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

Use any software to plot or animate the first three eigenfunctions

with .

Choose the correct statement related to your observations:

Answer this question on the provided paper. Your response here will not be marked. Make sure to fill out all the details on the front cover and hand it in to receive marks.

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

Use any software to plot or animate the first three eigenfunctions

with .

Choose the correct statement related to your observations:

The trigonometric sum 

is shown in which of these graphs?  (Use any software to plot this sum.)

Consider the periodic function 

If this has Fourier representation

what is the value of ?

Evaluate the function at .

Evaluate the integral .