Calculators and Computers
Slope Fields and Differential Equations
on the TI-89
Slope Fields –
(direction field) - a graphical tool to qualitatively visualize, or aid
in numerical approximation of, solutions to differential equations. Using slope fields, one can find the integral
both graphically and numerically.
Differential Equation - an equation that defines a relationship between a function and
one or more derivatives of that function
Links to Class
Assignments:
Cabri-Jr
Lesson Plan: Angles formed by two parallel lines when cut by a transversal
For more information
and activities on slope files using the TI-89 please refer to:
Help with
Slope Fields on the TI-89
Activity
1 - In this activity, students learn
what a slope field represents in terms of dy/dx. Students create a slope field
for a given differential equation. This can be used as a first introduction
into slope fields. This activity has
teacher notes with a lesson plan.
Activity
2 - In this activity, students identify whether a slope field approximately
reflects a differential equation. They also determine whether a potential
solution fits the slope field. A great
source of information for this activity comes from here, which includes teacher notes and a
lesson plan.
Activity
3 - students investigate
the use of the differential equation graphing mode to solve various
differential equations. They learn and explore to use numerical and graphical
methods for solving various differential equations. Once again be sure to download the
information for the activity with teacher notes and a lesson plan here.
Activity 4 - In this Computer Algebra System (CAS) activity, students investigate differential equations analytically, graphically and numerically and see relationships between the three approaches.