Objectives
- Describe the idea behind slope fields in terms of visualization of the family of solutions to a differential equation
- Describe the slope of a tangent line at a point on the graph of a solution to a differential equation
- Describe the general nature of a solution to a differential equation as suggested by a slope field
- Use the TI-Nspire built-in function deSolve to find the general family of solutions to a differential equation
- Match a differential equation with its corresponding slope field
Vocabulary
- slope field
- first order differential equation
- family of solutions
- particular solution
About the Lesson
This lesson involves the concept of a slope field, a graphical representation of the family of solutions to the first order differential equation, y'=g(x,y). As a result, students will:
- Understand that a slope field is a visualization of the family of solutions to a differential equation.
- Use characteristics in a slope field to describe the general nature of a solution to a differential equation.
- Be able to match a differential equation with the appropriate slope field and find the family of solutions using the TI-Nspire.