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04-BS-5: December 2015

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

  1. Question 1 Sturm–Liouville Eigenvalue Problem
  2. Question 2 Fourier Series and a Classical Identity
  3. Question 3 Fourier Transform of a Two-Sided Exponential Pulse
  4. Question 4 Polynomial Interpolation — Newton Divided Differences and Lagrange
  5. Question 5 Romberg Integration of Tabulated Data
  6. Question 6 Root-Finding — Newton, Fixed-Point Iteration, and Bisection
  7. Question 7 Doolittle LU Decomposition and Linear System Solve

Start with Question 1 →

EGBC National Examination — 04-BS-5 Advanced Mathematics, December 2015. Closed-book, 3-hour exam; candidates were permitted one 8.5"x11" aid sheet (both sides) and an approved calculator. The exam instructs that any five questions constitute a complete paper (first five answers in the answer book are marked); every question is solved below as a full study resource.

Reference texts: Kreyszig, Advanced Engineering Mathematics, 10th ed. — Ch.11 (Fourier series/transforms, Sturm–Liouville problems), Ch.19–20 (interpolation, numerical integration, root-finding, LU decomposition).