The site contains an interactive GeoGebra tool for visualizing vector fields associated with differential equations. The methods of Euler and Runge-Kutta 2 integration of a vector field are given by a function of x&y.
Type of Material:
Simulation
Recommended Uses:
This is a good tool for review, individual study and exploration, and for in-class demonstration. An instructor could use it in classrooms, for homework assignments, individual learning, or group exploration in mathematics-related courses. The site would be best for individual review or investigation but could also be incorporated into a homework assignment.
Technical Requirements:
Any browser.
Identify Major Learning Goals:
The purpose of this resource is help users to visualize the vector field associated with given differential equation. The users can develop intuition for curves, surfaces, and differential equations by exploring and experimenting with interactive visual models.
Target Student Population:
College Lower Division, Graduate
Prerequisite Knowledge or Skills:
Differential calculus, functions, parametric curves. Basic understanding of functions, trigonometry, and calculus concepts (derivatives, integrals, vectors fields).
Content Quality
Rating:
Strengths:
This resource is an interactive GeoGebra tool that helps users to visualize the vector field associated with a given differential equation. Users can choose from four pre-programmed example differential equations or can enter their own equation directly. Clicking on the keyboard icon at the far right of the equation box provides users with a “mathtype” menu to make entry easier. Users have the ability to change the initial value by dragging and dropping the point on the graph. A slider bar also allows users to change the discretization step.
In a summary, the tool is clear, accurate, visually engaging, and flexible in classroom use.
Concerns:
There are adds that pop up on the bottom of the screen, but these can be minimized and are not very distracting. The tool might be improved by linking to OER resources to provide background information and additional examples.
Also, the tool lacks written instructional guidance, and it is not self-contained (cannot be used without requiring an assignment or context)
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This resource is highly interactive and presents information in a very visual manner. It would be a great tool for in class demonstrations. It is an excellent tool for exploration and reinforcing concepts visually. Supports student-centered learning.
Concerns:
The lack of built-in practice problems or step-by-step explanations may limit its effectiveness as a stand-alone teaching tool.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The tool is easy to use, runs smoothly, highly interactive, and making abstract concepts more concrete. It is also very visual and intuitive.
Concerns:
None.
Creative Commons:
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