,
,MATHEMATICAL FORMULAS*
Quadratic Formula Derivatives and Integrals
_______
− b ± √b 2 − 4ac
If ax2 + bx + c = 0, then x = _____________
d sin x = cos x
___
xdx = −co
sin
2a dx
Binomial Theorem d cos x = − sin x
___
cos x dx = sin
dx
d e x= e x
(1 + x)n = 1 + ___
1!
n(n − 1)x 2
nx + _________
2!
+ . . . (x 2< 1) ___
dx
e x dx = e x
Products of Vectors
_______
√
dx = ln(x + x2 + a2 )
_________
x 2 + a 2
→
Let θ be the smaller of the two angles between →
a and b .
x dx = − __________
__________ 1
Then (x 2+ a 2) 3/2
(x 2
a 2)1/2
+
→ →
→
a ⋅ b = b ⋅ →
a = axbx + ayby + azbz = ab cos θ 2 dx 2 3/2 = ____________
__________ x
(x + a ) a 2(x 2 + a 2)1/2
| |
iˆ jˆ kˆ
→ →
→
a × b = − b × →
a = ax a y a z Cramer’s Rule
x by bz
b Two simultaneous equations in unknowns x and y,
ay a z ax a z ax a y a1x + b1 y = c1 and a2x + b2 y = c2,
 |
= ˆi
by bz | |
− ˆj
bx bz | | |
ˆ
+ k
bx by have the solutions
= (aybz − by az)ˆi + (azbx − bz ax)ˆj+ (axby − bx ay)k
ˆ
→
|
x = _______
|
c b
1 1
c 2 b c b − c b
2 __________
= 1 2 2 1
| →
a × b |= ab sin θ
| a 1 b
a 2 b |
1 a1b2 − a2b1
2
Trigonometric Identities and
a1 c1
sin α ± sin β = 2 sin _ 12 (α ± β)cos _ 12 (α ∓ β) | |
a c a1c2− a2c1
y = _______
2 2 = __________
.
cos α + cos β = 2 cos _ 12 (α + β)cos _ 12 (α − β)
| a b
|
a b − a2b1
1 1 1 2
a 2 b
2
*See Appendix E for a more complete list.
SI PREFIXES*
Factor Prefix Symbol Factor Prefix Symbol
24 −1
10 yotta Y 10 deci d
1021 zetta Z 10−2 centi c
1018 exa E 10−3 milli m
1015 peta P 10−6 micro μ
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*
Quadratic Formula Derivatives and Integrals
_______
− b ± √b 2 − 4ac
If ax2 + bx + c = 0, then x = _____________
d sin x = cos x
___
xdx = −co
sin
2a dx
Binomial Theorem d cos x = − sin x
___
cos x dx = sin
dx
d e x= e x
(1 + x)n = 1 + ___
1!
n(n − 1)x 2
nx + _________
2!
+ . . . (x 2< 1) ___
dx
e x dx = e x
Products of Vectors
_______
√
dx = ln(x + x2 + a2 )
_________
x 2 + a 2
→
Let θ be the smaller of the two angles between →
a and b .
x dx = − __________
__________ 1
Then (x 2+ a 2) 3/2
(x 2
a 2)1/2
+
→ →
→
a ⋅ b = b ⋅ →
a = axbx + ayby + azbz = ab cos θ 2 dx 2 3/2 = ____________
__________ x
(x + a ) a 2(x 2 + a 2)1/2
| |
iˆ jˆ kˆ
→ →
→
a × b = − b × →
a = ax a y a z Cramer’s Rule
x by bz
b Two simultaneous equations in unknowns x and y,
ay a z ax a z ax a y a1x + b1 y = c1 and a2x + b2 y = c2,
 |
= ˆi
by bz | |
− ˆj
bx bz | | |
ˆ
+ k
bx by have the solutions
= (aybz − by az)ˆi + (azbx − bz ax)ˆj+ (axby − bx ay)k
ˆ
→
|
x = _______
|
c b
1 1
c 2 b c b − c b
2 __________
= 1 2 2 1
| →
a × b |= ab sin θ
| a 1 b
a 2 b |
1 a1b2 − a2b1
2
Trigonometric Identities and
a1 c1
sin α ± sin β = 2 sin _ 12 (α ± β)cos _ 12 (α ∓ β) | |
a c a1c2− a2c1
y = _______
2 2 = __________
.
cos α + cos β = 2 cos _ 12 (α + β)cos _ 12 (α − β)
| a b
|
a b − a2b1
1 1 1 2
a 2 b
2
*See Appendix E for a more complete list.
SI PREFIXES*
Factor Prefix Symbol Factor Prefix Symbol
24 −1
10 yotta Y 10 deci d
1021 zetta Z 10−2 centi c
1018 exa E 10−3 milli m
1015 peta P 10−6 micro μ
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.
,
