In this tutorial we are going to talk about Slope Fields for Differential Equations. The Slope Field (also called Direction Field) is a graphical representation of the solutions of a first-order differential equation. It is useful because it can be created without solving the differential equation analytically. The representation may be used to qualitatively visualize solutions, or to numerically approximate them. So, first, we are going to introduce some important things to remember about this topic and see graphical explanation of it. Then we are going to do several examples.
If you are doing
this by hand, look for symmetry to help speed up the work involved!
Draw enough field
marks to see the flow of solutions.
There is a great
piece of MATLAB code for this called pplane.
You will probably
see much more on this topic if you take a course in differential
Slope Fields for Differential Equations
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.