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04-BS-1: December 2014

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

  1. Question 1 Two Linear ODEs — Variation of Parameters with a Secant Forcing, and a Resonant Polynomial+Exponential Forcing
  2. Question 2 Cauchy–Euler Equation with a Resonant Power-Law Forcing
  3. Question 3 Two Lines in Space — Intersection, Orthogonal Line, and Common Plane
  4. Question 4 Closed-Surface Flux Through a Cone via the Divergence Theorem
  5. Question 5 Line Integral via Stokes' Theorem, Clockwise Orientation
  6. Question 6 Volume Outside a Cylinder, Inside an Ellipsoid
  7. Question 7 Eigenvalues/Eigenvectors of a $3\times3$ Matrix, and the Associated Linear System
  8. Question 8 Tangent Plane to a Logarithmic Surface and Linear Approximation

Start with Question 1 →

National Exams — December 2014 — 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, Cauchy–Euler equations, surface/flux integrals, Stokes' theorem; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — lines and planes in space, volumes of revolution, tangent-plane linear approximation; Strang, Introduction to Linear Algebra (6th ed.) — eigenvalues/eigenvectors and linear systems of ODEs.