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04-BS-5: May 2014

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

  1. Question 1 Sturm–Liouville Eigenvalue Problem
  2. Question 2 Fourier Series and a Classical Series Identity
  3. Question 3 Fourier Transform of a Trapezoidal Pulse
  4. Question 4 Least-Squares Curve Fitting and an Interpolating Polynomial
  5. Question 5 Romberg Integration from Tabulated Data
  6. Question 6 Root-Finding by Bisection, Newton's Method, and Fixed-Point Iteration
  7. Question 7 Cholesky Factorization and Solving a Linear System

Start with Question 1 →

National Exams — May 2014 — 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) — Sturm–Liouville eigenproblems, Fourier series and the Fourier transform (Ch. 11), least-squares curve fitting, Lagrange/Newton interpolation, Romberg integration, and root-finding by bisection/Newton/fixed-point iteration (Ch. 19), Cholesky factorization (Ch. 20); Strang, Introduction to Linear Algebra (6th ed., Wellesley-Cambridge) — symmetric positive-definite systems and Cholesky factorization.