Notation Quiz for the Mathematics-Physics Workshop, June 1999, updated with comments from
participants, July 1999
We all know that we use different conventions for notation, even within math and physics. It is
enlightening to explore some of these differences before we begin team-teaching! Here is a quiz based on
differences I experienced. Drs. Dunbar and Fuller also contributed, as well as participants in the June 1999
mathphys Montana workshop.
1.
We commonly denote an infinitesimal piece of arclength by
a.) dl
b.) ds
2.
Consider two points, P1 and P2 . The vector r12
a.) begins at P1 and goes to P2 .
b.) begins at P2 and goes to P1 .
3.
In drawing the x-y-z axes for 3D Cartesian coordinates, the preferred orientation is: (or indicate if you
prefer a corresponding left hand frame!)
4.
In discussing the normal to the plane, one discusses the tangent vectors to the surface in the x direction
and the y direction. You denote these vectors by Tx and Ty . This use of notation is
a.) very natural.
b.) mildly confusing; perhaps use T1 and T2 .
c.) incredibly confusing! You have permanently damaged young minds who have only recently
become convinced that subscripts x and y mean the vector components!
5.
When writing multiple integrals, the notation
  f ( x, y)dxdy
x y
a.) is fine.
b.) is terrible! You must use
  f ( x, y)dydx
x y
c.) This is even better!



 dx
f
(
x
,
y
)
dy
x  y


d.) why not
 dx  dy
x
6.
f ( x, y ) ?
y
In standard unit vector notation, you should write
Txi  Ty j
b.) iTx  jTy
a.)
Tx x  Ty y
 x  yT
 y
d.) xT
c.)
7.
We always seem to need another variable that should be called r. We first use r and second use R,
and then
a.) r
r
b.) ~
c.) 
8.
If you check that fount of all truth, THE WEB, to find the standard convention used for spherical
coordinates, you will find:
a.) (r, , ) where  is the polar angle in the equatorial plane (longitude) and  is the angle from the
‘North pole.’
b.) (r, , ) where  is the angle from the “North pole” and  is the longitude.
c.) (r, , ) where  is the angle from the “North pole” and  is the longitude.
d.) (r, , ) where  is the longitude and  is the angle from the “North pole.”
e.) (, , r) where  is the longitude and  is the latitude (the angle from the equator.)
f.) (, , r) where  is the longitude and  is the latitude.
g.) (r, , ) where  is the longitude and  is the latitude.
h.) (r, , ) where  is the latitude and  is longitude.
9.
A car goes down a road ( or a pendulum swings back and forth, or spring with a mass attached is
stretched and released, or...). Its position as a function of time is referred to as
a.) the distance (or distance function)
b.) the displacement (as a function of time)
10. The small letter i represents
a.) the current in a wire
b.) the square root of -1
c.) a unit vector in the x-direction
11. A mass is 3.2 kg. Its acceleration is 9.8 m/s^2. The gravitational force on the mass is
a.) 31.3 N
b.) 31.36 N
c.) 31.4 N
d.) 31.36
e.) 31
f.) 31 N
12. The relation between potential and the associated vector function is
a.)  f = F
b.) - f = F