Engineering Mathematics Flashcards

Green's theorem relates a line integral around a closed curve to:

Answer: A double integral over the enclosed region

Green's theorem converts a line integral around a simple closed curve C to a double integral over the plane region D bounded by C, connecting circulation and flux to area integrals.

What is the condition number of a matrix used for?

Answer: Measuring sensitivity of the solution to input perturbations

The condition number measures how much the output changes for a small change in input. A large condition number indicates an ill-conditioned matrix where solutions are numerically unstable.

The Gauss-Seidel iterative method differs from Jacobi's method in that it:

Answer: Uses updated values as soon as they are computed

Gauss-Seidel immediately uses newly computed values in subsequent equations within the same iteration, often leading to faster convergence than Jacobi's method.

What is the Wronskian used for in differential equations?

Answer: Testing linear independence of solutions

The Wronskian determinant tests whether a set of functions are linearly independent. If the Wronskian is non-zero, the functions form a fundamental set of solutions.

A Poisson distribution is most appropriate for modeling:

Answer: The number of events in a fixed interval when events occur independently at a constant rate

The Poisson distribution models the count of independent events occurring at a constant average rate in a fixed interval of time or space, such as defects per unit or arrivals per hour.

The convolution integral f*g is commutative, meaning:

Answer: f*g = g*f

Convolution is commutative: the order of the two functions does not matter. This property is important in signal processing and systems analysis.