Thinking About Equations
A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering
Chapter One
EQUATIONS REPRESENTING
PHYSICAL QUANTITIES
Some equations model systems or processes that occur in the real, physical
world. Most of the variables that appear in these equations have dimensions,
and they carry certain physical units. For example, a variable d describing
distance has the dimension of length and carries a specific unit such as meters,
microns, or miles. The numerical value of the variable d is given as a multiple
of the unit we choose, and the specific unit is usually chosen so that the numerical
values are convenient to work with.
Without a unit, the physical meaning of the numerical value associated with
a dimensioned variable contains no useful information. For example, to say
the distance between points A and B is "d = 8" is not useful for scientific and
engineering purposes. We also have to specify a unit of length, such as d = 8in,
d = 8m, or d = 8 li ... read full excerpt from Thinking About Equations: A Practical Guide for Developing Mathematical Intuitionin the Physical Sciences and Engineering ebook
