SCE Engineering Mathematics 4

Question 1

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

Accepted Answer

A double integral over the enclosed region

Answer

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.

Question 2

What is the condition number of a matrix used for?

Accepted Answer

Measuring sensitivity of the solution to input perturbations

Answer

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.

Question 3

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

Accepted Answer

Uses updated values as soon as they are computed

Answer

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

Question 4

What is the Wronskian used for in differential equations?

Accepted Answer

Testing linear independence of solutions

Answer

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.

Question 5

A Poisson distribution is most appropriate for modeling:

Accepted Answer

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

Answer

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.

SCE Engineering Practice Test

SCE Engineering Practice Test

SCE Engineering Mathematics 4