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04-BS-5: May 2013

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 and a Classical Series Identity
  3. Question 3 A Cosine Pulse and Its Fourier Transform
  4. Question 4 Least-Squares Parabola and Lagrange Interpolation
  5. Question 5 Romberg Integration of Tabulated Data
  6. Question 6 Root-Finding by Halley-Form Iteration and Fixed-Point Iteration
  7. Question 7 Cayley–Hamilton Theorem, Matrix Inverse, and a Linear System

Start with Question 1 →

National Exams — May 2013 — 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); 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 (Ch. 5), Fourier series and the Fourier transform (Ch. 11), least-squares curve fitting, Lagrange interpolation, Romberg integration and root-finding (Ch. 19); Strang, Introduction to Linear Algebra (6th ed., Wellesley-Cambridge) — the Cayley–Hamilton theorem and matrix inversion.