Mathematics Flashcards

Solve the differential equation y'' + 4y = 0. The general solution is:

Answer: y = C₁cos(2x) + C₂sin(2x)

The characteristic equation r² + 4 = 0 gives r = ±2i, leading to a sinusoidal solution.

The Fourier series of a function requires the function to be:

Answer: Periodic

Fourier series represent periodic functions, though convergence conditions (Dirichlet conditions) may vary.

What is the cross product A × B if A = (1, 0, 0) and B = (0, 1, 0)?

Answer: (0, 0, 1)

i × j = k, so (1,0,0) × (0,1,0) = (0,0,1).

A binomial distribution with n = 10 and p = 0.3 has a mean of:

Answer: 3

The mean of a binomial distribution is μ = np = 10 × 0.3 = 3.

Which method is best suited for finding roots of a nonlinear equation numerically?

Answer: Newton-Raphson method

Newton-Raphson is an iterative root-finding method for nonlinear equations.

The Divergence Theorem relates a volume integral of divergence to:

Answer: A surface integral over the bounding surface

Gauss's Divergence Theorem states ∭∇·F dV = ∯F·dS over the closed bounding surface.

If the standard deviation of a data set is 0, what can be concluded?

Answer: All values are identical

A standard deviation of 0 means there is no variability; all values equal the mean.