NivaarExam PrepOfficial exam papers ↗

04-BS-5: December 2017

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

  1. Question 1 Sturm–Liouville Eigenvalue Problem
  2. Question 2 Fourier Series of a Piecewise-Quadratic Function
  3. Question 3 Fourier Transform of a Two-Sided Exponential
  4. Question 4 Lagrange Interpolation and Forward-Difference Derivatives
  5. Question 5 Romberg Integration of Tabulated Data
  6. Question 6 Fixed-Point Iteration, Bisection/Newton, and Extrema of a Quartic
  7. Question 7 Crout LU Decomposition and Linear System Solution

Start with Question 1 →

National Examinations, December 2017 — 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: LU/Crout factorization). Supporting: Chapra & Canale, Numerical Methods for Engineers, 7th ed. — Ch. 5–6 (bracketing and open root-finding methods), Ch. 18 (interpolation), Ch. 22 (Romberg integration); Strang, Introduction to Linear Algebra, 6th ed. — Ch. 2 (LU factorization).