Organizing and Fine Tuning in Differential Equations

  1. 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.

  2. In order to quickly organize formulas in a logical structure, we should derive the key formula first.
        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)] [Guo, p.504, (3) & (4)].