Theory

If the project requires a design method or some special analysis to interpret the results, then you may need to have a section dedicated to Theory. Such a section would likely contain theoretical and/or mathematical developments. The typesetting of mathematical equations and how they should be referenced is discussed in Chapter 9. Make sure that there is enough new material to warrant a separate section in the report. If the analysis is relatively simple and short (e.g., a few equations) it can be presented in the Introduction, in the Discussion, or it can be included in the Results. If you have detailed analyses that are not essential to the interpretation of the results, you must certainly mention them but you should include them in an Appendix.

If the analysis or method was taken from referenced material, do not repeat the derivation. Cite the author, give a summary of the assumptions and general theory, and then produce the final result. However if you are substantially modifying a theory or design method, it is best to reproduce it to situate the reader. This will facilitate the comparison of the two schemes.

You will sometimes be required to use theory derived from two different sources. Due to personal preferences of the authors, the nomenclature of variables will most likely be incompatible. Faced with this dilemma, choose one of the two nomenclatures and rewrite the second source using the new nomenclature. Using many different letters to express the same variable leads to great confusion.

Complicated derivations are by definition hard to follow. Do not make them incomprehensible by deleting seventeen steps and stating it can be shown that or it is obvious that. What is obvious to the author is usually hard to find out for the reader. A mistake in a venerable electromagnetic theory textbook was recently corrected by sifting through seven different instances of it can be shown that. The author had lost a minus sign in three of these shortcuts. To make the task even more daunting, two of these mistakes cancelled each other out. This implied that intermediate formulae in the derivation were sometimes erroneous, sometimes accurate. Finding the correct derivation was tedious.

A Theory section is often used as a filler to make the report seem important (by its sheer size and weight). This tactic is usually self-defeating. Many supervisors will flatly refuse to read a report until it has been condensed to a reasonable length. To coin a new adage: the thickness of the report often reflects the thickness the author.