9781118230725.pdf

(Chris Devlin) #1
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:



ax
bx


ay
by


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*

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