,MATHEMATICAL FORMULAS*
Quadratic Formula Derivatives and Integrals
If ax2 bx c 0, then x
b 1b2 4ac
2a
d
dx
sin x cos x sin x dx cos x
Binomial Theorem
d
dx
cos x sin x cos x dx sin x
nx n(n 1)x2
(1 x)n 1 ... (x2 1)
1! 2! d x
e ex ex dx ex
dx
Products of Vectors
Let u be the smaller of the two angles between a and b . : :
dx
2x2 a2
ln(x 2x2 a2)
Then
: :
a b b a axbx ayby azbz ab cos u
: :
x dx
(x2 a2)3/2
2
1
(x a2)1/2
dx x
2 2
î ĵ k̂ (x2 a2)3/2 a (x a2)1/2
: : :
a b b :
a ax ay az
bx by bz Cramer’s Rule
Two simultaneous equations in unknowns x and y,
î
ay az
by bz
ĵ
ax
bx
az
bz
k̂
ax
bx
ay
by a1x b1 y c1 and a2x b2 y c2,
have the solutions
(aybz by az)î (azbx bzax)ĵ (axby bxay)k̂
: :
|a b | ab sin u x
c1
c2
b1
b2
c1b2 c2b1
a1
a2
b1
b2 a1b2 a2b1
Trigonometric Identities
and
sin a sin b 2 sin 12(a b) cos 12(a b)
y
a1 c1
a2 c2
a1c2 a2c1
.
cos a cos b 2 cos b) cos b)
1 1
2 (a 2 (a a1 b1 a1b2 a2b1
a2 b2
* See Appendix E for a more complete list.
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.
, E X T E N D E D
FUNDAMENTALS OF PHYSICS
T E N T H E D I T I O N
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Quadratic Formula Derivatives and Integrals
If ax2 bx c 0, then x
b 1b2 4ac
2a
d
dx
sin x cos x sin x dx cos x
Binomial Theorem
d
dx
cos x sin x cos x dx sin x
nx n(n 1)x2
(1 x)n 1 ... (x2 1)
1! 2! d x
e ex ex dx ex
dx
Products of Vectors
Let u be the smaller of the two angles between a and b . : :
dx
2x2 a2
ln(x 2x2 a2)
Then
: :
a b b a axbx ayby azbz ab cos u
: :
x dx
(x2 a2)3/2
2
1
(x a2)1/2
dx x
2 2
î ĵ k̂ (x2 a2)3/2 a (x a2)1/2
: : :
a b b :
a ax ay az
bx by bz Cramer’s Rule
Two simultaneous equations in unknowns x and y,
î
ay az
by bz
ĵ
ax
bx
az
bz
k̂
ax
bx
ay
by a1x b1 y c1 and a2x b2 y c2,
have the solutions
(aybz by az)î (azbx bzax)ĵ (axby bxay)k̂
: :
|a b | ab sin u x
c1
c2
b1
b2
c1b2 c2b1
a1
a2
b1
b2 a1b2 a2b1
Trigonometric Identities
and
sin a sin b 2 sin 12(a b) cos 12(a b)
y
a1 c1
a2 c2
a1c2 a2c1
.
cos a cos b 2 cos b) cos b)
1 1
2 (a 2 (a a1 b1 a1b2 a2b1
a2 b2
* See Appendix E for a more complete list.
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.
, E X T E N D E D
FUNDAMENTALS OF PHYSICS
T E N T H E D I T I O N
, This page intentionally left blank
