Allied & ICAR Exam Bank • ALLIED_2665 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Fourier, Taylor and MacLaurin series

Question Statement:

The Fourier series representation of a periodic function $f(t)$ with period $T$ and fundamental frequency $\omega_0 = 2\pi/T$ is valid if $f(t)$ satisfies:

Options:

  • (A) Dirichlet conditions
  • (B) Navier–Stokes conditions
  • (C) Rankine–Hugoniot conditions
  • (D) Bernoulli conditions

Answer Key:

A

Step-by-Step Solution & Explanation

Dirichlet conditions (single-valued, finite number of discontinuities and extrema per period, absolutely integrable) guarantee Fourier series convergence.
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