NivaarExam PrepOfficial exam papers ↗

04-BS-5: December 2014

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

  1. Question 1 Power-Series Solution of a Variable-Coefficient ODE
  2. Question 2 Fourier Series of an Odd Function and a Series Identity
  3. Question 3 Laplace-Kernel Function — Area, Fourier Transform, and the $a\to0$ Limit
  4. Question 4 Newton Divided-Difference Interpolation and Numerical Differentiation
  5. Question 5 Romberg Integration of Tabulated Data
  6. Question 6 Newton’s Method and Fixed-Point Iteration
  7. Question 7 LU (Crout) Decomposition and Solution of a Linear System

Start with Question 1 →

National Exams — December 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) — power-series solutions of ODEs about an ordinary point (Ch. 5), Fourier series and the Fourier transform (Ch. 11), Newton divided-difference interpolation, numerical differentiation, Romberg integration, Newton’s method and fixed-point iteration (Ch. 19), Doolittle/Crout LU factorization and forward/back substitution (Ch. 7).