NivaarExam PrepOfficial exam papers ↗

04-BS-5: May 2015

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

  1. Question 1 Power-series solution of a second-order ODE
  2. Question 2 Fourier series of $F(x)=x^2$ and the Basel-sum identity
  3. Question 3 Fourier transform of a triangular pulse
  4. Question 4 Least-squares parabola (proof) and a linear least-squares fit
  5. Question 5 Romberg integration from tabulated data
  6. Question 6 Root finding by bisection then Halley's iteration
  7. Question 7 Cholesky factorization of a symmetric positive-definite matrix

Start with Question 1 →

National Exams — May 2015 — 04-BS-5 Advanced Mathematics. Three-hour, closed-book exam (one double-sided 8.5"×11" aid sheet permitted; approved Casio/Sharp calculator allowed). Format: seven questions of equal value (20 marks each, with internal splits as marked); any five constitute a complete paper and only the first five appearing in the answer book are marked. All seven are solved below for completeness.

Reference texts: Kreyszig, Advanced Engineering Mathematics (10th ed., Wiley) — power-series solutions of ODEs about an ordinary point (Ch. 5), Fourier series and the Fourier transform (Ch. 11), least-squares curve fitting and Cramer’s rule (Ch. 7, 19.7), Romberg integration, bisection and Halley’s (second-order Newton) iteration (Ch. 19), Cholesky factorization of a symmetric positive-definite matrix (Ch. 20.4).