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04-BS-5: Undated paper

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 Wave and a Series Identity
  3. Question 3 Area, Fourier Transform and Limiting Behaviour of a Raised-Cosine Pulse
  4. Question 4 Newton's Divided-Difference Interpolating Polynomial
  5. Question 5 Romberg Integration of a Tabulated Experimental Curve
  6. Question 6 Bisection, Newton–Raphson and Fixed-Point Iteration
  7. Question 7 Matrix Inverse by the Cayley–Hamilton Theorem

Start with Question 1 →

Paper format. National Examinations, 04-BS-5 Advanced Mathematics — three-hour closed-book paper; one approved Casio or Sharp calculator and one 8.5″×11″ two-sided aid sheet are permitted. Seven questions are printed and any five constitute a complete paper, all questions being of equal value (20 marks each). All seven questions are solved below, because the set is a study resource rather than an examination attempt.

Reference texts for 04-BS-5 Advanced Mathematics. E. Kreyszig, Advanced Engineering Mathematics, 10th ed. — Ch. 5 (series solutions of ODEs), Ch. 11 (Fourier series and Fourier transforms), Ch. 19 (numerics: root finding, interpolation, integration), Ch. 20 (numeric linear algebra); R. L. Burden and J. D. Faires, Numerical Analysis, 9th ed. — Ch. 2 (bisection, Newton, fixed-point iteration), Ch. 3 (divided-difference interpolation), Ch. 4 (Romberg integration); G. Strang, Introduction to Linear Algebra, 6th ed. — Ch. 6 (eigenvalues, Cayley–Hamilton).

Reading of the paper. Where a printed symbol is unclear, the reading adopted is stated explicitly and justified from the paper's own internal evidence (for example Question 7's matrix, which is recovered exactly from the characteristic equation the question prints).