How does the drum make the sound?
How does heat conduct inside a long and thin rod?
How does material diffuse inside gas, liquid, or solid?
How does heat conduct inside a thin membrane?
How does pollutant outlet from a chimney diffuse into atmosphere, etc.?
Traveling around the world with Diffeq, a graduate school student, we will be surprised that the questions above raised in our daily life can be explained by partial differential equations. We can get the answers to many more questions as well as the ones above by solving partial differential equations.
Learning engineering math, we don't want to simply hear words in lectures, just read letters and numbers in the books, and merely do the problem sets, but really want to:
Actually and vividly picture what the questions are about
See how the equations work doing real examples
Get the point of the equations
And have Fun doing the work.