MATH 1910 Workshop
is one important tool for solving engineering problems.
Dimensional analysis is the practice of keeping track of all units in a problem and making sure
the results have the expected units, or dimensions. Numbers by themselves are meaningless
without the corresponding units: 1 meter = 100 centimeter, but 1 does not equal 100. The
number and the unit are inseparable, at least in principle! Writing 1 meter rather than 1
is called “carrying the unit.” As a general rule, units should be carried in all engineering
computations and treated as algebraic quantities.
It is best to work out the equations in
symbolic form, replacing each symbol by its number and unit only at the very end.
Dimensional analysis is a powerful way to check that an answer is at least consistent with
the expected outcome. Getting the units right does not guarantee that the answer is right,
but getting them wrong is a clear indication of an error.
The units we will use in this workshop are Coulombs (the standard unit of charge, denoted