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04-BS-1: May 2016

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

  1. Question 1 Three First- and Second-Order ODEs
  2. Question 2 Forced Second-Order IVP
  3. Question 3 Linear System of ODEs (Eigenvalue Method with Resonant Forcing)
  4. Question 4 Constrained Minimum via Lagrange Multipliers
  5. Question 5 Tangent Line to the Intersection of Two Surfaces
  6. Question 6 Volume Between a Paraboloid and a Plane, Outside a Cone
  7. Question 7 Surface Area of a Cone in the First Octant
  8. Question 8 Line Integral via Stokes' Theorem

Start with Question 1 →

National Exams — May 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.