 ##### The transient solution contains the time dependent behavior of each node in the discretized reactor.  ##### Department 1: 1 person.   ##### We can do different things with different key presses.  ##### Python provides a sum function to compute the sum of a list. ##### Suppose now we have nested lists. ##### For completeness, we also examine the steady state solution. ##### In the next block of code, we get the transient solutions, and the steady state solution. ##### It can be tedious to try to add the customization code to the existing code that makes the plot. ##### If you have many plots it can be tedious to try setting each text property. ##### Each row contains the concentration as a function of volume at a specific time point. ##### In this example we show how to click on a data point, and show which point was selected with a transparent marker, and show a label which refers to the point.   ##### You can see from the animation that after about 10 time units, the solution is not changing further, suggesting steady state has been reached. ##### Here we use the legend. ##### Often your goal in plotting both data sets is to compare them, and it is easiest to compare plots when they are perfectly lined up. ##### That is due to the approximation in discretizing the reactor volume.    ##### The solver is in the pycse module.      ##### There is not yet a PDE solver in scipy.   ##### We use interpolation to estimate the curve between data points. ##### We are going to discretize this equation in both time and space to arrive at the solution. ##### List_of_colors and parsed it into a dictionary of hex codes for new colors. ##### ODES at each node point'.  ##### There are many other things you can do! ##### We choose an exponential decay as a guess.   ##### We illustrate finding peak maxima in a range, shading a region, shading peaks, and labeling a region of peaks. ##### Sometimes you can scale one dataset so it has a similar magnitude as the other data set. ##### The discretization looks like this.    ##### This kind of structured data might come up if you had grouped several things together. ##### If you make the time step too big, the method is not stable, and large oscillations may occur. ##### With these commands you can find all the text instances, and change them all at one time!     ##### Sometimes you will have two datasets you want to plot together, but the scales will be so different it is hard to seem them both in the same plot. ##### Pressing a key is different than pressing a mouse button.    ##### In this example we used 100 nodes. ##### You may notice the axis tick labels are not consistent with the labels now.  ##### Let us make a graph with a parabola in it, and draw the shortest line from a point clicked on to the graph.  ##### After watching his friend van Gogh cut off his own ear out of frustration with the ugly default colors, Picasso had to do something different.  ##### This version of the graphical solution is not that easy to read, although with some study you can see the solution evolves from the initial condition which is flat, to the steady state solution which is a linear temperature ramp.      ##### We can even do different things with different mouse clicks.  ##### We will solve this problem with recursion. ##### In Matlab there is the pdepe command.      rcskyekm 