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04-BS-5: May 2017

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

  1. Question 1 Power-Series Solution about an Ordinary Point
  2. Question 2 Fourier Series of a Square Wave and the Leibniz Series
  3. Question 3 Fourier Transform of a Raised-Cosine Pulse
  4. Question 4 Newton’s Divided-Difference Interpolation
  5. Question 5 Romberg Integration from a Table
  6. Question 6 Bisection, Newton–Raphson and Fixed-Point Iteration
  7. Question 7 Cayley–Hamilton, Matrix Inversion and a Linear System

Start with Question 1 →

National Examinations, May 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. 5 (Series Solutions of ODEs), Ch. 11 (Fourier Series, Integrals and Transforms), Ch. 19 (Numerics in General: interpolation, integration, solution of equations by iteration), Ch. 20 (Numeric Linear Algebra). 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. 6 (eigenvalues, Cayley–Hamilton).