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*