HUNTERTUTORING

Answer Key — Calculus of variations

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Methods of applied mathematics

Do not share with students before practice tests.

Worksheets — Sets 1–10

| Set | Guidance | | --- | --- | | Set 1 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 2 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 3 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 4 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 5 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 6 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 7 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 8 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 9 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 10 | Calculus of variations — verify written work and accept reasonable drawings. |

Worksheets — Sets 11–20

| Set | Guidance | | --- | --- | | Set 11 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 12 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 13 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 14 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 15 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 16 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 17 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 18 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 19 | Calculus of variations — verify written work and accept reasonable drawings. | | Set 20 | Calculus of variations — verify written work and accept reasonable drawings. |

Review tiers 1–10

  • Checklists are parent-judged.
  • Written items: verify against practice set patterns.
  • Standard text: Euler–Lagrange equation and variational principles Brachistochrone and classical problems Constraints and Lagrange multipliers in variational problems Hamilton's principle and mechanics (introduction) Rayleigh–Ritz 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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