Recommendations for problem solutions, courtesy Tristan Hubsch, Howard University):
The purpose of problem solutions is to communicate to the instructor (grader) that you have understood the subject matter, know how to apply it in the context of the assigned problems, and know how to obtain a reasonable solution to the problem. As with any communication, clarity is precious. While the subsequent suggestions focus on problem sets, they may be equally useful for lab reports, exams, quizzes, and all other types of communication.
The following suggestions should assist you in developing and formulating systematic, sensible, and systematically comprehensible solutions. Your own variations are encouraged; however, no credit can possibly be given to unlegible work, as it communicates nothing favorable.
Start with a few short sentences that outline the method you intend to use to solve the problem, and a rationale why that method is appropriate. This might include physical laws, simplifying assumptions, and anything else you deem important.
Set up the problem (give the starting equations, relations, diagrams, etc.). Follow up with the essential steps (mathematical, logical) of the derivation starting from the stated initial point(s). Comment on the important steps, or any other important feature of your derivation.
Present the solution in a simple form, and using appropriate units. Identify your final answer(s) clearly, by underlining, encircling, framing, etc. Show a proof or a check that your solution is reasonable (e.g., verify units!).
Recall that diagrams need
complete labeling (axes, marked points, regions, objects, etc.) to be
meaningful. “A picture is worth a thousand words,” but an ill-labeled
picture
amounts to a thousand words of rampant gibberish, or noise at best.
Solutions will be
evaluated. The above suggestions should help organize your work in
a logical way, and so contribute to favorable evaluation. The final
touch then
is in presenting the whole problem set.
Seems obvious, but it isn't: at the top of the problem set, clearly state (1) your name, and perhaps your student ID number (in case there is another student with a similar name), (3) the problem set (by number, by due date, etc.), (4) each individual problem (by number, by page in the textbook, etc.). DO NOT copy the text of the problem from the problem sheet or textbook - it is referred to by having identifying the problem by number.
Identify the symbols in a formula (e.g., "where F is the force, m the mass, and a the acceleration of a particle"), but do not recast a formula into sentence(s). Conversely, however, a deductive line of reasoning - in words - may be conveniently summarized in a mathematical expression: as it increases clarity without creating clutter. Similarly, a well-labeled diagram needs no explanation, but subsequent deductions may benefit from a few words of explanation (e.g., “We see from the diagram that the triangle ABC is similar to BCD, so that the ratio of lengths AB/BC = CB/BD.”).
Alternate conventions exist for ease of expression, and should not be used to breed confusion. For example, vectors may be indicated by an arrow over the symbol, or by using boldfaced letters. You may use either of the two, but: pick your convention and then stick to it; in particular, do not arbitrarily omit the "vector identifier" of your choice. Remember that the instructors and the graders only see (and grade) what is clearly written down in your assignments, not what you intended to imply.