# Advanced Engineering Mathematics 10th Edition

**Topics:**Partial differential equation, Fourier analysis, Ordinary differential equation

**Pages:**6162 (566180 words)

**Published:**March 12, 2013

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.

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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 dx

uv

uv

u

()

v

uv dx

x n dx

v

u

Integration

c

cos x

c

ex

(Chain rule)

cos x dx

sin x

tan x dx

c

ln cos x

c

1

cot x dx

tan x

c

csc x dx

a x ln a

ln sec x

ln csc x

cot x

c

ae ax

(a x)

c

sec x dx

(e ax)

ln sin x

1

x

arctan

a

a

dx

(sin x)

cos x

(cos x)

(tan x)

x

2

a

2

c

x

a

c

dx

sin x

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