NivaarExam PrepOfficial exam papers ↗

04-BS-5: May 2018

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 Piecewise-Linear Tent Function
  3. Question 3 Fourier Transform of a Finite Cosine Window
  4. Question 4 Least-Squares Parabola Normal Equations & Newton Divided-Difference Interpolation
  5. Question 5 Romberg Integration of Tabulated Data
  6. Question 6 Root-Finding by Bisection, Newton's Method, and Fixed-Point Iteration
  7. Question 7 Cholesky Decomposition and Solution of a Linear System

Start with Question 1 →

National Examinations, May 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. 5 (Series Solutions of ODEs about an ordinary point), Ch. 11 (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/LU 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 (Cholesky/LU factorization).