This site contains a simple applet that plots direction fields for simple first order differential equations of the form y′ = f(x,y).
Type of Material:
Simulation
Recommended Uses:
Homework, in-class examples, computer lab sessions for courses in differential equations.
Technical Requirements:
Users can access this site using any JAVA script enabled browser.
Identify Major Learning Goals:
To illustrate the concept of a vector field and its associated flow lines as used in vector analysis, differential equations, physics, and chemistry.
Target Student Population:
Students taking Differential Equations or related upper math classes can benefit from this site.
Prerequisite Knowledge or Skills:
Basic ordinary differential equations course.
Content Quality
Rating:
Strengths:
This tool is designed to accompany a textbook on Differential Equations. The applet is simple but informative. The interface allows the user to input a functions f(x,y), then the vector field is sketched. This applet provides a simple and effective illustration of a vector field. The graphical display is very clear and looks like a standard DE textbook illustration. Window settings for the graph can be entered independently.
Concerns:
The site containing the applet would benefit from some introductory text (outside of the help window) on vector fields.
It would be nice if the user could select an initial point, using the mouse, and the flow line through that point will be sketched.
When the x and y bounds are changed, the size of the screen is also changed instead of keeping the screen size the same and adjusting the scale. For example, setting -.1 < x < .1, -.1 <y < .1 makes the viewing rectangle tiny.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The applet does one thing and does it well. As a support and demonstration tool, instructors can use the site to illustrate textbook examples and homework assignments. Students could benefit from visiting the site and spending 20-30 minutes checking their homework or working through a planned worksheet.
Concerns:
A screen capture of the applet in use together with a textbook example, placed on the same page as the applet, would be a plus.
Because of the problems with setting the window size, an instructor must be careful only to assign differential equations that can be viewed with x and y large enough, but not too large. It would be nice to have a sample question set that fit in well with the restrictions of this app.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This is a very straightforward applet to use. The average user should be able to run it immediately. Because there are very few entry fields, students can create direction fields quickly.
Concerns:
A simple way to print different plots might be useful.
The expression entry is not flexible. For example, 2x+3y produces an error, since “*” is required for multiplication. Also, e^x produces an error. With the help link broken, students will become frustrated when they are given an error message with no reference materials to help them fix the error.
With the limitations of the changing of the bounds, students will have a difficult time when the proper viewing rectangle is too large or too small. When the range is large, such as -1000 to 1000, the app freezes, since it is making 1,000,000 computations, instead of rescaling more reasonably.
Creative Commons:
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