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04-BS-1: May 2017

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

  1. Question 1 Three First- and Second-Order ODEs
  2. Question 2 Euler–Cauchy Equation with a Non-Resonant Power Forcing
  3. Question 3 Extrema of a Linear Function on a Sphere via Lagrange Multipliers
  4. Question 4 Initial Value Problem for a 2×2 Linear System with Complex Eigenvalues
  5. Question 5 Plane Through Three Points and Its Intersection with a Second Plane
  6. Question 6 Line Integral via Stokes' Theorem, Clockwise Orientation
  7. Question 7 Closed-Surface Flux Through a Paraboloid Cap via the Divergence Theorem
  8. Question 8 Damped Mass–Spring Response to a Square-Wave Force

Start with Question 1 →

National Exams — May 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) — Lagrange multipliers, planes and surfaces in space.