I need help with this question, particularly 1a. I have to answer this in Python coding format. This particular snip is of Python but in Jupyter Notebook. Please explain the code you are using and what exactly you are doing and why so I can follow easily. Thank you for your help! It only allows me to pick one subject, but this class is called Environmental Modeling and Health and is essentially using mathematical models in Python to explain environmental behavior.

1D linear convection The one-dimensional linear convection equation is the simplest, most basic model that can be used to learn something about numerical solution of PDEs. It's surprising that this little equation can teach us so much! Note that if u in the equation below was replaced by "c (i.e, concentration) and the c in the equation below by a constant velocity term, then we would have the advection equation discussed in class. Here it is: The equation represents a wave propagating with speed c in the x direction, without change of shape. For that reason, it's sometimes called the one-wa)y wave equation (sometimes also the advection equation) Question 1a With an initial condition u(x, 0) -uo(x), show that the equation has an exact solution given by: u(x,t) = uo(x-ct) Question 1b Why do we call this a linear equation? Look at the exact solution for a moment we know two things about it 1. Its shape does not change, being always the same as the initial wave, uo, only shifted in the x-direction; and 2. it's constant along so-called characteristic curves, x-ct =constant. This means that for any point in space and time, you can move back along the characteristic curve to0 to know the value of the solution 1D linear convection The one-dimensional linear convection equation is the simplest, most basic model that can be used to learn something about numerical solution of PDEs. It's surprising that this little equation can teach us so much! Note that if u in the equation below was replaced by "c (i.e, concentration) and the c in the equation below by a constant velocity term, then we would have the advection equation discussed in class. Here it is: The equation represents a wave propagating with speed c in the x direction, without change of shape. For that reason, it's sometimes called the one-wa)y wave equation (sometimes also the advection equation) Question 1a With an initial condition u(x, 0) -uo(x), show that the equation has an exact solution given by: u(x,t) = uo(x-ct) Question 1b Why do we call this a linear equation? Look at the exact solution for a moment we know two things about it 1. Its shape does not change, being always the same as the initial wave, uo, only shifted in the x-direction; and 2. it's constant along so-called characteristic curves, x-ct =constant. This means that for any point in space and time, you can move back along the characteristic curve to0 to know the value of the solution