This is an interactive site which provides users with plots of direction fields for differential equations of the form dy/dx = f(x,y).
Type of Material:
Simulation
Recommended Uses:
Homework, in-class examples, computer lab sessions for courses in differential equations.
Technical Requirements:
Any 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 site allows users to input a differential equation of the form f(x,y). Users are then provided with a sketch of the direction field for this differential equation. Users have the ability to adjust the window and the number of direction arrows displayed in each row/column. This plotter could be a helpful resource to Differential Equations students in that it provides a clear and simple visualization of the direction field.
This tool is designed to accompany a textbook on Differential Equations. The applet is simple but informative. The one-line 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. A link to such material would also be a plus.
A link to a more sophisticated field plotter is included in this stie. However, the link appears to be broken.
The single-line interface allows users to type in the differential equation of their choice. While the notation used for this line is “dy/dt”, it does allow users to input equations in terms of x rather than t. This may be a bit confusing for some users.
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.
This is a great tool for helping students to visualize a direction field. It would be well suited for use in an in-class demonstration. This site could also be very helpful to students in that it would allow them to check solutions to homework/practice problems.
Concerns:
Although a statement regarding how to enter equations involving multiplication and/or evaluation has been included, students might benefit from an in included example of how this plotter could be used in conjunction with the textbook.
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.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This site is very intuitive and easy to use. Being able to adjust the window, arrow length, and number of arrows provides users with control over the look of the plot without being overwhelming.
Concerns:
A simple way to print different plots might be useful.
Creative Commons:
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