The following TI-92 help modules will be useful for this module.
Discrete Dynamical Systems
Begin by defining the supply and demand functions as shown in the screen below.
Next make sure that your TI-92 graphics mode is set to sequence as described in the help modules above and then describe this dynamical system in the Y= screen as shown in the screen below.
Set your WINDOW screen and TblSet screen as shown below
Next store the appropriate value of k as shown below.
Then press TABLE and GRAPH to see the results numerically and graphically as shown in the screens below.
You can do the remaining problems for discrete dynamical systems by changing the initial value, u1(1), and by changing k.
Continuous Dynamical Systems or Initial Value Problems
Begin by going to the TI-92 help module on Numerical Solutions of Differential Equations of the form y' = f(t, y) and downloading the program rk1. The same help module describes how to use this program to solve initial value problems on the TI-92.
The first step is to define the function rk1f that appears on the right side of the differential equation
as shown in the screen below.
The Y= screen should be set up as shown below.
Next enter the value of h and k as shown in the screen below. The constant k is part of the original problem. The constant h controls how accurate an approximation you will get for the solution of this initial value problem. If h is small you will get a better approximation but it will take longer. We suggest h = 0.2 as a good compromise.
The WINDOW screen should be set up as shown below if h = 0.2. In general nmax and xmax should be 20 / h.
Now press GRAPH to see the solution as shown in the screen below.
You can do the remaining problems for continuous dynamical systems by changing the initial value, ui2, and by changing k.