Organizing and Fine Tuning in Differential Equations
When it is inconvenient for an author to typeset the details of a long calculation,
he should at least divide the procedure of calculation into several stages. At
the end of each stage, he should summarize the result to show the progress he
has made. This allows the reader to easily locate his mistakes if he fails to
follow the argument. For a long calculation, we would like to look for improvements
by finding a short cut, avoiding repetition, or increasing cancellations, etc. [Leb,
p.253, l.-4-p.254, l.-2]
is a good example of assisting the readers throughout a long calculation.
In order to quickly organize formulas in a logical structure, we should derive the key formula
For example, in [Guo, §9.4], we should derive [Guo, p.504, (5)] first using [Guo,
p.504, (2) & (4)]. Then, by Cramer's rule, we may easily see [Guo, p.504, (1) &
(2)] Û [Guo, p.504, (3) & (4)].