# Work through an engineering or math calculation step by step

A fully worked solution with every formula, intermediate value, and a check, so you can follow and repeat it.

- Topic: Learning & Teaching
- Framework: Few-Shot
- Level: Standard
- Tags: Code, Fill-in Template, Step-by-step
- Source: https://www.thinkwithprompt.com/prompts/work-through-an-engineering-or-math-calculation-step-by-step

## Prompt

```text
Work through this calculation step by step so I can follow and repeat it.

**Problem:** [PASTE THE PROBLEM — e.g. "compute the MDCT of x(n) = [1, 2, 3, 4]", "find the beam deflection at midspan"]
**Given values and units:** [VALUES]
**Course or context:** [e.g. "signals and systems", "statics", "thermodynamics"]
**Method required, if any:** [e.g. "use the definition, not a library function"]
**My level:** [what I already know]

Structure the answer:
1. **Identify:** what is being asked, the knowns, unknowns, and any sizes or parameters (e.g. N, 2N, boundary conditions).
2. **Formula:** the governing equation with every symbol defined, and why it applies.
3. **Substitution:** plug in values one step at a time. When there are many repeated terms (sums, matrices, cosine or sine values), show them in a table so nothing is hidden.
4. **Result:** the final answer with units and sensible rounding.
5. **Check:** a sanity test — dimensions, a limiting case, symmetry, an estimate, or a short code snippet I can run to verify.
6. **Watch out for:** the two or three mistakes students most often make on this type of problem.

Rules:
- Do not skip algebra or arithmetic steps.
- If the problem is ambiguous (conventions, normalization, index starting point), state the assumption and show how the answer would change.
- Then give me a similar practice problem with the answer only, so I can test myself.
```

## What to fill in

- VALUES
- e.g. "signals and systems", "statics", "thermodynamics"
- e.g. "use the definition, not a library function"
- what I already know

Free to copy and use. From ThinkWithPrompt (https://www.thinkwithprompt.com/), a library of 2,663 curated AI prompts.