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04-BS-1: December 2017

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

  1. Question 1 Resonant Initial Value Problem for a Forced Harmonic Oscillator
  2. Question 2 Euler–Cauchy Equation with Non-Resonant Exponential–Polynomial Forcing
  3. Question 3 Eigenvalues/Eigenvectors and a Linear System Initial Value Problem
  4. Question 4 Volume Inside a Sphere and Above a Cone (Spherical Coordinates)
  5. Question 5 Line Integral via Stokes' Theorem (Cylinder ∩ Tilted Plane)
  6. Question 6 Laplace-Transform Response of a Damped Mass-Spring System to a Square-Wave Force
  7. Question 7 Tangent Plane and Linear Approximation
  8. Question 8 Closed-Surface Flux Integral via the Divergence Theorem (Quarter-Elliptical Cylinder)

Start with Question 1 →

National Exams — December 2017 — 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, Laplace transforms, line/surface integrals, Stokes'/divergence theorems; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — spherical coordinates, tangent planes and linear approximation, triple integrals.