First Lesson in Applied
Mathematics
In the beginning, every young engineer is taught the
basic form of the sum of one plus one is written as
This form is banal and encourages bad style.
All first semester students know that
as well as that
But it is also obvious to the expert reader that
Therefore, one can express
more scientifically and clearly
for all engineers in the form
Furthermore, one can quickly see that
and
Therefore, one can write the previous form
in the following simplified and
more easily understood form
Next, let the reader consider that
Also consider that the inverse of the transpose of a
matrix equals the transpose of the inverse of that
matrix. So further simplification is gained with the
introduction of the vector in one-dimensional
space, where the following is valid
Now combine
with
and the following equation is obtained
Substitute the previous equation into the following
and one obtains the more
understandable and simplified form...
Every engineer can obviously see that the preceeding
equation is clearer and easier to understand than
There are many, many more methods
to write the equation
in a simplified form.
These will be discussed in the Second Lesson when
the engineer fully understands the applied basic
principles presented here.