AM II QUIZ

Which of the following is an entire function?

• f(z) = e^z

• f(z) = 1/z

• f(z) = |z|

• f(z) = Re(z)

The Cauchy-Riemann equations are satisfied for a function f(z) if:

• f is differentiable at a point

• f is continuous

• f is analytic

• f has a real derivative

The residue of f(z) = 1/(z^2 + 1) at z = i is:

• 1/(2i)

• -1/(2i)

• i/2

• -i/2

The integral of a function around a closed contour is zero if the function is:

• Real

• Harmonic

• Analytic

• Discontinuous

A pole of order 2 at z = 1 means:

• f(z) has a zero of order 2

• f(z) has a removable singularity

• f(z) has a simple pole

• f(z) behaves like 1/(z-1)^2 near z=1

The Laplace transform of f(t) = 1 is:

• 0

• 1

• 1/s

• s

The Laplace transform exists for:

• All functions

• Only bounded functions

• Exponentially bounded functions

• Periodic functions only

What is the Laplace transform of e^(at)?

• 1/(s+a)

• 1/(s-a)

• s/(s+a)

• a/(s+a)

The Laplace transform of f''(t) is:

• sF(s)

• s^2F(s) - sf(0) - f'(0)

• s^2F(s) + sf(0) + f'(0)

• F''(s)

The Fourier series represents a function as:

• A sum of polynomials

• A sum of sinusoids

• A sum of exponentials

• A product of functions