For convenience, we plot these graphs (the graphs are in the given order)

The wave equation

requires how many initial conditions to be completely solved?

Consider Laplace's equation

on the disc

with boundary condition

The function ...

(choose the most appropriate completion)

Which of the following is a solution to Laplace's equation on the annulus ?  (Choose all that satisfy the equation.)

Using separation of variables, the solution to the partial differential equation

 where is a separation constant and , , and are arbitrary constants, is:

Which of the following gifs could represent a solution to the heat equation 

on a domain with one spatial dimension (shown as the horizontal axis)?

The heat equation in a bar with its ends and kept at temperature zero, allows for solutions defined by the eigenfunctions .

In MATLAB, plot or animate the first three eigenfunctions

with .

Choose the correct statement related to your observations:

Which of the following equations are partial differential equations?