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04-BS-1: December 2015

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

  1. Question 1 Two First- and Second-Order ODEs
  2. Question 2 Two Initial Value Problems
  3. Question 3 Two Lines in Space — Intersection, Common Perpendicular, and Containing Plane
  4. Question 4 Constrained Max/Min via Lagrange Multipliers (Ellipsoid Constraint)
  5. Question 5 Closed-Surface Flux Integral via the Divergence Theorem (Paraboloid Capped by a Disk)
  6. Question 6 Angle of Intersection Between a Line and a Hyperboloid
  7. Question 7 Line Integral via Stokes' Theorem (Cylinder ∩ Tilted Plane)
  8. Question 8 Volume Inside an Ellipsoid and Above a Cone

Start with Question 1 →

National Exams — December 2015 — 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 lines in space, surface/flux integrals, volumes.