9781118230725.pdf

Quadratic Formula

If , then

Binomial Theorem

... (x^2 1)

Products of Vectors

Letube the smaller of the two angles between and.

Then

  axbx ayby azbz abcosu

Trigonometric Identities

• See Appendix E for a more complete list.

cosacosb2 cos^12 (ab) cos^12 (ab)

sinasinb2 sin^12 (ab) cos^12 (ab)

|a::b|ab sin u

(aybzbyaz)iˆ(azbxbzax)jˆ(axbybxay)kˆ

iˆ

ay

by

az

bz

jˆ

ax

bx

az

bz

kˆ

ax

bx

ay

by

a:b

:

b

:

a:



iˆ

ax

bx

jˆ

ay

by

kˆ

az

bz



b a:

:

b

:

a:

b

:

a:

(1x)n 1 

nx

1!



n(n1)x^2

2!



x

b 1 b^2  4 ac

2 a

ax^2 bxc 0

Derivatives and Integrals

Cramer’s Rule

Two simultaneous equations in unknowns xandy,

a 1 xb 1 yc 1 and a 2 xb 2 yc 2 ,

have the solutions

and

y.



a 1

a 2

c 1

c 2 



a 1

a 2

b 1

b 2 



a 1 c 2 a 2 c 1

a 1 b 2 a 2 b 1

x



c 1

c 2

b 1

b 2 



a 1

a 2

b 1

b 2 



c 1 b 2 c 2 b 1

a 1 b 2 a 2 b 1



dx

(x^2 a^2 )3/



x

a^2 (x^2 a^2 )1/



xdx

(x^2 a^2 )3/



1

(x^2 a^2 )1/



dx

2 x^2 a^2

ln(x 2 x^2 a^2 )

exdxex

d

dx

exex

cosxdxsinx

d

dx

cos xsinx

sinxdxcosx

d

dx

sin xcosx

SI PREFIXES*

Factor Prefix Symbol Factor Prefix Symbol

1024 yotta Y 10 –1 deci d

1021 zetta Z 10 –2 centi c

1018 exa E 10 –3 milli m

1015 peta P 10 –6 micro m

1012 tera T 10 –9 nano n

109 giga G 10 –12 pico p

106 mega M 10 –15 femto f

103 kilo k 10 –18 atto a

102 hecto h 10 –21 zepto z

101 deka da 10 –24 yocto y

*In all cases, the first syllable is accented, as in ná-no-mé-ter.

MATHEMATICAL FORMULAS*