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04-BS-5: May 2016

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

  1. Question 1 Power-Series Solution of $y''-4xy=0$
  2. Question 2 Fourier Series of a Saturating Triangular Wave
  3. Question 3 Windowed-Cosine Pulse — Area and Fourier Transform
  4. Question 4 Least-Squares Normal Equations and Newton Divided-Difference Interpolation
  5. Question 5 Romberg Integration from Tabulated Data
  6. Question 6 Modified Newton’s Method for a Root and a Minimum
  7. Question 7 Cholesky ($LL^{T}$) Decomposition and Linear-System Solve

Start with Question 1 →

EGBC National Examination — 04-BS-5 Advanced Mathematics, May 2016. Closed-book, 3-hour exam; candidates were permitted one 8.5"x11" aid sheet (both sides) and an approved Casio/Sharp calculator. The exam instructs that any five (5) questions constitute a complete paper (only the first five answers as they appear 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.5 (Power Series Solutions of ODEs), Ch.11 (Fourier Series and Integrals), Ch.19–20 (Interpolation, Numerical Integration, Root-Finding, LU/Cholesky Factorization).