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04-BS-1: May 2013

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

  1. Question 1 Second-Order IVP by Undetermined Coefficients
  2. Question 2 General Solutions of Three First/Second-Order ODEs
  3. Question 3 Eigenvalues/Eigenvectors and a Nonhomogeneous Linear System
  4. Question 4 Tangent Plane and Linear Approximation
  5. Question 5 Surface Area of a Cone in the First Octant
  6. Question 6 Two Lines in Space — Intersection, Orthogonal Line, Common Plane
  7. Question 7 Line Integral via Stokes' Theorem
  8. Question 8 Volume Inside an Ellipsoid and Above a Cone

Start with Question 1 →

National Exams — May 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' theorem; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — partial derivatives/tangent planes, surface area, multiple integrals; Strang, Introduction to Linear Algebra (6th ed.) — eigenvalues and eigenvectors.