Engineering Mathematics Flashcards
6 cards from real Fundamentals of Engineering practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Engineering Mathematics flashcards as text
What does the Fourier series represent for a periodic function?
Answer: A sum of sinusoidal components at integer multiples of the fundamental frequency
The Fourier series decomposes a periodic function into sinusoidal components at integer multiples of the fundamental frequency.
In probability, if events A and B are mutually exclusive, then P(A ∪ B) equals:
Answer: P(A) + P(B)
For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
What is the general solution to the ordinary differential equation dy/dx + 2y = 0?
Answer: y = Ce^(-2x)
This first-order linear ODE has solution y = Ce^(-2x) obtained by separation of variables.
The Taylor series expansion of sin(x) about x = 0 begins with which terms?
Answer: x - x³/6 + x⁵/120 - ...
The Maclaurin series of sin(x) is x - x³/3! + x⁵/5! - ..., which matches x - x³/6 + x⁵/120.
Which of the following is the correct formula for the determinant of a 2×2 matrix [a b; c d]?
Answer: ad - bc
The determinant of a 2×2 matrix is calculated as ad - bc.
What is the dot product of vectors A = (2, 3, 1) and B = (1, -1, 4)?
Answer: 3
The dot product A·B = (2)(1) + (3)(-1) + (1)(4) = 2 - 3 + 4 = 3.