When writing up a mathematical derivation, one should always define why you are doing this at the beginning, show the derivation, and then discuss the meaning of the results in terms of the physics as well as the mathematics. Specifically:
1. Motivate the derivation. Be sure to describe the physics problem to be solved and why you need to solve it.
2. Write the governing equation(s). Describe in words why they govern your problem.
3. Define all variables and notation in the governing equations, even where “obvious.”
4. Explain your approach to solving the problem. Include references if the technique is not standard.
5. Explain why this is the best approach to solving the problem.
6. Solve the problem. Include lines of text between equations to describe your steps. Only skip steps where the math is trivial. Include enough steps and description that someone could easily repeat your calculation. Define notation and variables introduced along the way.
7. Present the final solution.
8. Explain the meaning of the mathematics of the solution. Sometimes, this will include explaining term by term.
9. Explain the physics of the solution. What does it mean? How does it enlighten you about the solution of your problem?
10. Optional: In many cases, you will plot your solution or model it numerically. This will greatly aid in interpreting the result and painting a picture of its meaning.
Sue Ellen Haupt
This page was last updated by George Young on March 20, 2008