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04-BS-5: December 2018

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

  1. Question 1 Sturm–Liouville Eigenvalue Problem
  2. Question 2 Fourier Series of $x^2$ and of Its Derivative
  3. Question 3 Fourier Transform of a Triangular Pulse
  4. Question 4 Least-Squares Parabola Proof and Lagrange Interpolation
  5. Question 5 Romberg Integration and the Area Between Two Curves
  6. Question 6 Root-Finding — Bisection, Modified Newton, and Fixed-Point Iteration
  7. Question 7 Cholesky Decomposition and Linear System Solution

Start with Question 1 →

National Examinations, December 2018 — 04-BS-5 Advanced Mathematics, 3 hours, closed book (approved Casio/Sharp calculator and one double-sided aid sheet permitted). Any five of the seven questions constitute a complete paper and all questions are of equal value; all seven are answered below as a full study resource.

Reference texts: Kreyszig, Advanced Engineering Mathematics, 10th ed. (Wiley) — Ch. 11 (Sturm–Liouville Problems, Fourier Series, Fourier Integrals and Transforms), Ch. 19 (Numerics in General: interpolation, numerical differentiation, Romberg integration, iterative equation solving), Ch. 20 (Numeric Linear Algebra: Cholesky factorization). Supporting: Chapra & Canale, Numerical Methods for Engineers, 7th ed. — Ch. 5–6 (bracketing and open root-finding methods), Ch. 17 (least-squares regression), Ch. 18 (interpolation), Ch. 22 (Romberg integration).