Peer Review

Phase plane plotter

Material Detail page

Reviewed:: Jan 26, 2021 by Mathematics

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Ratings

Overall Rating:

Content Quality:

Effectiveness:

Ease of Use:

Overview:

This tool plots a system of differential equations of the form dx/dt = f(x,y), dy/dt = g(x,y).

The direction field solver solves trigonometric, logarithmic and exponential functions.

The phase plane plotter has the option of enabling the x & y interval (min & max), the number of arrows, length of the arrow and a check box to display variable length arrows.

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 browser.

Identify Major Learning Goals:

Illustrates the concept of a direction field and phase plane with associated flow lines.
It enables the user to adjust the arrow length and number of arrows in the plot with a check box to display the variable-length arrows.
These features make the plot interesting

Target Student Population:

Students taking Differential Equations or related upper math classes.

Prerequisite Knowledge or Skills:

Ordinary differential equations course.

Ideally, courses in multivariable calculus and linear algebra

Content Quality

Rating:

Strengths:

This tool is designed to accompany a textbook on Differential Equations. The applet is simple but informative. The simplistic interface allows the user to input two functions f(x,y) and g(x,y), then after one click, the vector field of the phase plane associated with a system of differential equations of the form dx/dt=f(x,y), dy/dt=g(x,y) is sketched. A simple click with a mouse on the generated vector field produces a graph of the flow line. This applet provides a simple and effective illustration of a phase plane. The graphical display is very clear and looks like a standard DE textbook illustration. Window settings for the graph can be entered independently.

The direction field solver solves trigonometric, logarithmic and exponential functions.

The phase plane plotter has the option of enabling the x & y interval (min & max), the number of arrows, length of the arrow and a check box to display variable length arrows.

Concerns:

The site containing the applet would benefit from some introductory text (outside of the help window) on vector fields or, at least, a link to the corresponding material on the Web.

Introductory note on the objective of the applet and a brief theory or link should be there.

Phase portrait not displayed.

WolframAlpha Widget offers a better interactive interface and a sharable link for classroom discussion, assignments, homework etc. https://www.wolframalpha.com/widgets/

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.

It can be used by the instructor effectively the phase plane plot
It also allows adjusting the intervals, arrow length for better display of the graph.
It is a useful tool for homework assignments and to solve textbook examples.

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.

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:

Printing the plots option not available.

The link MATLAB plotter not working (404, not available)

Other Issues and Comments:

The instructor has to explain the subject and use this applet vis-a-vis textbook to explain the concept.

Phase portrait not displayed.

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