3
128 fl oz
4546.087 cm3
1.200949 U.S. gallons
14.59390 kg
1 pound (lb)
4.448444 nt
1 British thermal unit (Btu)
1 calorie (cal)
°C • 1.8
1054.35 joules
1 joule
3414.4 Btu
105 dynes
107 ergs
3.6 • 106 joules
2542.48 Btu/h
1 horsepower (hp)
1 kilowatt (kW)
1 newton (nt)
4.1840 joules
178.298 cal/sec
1 kilowatt-hour (kWh)
°F
30.480000 cm
1.853184 km
1 fluid ounce
1 slug
12 in.
1000 watts
32
3414.43 Btu/h
0.74570 kW
238.662 cal/s
1°
60
3600
0.017453293 radian
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.
fendpaper.qxd
11/4/10
12:05 PM
Page 3
Differentiation
(cu)
(u
cu
(c constant)
v)
(uv)
uv
uv
uv
x n ln x
v
du dx (x n)
nxn
(e x)
(n
1)
c
sin x dx
du dy
•
dy dx
c
1
1 ax ae eax dx
2
u v dx (by parts)
n1
1
x
References: Press, 2010. 19. x 5 0.0286 (error 0.0093), x 10 0.2196 (error 0.0189) 3.1