Answer Key — Error analysis and root finding

Numerical methods for engineers

Do not share with students before practice tests.

Worksheets — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 2 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 3 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 4 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 5 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 6 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 7 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 8 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 9 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 10 | Error analysis and root finding — verify written work and accept reasonable drawings. |

Worksheets — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 12 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 13 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 14 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 15 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 16 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 17 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 18 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 19 | Error analysis and root finding — verify written work and accept reasonable drawings. | | Set 20 | Error analysis and root finding — verify written work and accept reasonable drawings. |

Review tiers 1–10

• Checklists are parent-judged.
• Written items: verify against practice set patterns.
• Standard text: Sources of error: truncation, round-off, and propagation Taylor series review for error estimates Bisection, Newton–Raphson, and secant methods Fixed-point iteration and convergence criteria Systems of nonlinear equations (Newton's method introduction)

Practice test scoring

| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |

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