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04-BS-1: May 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 Extrema of a Linear Function on a Sphere
  3. Question 3 Tangent Line to the Intersection of Two Surfaces
  4. Question 4 Eigenvalues/Eigenvectors of a $2\times2$ Matrix, and the Associated Linear IVP System
  5. Question 5 Closed-Surface Flux Through a Paraboloid Cap via the Divergence Theorem
  6. Question 6 Volume Between a Paraboloid and a Plane, Outside a Cone
  7. Question 7 Line Integral via Stokes' Theorem, Clockwise Orientation
  8. Question 8 Damped Mass-Spring System Driven by a Square Pulse (Laplace Transform)

Start with Question 1 →

National Exams — May 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, Laplace transforms/unit-step forcing, surface/flux integrals, Stokes' theorem; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — Lagrange multipliers, planes/tangent lines in space, volumes of revolution; Strang, Introduction to Linear Algebra (6th ed.) — eigenvalues/eigenvectors and linear systems of ODEs.