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04-BS-1: December 2013

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

  1. Question 1 Two Linear ODEs — Resonant IVP and a Reducible Second-Order Equation
  2. Question 2 Classifying and Diagonalizing a Quadratic Form (Conic Section)
  3. Question 3 Constrained Minimum via Lagrange Multipliers
  4. Question 4 Plane Through Three Points, and Its Intersection Line With Another Plane
  5. Question 5 Closed-Surface Flux Integral via the Divergence Theorem
  6. Question 6 Line Integral via Stokes' Theorem
  7. Question 7 Angle of Intersection Between a Line and a Hyperboloid
  8. Question 8 Driven Damped Mass-Spring System (2nd-Order IVP)

Start with Question 1 →

National Exams — December 2013 — 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; Strang, Introduction to Linear Algebra (6th ed.) — quadratic forms and principal-axis diagonalization.