Electricity and Magnetism I (P331)
M. R. Shepherd
September 3, 2008
1
Vector Calculus
1.1
Notation
1.1.1
Denoting a vector
Throughout the text vectors are typically noted in boldface upright characters.
For example, the vector
electric field is given by
E
.
Scalars are noted by normal italic letters; the scalar potential is given, for
example, by
V
. It is really impossible to designate boldface letters on the blackboard so you will often see
me write
E
instead of
E
.
1.1.2
Functions
We will also be dealing primarily with quantities that are a function of spatial coordinates.
To be more
compact, instead of writing
E
(
x, y, z
) or
E
(
x, y, z
), we will simply write
E
or
E
. It is important to remember
that these quantities are functions and have a spatial (and, later in the course, time) dependence.
1.1.3
Unit vectors
Note also that unit vectors appear with a hat. For example the quantity ˆ
x
means a vector with a length of
one unit pointing in the direction of the
x
axis. Some of you may be used to the notation
ˆ
i
,
ˆ
j
,
ˆ
k
to denote
the unit vectors of the
x
,
y
, and
z
axes. Our text uses ˆ
x
, ˆ
y
, ˆ
z
.
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 Fall '09
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 Vector Calculus, Magnetism, Vector field, twodimensions

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