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Massachusetts Institute of Technology
Department of Physics
8.022 Spring 2004
Assignment 0: Math review/practice
Post date: Tuesday, February 3rd
Due date: Thursday, February 5th
Be sure to write your
name
and
section number
on your pset
Please
staple
multiple pages together
The purpose of this assignment is to give you some inkling of the kind of math that you will
be doing in 8.022.
1. Circle your recitation section:
(a) R01
(b) R02
(c) R03
(d) R04
Remember your answer and write it on all 8.022 assignments (including this one!) and
exams.
2. Partial derivatives and coordinate conversions (20 pts)
(a)
f
(
x,y,z
) = 1
/
√
x
2
+
y
2
+
z
2
. Compute
∂f/∂x
,
∂f/∂y
, and
∂f/∂z
.
(b) De±ning the radial displacement vector
~
r
=
x
ˆ
x
+
y
ˆ
y
+
z
ˆ
z
, write down a very simple
form for the following quantity:
~
∇
f
≡
ˆ
x
∂f
∂x
+ ˆ
y
∂f
∂y
+ ˆ
z
∂f
∂z
.
(Note that the symbol
≡
means “is equivalent to” or “is de±ned as”. The symbol
~
∇
is the gradient operator; some of you may already be familiar with it. The rest of you
will be very soon!)
(c) Convert to cylindrical coordinates. Put
x
=
r
c
cos
φ
,
y
=
r
c
sin
φ
; leave
z
untouched.
Compute
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This homework help was uploaded on 04/11/2008 for the course PHYSICS 8.022 taught by Professor Hughes during the Spring '08 term at MIT.
 Spring '08
 Hughes
 Mass

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