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04-BS-1: May 2018

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

  1. Question 1 Nonhomogeneous Euler–Cauchy Equation
  2. Question 2 Two Initial Value Problems — Separable and Constant-Coefficient
  3. Question 3 Tangent Plane and Tangent Line to a Surface Intersection
  4. Question 4 General Solution of a Resonantly-Forced Linear System
  5. Question 5 Angle Between a Line and a Surface
  6. Question 6 Line Integral via Stokes' Theorem (Cylinder ∩ Tilted Plane)
  7. Question 7 Closed-Surface Flux Integral via the Divergence Theorem (Paraboloid Cap)
  8. Question 8 Lagrange Multipliers — Minimum on an Ellipsoid

Start with Question 1 →

National Exams — May 2018 — 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, tangent planes, line/surface integrals, Stokes'/divergence theorems, Lagrange multipliers; Stewart, Calculus: Early Transcendentals (9th ed., Cengage) — vectors, gradients, constrained optimization.