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PHY 103N Cheat Sheet
:
Average value of a series of measurements:
( 29
( 29
∑
∑
=
=
∆
∆
=
N
i
i
N
i
i
i
x
x
x
x
1
2
1
2
1
(eq. 0.1)
Uncertainty for average value:
( 29
∑
=
∆
=
=
∆
N
i
i
x
x
1
2
1
1
s
(eq. 0.2)
Error propagation for a function
f=f
(
x,y,z,…
):
...
+
∆
∂
∂
+
∆
∂
∂
+
∆
∂
∂
=
∆
z
z
f
y
y
f
x
x
f
f
(eq. 0.6)
Useful rules of differentiation:
•
( 29
1

=
n
n
anx
ax
dx
d
where
const
a
=
,
ℜ
∈
n
•
( 29
( 29 ( 29
q
q
q
a
a
a
d
d
cos
sin
=
and
( 29
( 29 ( 29
q
q
q
a
a
a
d
d
sin
cos

=
•
( 29
ax
ax
ae
e
dx
d
=
•
( 29 ( 29
( 29
( 29
( 29
dx
x
dg
dx
x
df
x
g
x
f
dx
d
+
=
+
•
( 29 ( 29
( 29 ( 29
( 29
( 29
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This note was uploaded on 03/30/2011 for the course PHYS 103N taught by Professor Chiu during the Spring '11 term at University of Texas at Austin.
 Spring '11
 Chiu
 Physics, Heat

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