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04-BS-1: December 2016

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

  1. Question 1 Euler–Cauchy Equation with Exponential–Polynomial Forcing
  2. Question 2 Forced Oscillator — Resonant and Non-Resonant Forcing Together
  3. Question 3 Constrained Extrema on an Ellipsoid via Lagrange Multipliers
  4. Question 4 Verifying an Eigenvector and Finding a Second Eigenpair
  5. Question 5 Tangent Plane and Tangent Line for Intersecting Surfaces
  6. Question 6 Closed-Surface Flux Through a Paraboloid Cap via the Divergence Theorem
  7. Question 7 Work Done by a Field Along a Helical Path — Conservative-Field Shortcut
  8. Question 8 Surface Integral Over a Half-Cylinder

Start with Question 1 →

National Exams — December 2016 — 04-BS-1 Mathematics. Three-hour, closed-book exam (one double-sided aid sheet permitted, approved calculator allowed). Format: eight questions offered; any five constitute a complete paper and only the first five appearing in the answer book are marked. All eight are solved below for completeness.

Reference texts: Kreyszig, Advanced Engineering Mathematics (10th ed., Wiley) — ODEs, systems of ODEs, line/surface integrals, Stokes'/divergence theorems; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — Lagrange multipliers, planes and surfaces in space, surface/flux integrals, volumes.