In this applet, the user applies Euler's Method to modeling population growth using the Malthus exponential model and the Verhulst constrained growth model. After finding the Euler solution, the user can check the solution with the Adaptive Euler Approximation or with a slope field. Also, the user can enter an exact solution obtained analytically and again check the Euler solution graphically.
Type of Material:
Simulation.
Recommended Uses:
As a part of an in-class demonstration or self-guided study.
Technical Requirements:
A Java-enabled Web browser.
Identify Major Learning Goals:
To facilitate an understanding of modeling with differential equations.
Target Student Population:
Students taking a first year course in Calculus or a course in Ordinary Differential Equations.
Prerequisite Knowledge or Skills:
Students should have had a course in Differential Calculus and have a basic understanding of how differential equations can represent physical systems.
Content Quality
Rating:
Strengths:
This applet is part of an excellent mother site called Principles of Calculus Modeling: An Interactive Approach (http://www.merlot.org/merlot/viewMaterial.htm?id=297526). However, the applet can easily stand alone for the purpose of classroom demonstration or tutorial. The applet should provide a good example of how mathematical modeling of physical systems works in real life. First, there is the matter of choosing a model for the given system. Here two models are considered, one a bit more sophisticated than the other. Some experimentation is also required in developing each of the models. Then there is the matter of finding solutions and checking them. Finally, the user is encouraged to compare the models relative to an exact solution obtained analytically and decide which model is the more realistic.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This applet should be quite useful for purposes of classroom demonstration of how modeling physical systems with differential equations works. The instructor can bring into the discussion various element of the process such as experimentation, approximation, and verification. Students can also experiment with the applet as a part of self-guided activity, or the instructor could easily design exercises utilizing the applet.
Concerns:
While zooming of the graph is possible, there is no obvious way to enlarge the applet as a whole, which might be a drawback for classroom demonstrations.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applet is quite intuitive. Also, a significant amount of explanation is provided, not only of how to use the applet but also of the underlying concepts.
Concerns:
None.
Creative Commons:
Search by ISBN?
It looks like you have entered an ISBN number. Would you like to search using what you have
entered as an ISBN number?
Searching for Members?
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.
Searching for Members?
You entered an email address. Would you like to search for members? Click Yes to continue. If no, materials will be displayed first. You can refine your search with the options on the left of the results page.
