Activity Overview
Students use the calculator to visualize a function using the equation describing its derivative and a single point on the function. They start with simple equations and later solve more complex and difficult differential equations.
Before the Activity
Set the calculator to the Differential Equation Graphing mode
See the attached PDF file for detailed instructions for this activity
Print pages 1 - 15 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Visual Solution:
Enter the differential equation on the calculator
Set the initial conditions and the graphing axes
Graph the solution to the differential equation
Compare the analytic solution with the graphed solution
Changing Initial Values:
Change the initial values and graph the solution
Observe that the solution corresponding to each set of initial values moves the starting point of the graph
Entering Several Initial Values:
Enter several sets of initial values and graph the data
Observe a shift in the graph
Slope Fields:
Use the slope field function to get a general shape of the family of solutions
A line segment from any initial point that is tangent to the graph is one of the solutions
Normal Probability Density Functions:
Enter the differential equation with initial values of y = -1, and x = -3 and the Min and Max values set at -3 and +3
Set the calculator to connect points every tenth and graph the solution
Observe the graph is a scaled version of the normal probability density function
Interactive Specification of Initial Values:
Graph the slope field associated with the differential equation
Graph solutions corresponding to specific initial values
Graphing 2 Equations Simultaneously:
Enter two differential equations and different initial values
Select separate style for each graph
Graph the solutions together
After the Activity
Students solve problems on the exercise page.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary