• ejs_model_functionxy.jar
• ejs_src_functionxy.zip

• Overview:

  This briefing document summarizes the key information available regarding the "EJS Mathematic function F(x), F(y) plot Applet" developed by Fu-Kwun Hwang and hosted on the Open Educational Resources / Open Source Physics @ Singapore platform. The document outlines the applet's purpose, functionality, credits, and context within the broader resources offered by the platform.

  Main Themes and Important Ideas/Facts:

  1. Purpose and Functionality:
  • The primary purpose of the applet is to visualize the plotting of mathematical functions where both the x and y coordinates are defined as functions of a parameter, typically denoted as 't'.
  • Users can input different mathematical functions for the x-coordinate (Fx(t)) and the y-coordinate (Fy(t)).
  • The simulation then plots the resulting parametric curve based on these user-defined functions.
  • A specific example provided highlights the applet's ability to generate Lissajous patterns: "For example: if you enter fx(t)=Asin(w1t), fy(t)=Bcos(w2t) It will draw Lissajous pattern for you."
  • The default setting is tailored for studying variations in Lissajous patterns due to added noise, as indicated by "The default setting is for someone who want to study variation of Lissajous pattern due to some other noise Csin(w2t)." This suggests a specific educational application related to signal processing or the superposition of periodic motions.
  1. Technical Details and Access:
  • The applet is likely built using Easy Java/JavaScript Simulations (EJS), given the "EJS" in the title and the availability of download links for "ejs_model_functionxy.jar" (a Java archive file) and "ejs_src_functionxy.zip" (likely the source code).
  • The applet is categorized under "Secondary" education and the topic of "Functions and graphs," indicating its intended educational level and subject area.
  • Download links are provided for both the compiled JAR file and the source code, promoting accessibility and potential modification or reuse.
  1. Attribution and Version Information:
  • The applet is credited to "Fu-Kwun Hwang."
  • A version link is provided: "http://phy01.phy.ntnu.edu.tw/ntnujava/index.php?topic=805.0," which likely points to a discussion or the original location of the applet.
  1. Context within Open Educational Resources / Open Source Physics @ Singapore:
  • The applet is hosted on a platform dedicated to Open Educational Resources (OER) and Open Source Physics. This aligns with the provision of download links and the Creative Commons license mentioned at the bottom of the page.
  • The surrounding links and lists on the webpage provide context, showcasing a wide variety of interactive simulations and resources available on the platform, covering topics from mathematics and physics to chemistry and even games for learning.
  • The inclusion of numerous other applets and resources highlights the platform's commitment to providing interactive learning tools across various subjects and educational levels. Examples include simulations for mechanics (pendulums, springs, gravity), optics, thermodynamics, chemistry (bonding, reactions), and mathematics (geometry, algebra).
  • The platform also features resources related to educational technology, teacher professional development, and the use of open-source tools in education.
  1. Licensing:
  • The content on the platform, including presumably this applet, is licensed under the "Creative Commons Attribution-Share Alike 4.0 Singapore License." This allows for the free use, adaptation, and sharing of the resource, provided appropriate attribution is given and any derivative works are shared under the same license.
  • A separate note indicates that commercial use of the EasyJavaScriptSimulations Library requires reading a specific license and contacting the developers at fem@um.es. This suggests that while the applet itself is likely openly licensed, the underlying development library might have specific terms for commercial applications.

  Quotes from the Source:

  • "You can change different mathematic function for x or y coordinate, i.e. Fx(t), Fy(t) This simulation will plot it for you."
  • "For example: if you enter fx(t)=Asin(w1t), fy(t)=Bcos(w2t) It will draw Lissajous pattern for you."
  • "The default setting is for someone who want to study variation of Lissajous pattern due to some other noise Csin(w2t)."

  Conclusion:

  The "EJS Mathematic function F(x), F(y) plot Applet" by Fu-Kwun Hwang is a valuable open educational resource for visualizing parametric equations, particularly for generating and studying Lissajous patterns. Its availability as a downloadable JAR file and source code, along with its placement within a broader collection of interactive simulations, underscores the commitment of Open Educational Resources / Open Source Physics @ Singapore to providing freely accessible and adaptable tools for learning and teaching science and mathematics. The applet's focus on allowing users to define custom functions for x and y coordinates makes it a flexible tool for exploring a wide range of mathematical curves and their properties.

Study Guide: EJS Mathematic Function Plot Applet

This study guide is designed to help you review your understanding of the EJS Mathematic function F(x), F(y) plot Applet as described in the provided source material.

Quiz: Short Answer Questions

Answer the following questions in 2-3 sentences each.

1. What is the primary function of the EJS Mathematic function F(x), F(y) plot Applet?
2. According to the description, what kind of input does the applet accept for the x and y coordinates?
3. What is a Lissajous pattern, and how can this applet be used to generate one?
4. Who is credited with creating this specific applet?
5. Where can users find the download links for the applet files?
6. What is the default setting of the applet designed to help users study?
7. Under what broader category on the website is this applet listed?
8. What do the terms "ejs_model_functionxy.jar" and "ejs_src_functionxy.zip" likely represent?
9. Besides the specific function plot applet, what other types of resources or tools are mentioned on the same webpage?
10. What license governs the use of the content on the "Open Educational Resources / Open Source Physics @ Singapore" website?

Quiz Answer Key

1. The primary function of the EJS Mathematic function F(x), F(y) plot Applet is to allow users to input different mathematical functions for the x and y coordinates and visualize the resulting plot. It essentially graphs parametric equations.
2. The applet accepts mathematical functions for the x and y coordinates that are dependent on a variable, often represented as 't'. Examples given include trigonometric functions like sine and cosine.
3. A Lissajous pattern is a complex curve generated by plotting two sinusoidal functions against each other, often with different frequencies and amplitudes. This applet can draw Lissajous patterns by inputting sinusoidal functions for Fx(t) and Fy(t).
4. Fu-Kwun Hwang is credited with creating the EJS Mathematic function F(x), F(y) plot Applet.
5. The download links for the applet files, specifically "ejs_model_functionxy.jar" and "ejs_src_functionxy.zip", are located directly below the title of the applet on the webpage.
6. The default setting of the applet is designed to help someone study the variation of Lissajous patterns due to the introduction of some other noise, exemplified by Csin(w2t).
7. On the website, this applet is listed under the broader categories of "Secondary" and "Functions and graphs."
8. "ejs_model_functionxy.jar" likely represents the executable Java archive file that runs the applet, while "ejs_src_functionxy.zip" likely contains the source code of the applet.
9. Besides the function plot applet, the webpage mentions various other interactive applets and simulations covering topics like geometry, physics, chemistry, and mathematics, as indicated by the extensive list of links.
10. The content on the "Open Educational Resources / Open Source Physics @ Singapore" website is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License.

Essay Format Questions

Consider the following questions and formulate well-structured essays in response.

1. Discuss the educational value of the EJS Mathematic function F(x), F(y) plot Applet in the context of teaching and learning about functions and their graphical representations. Provide specific examples of how it could be used in a classroom setting.
2. Analyze the purpose of providing both the executable (.jar) file and the source code (.zip) for the applet. What are the benefits and potential uses of each for educators and learners?
3. Based on the description and the surrounding content on the webpage, what conclusions can you draw about the goals and philosophy of the "Open Educational Resources / Open Source Physics @ Singapore" project? Support your answer with evidence from the text.
4. Explore the concept of Lissajous patterns and explain how the EJS applet facilitates their study. What mathematical principles underlie the formation of these patterns, and what real-world phenomena might they be used to model or understand?
5. Examine the role of interactive simulations and applets, like the one described, in modern science and mathematics education. What advantages do they offer compared to traditional teaching methods?

Glossary of Key Terms

• Applet: A small application, often written in Java, that runs within another application, typically a web browser.
• Function (Mathematical): A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
• Graph (of a function): A visual representation of a function, showing the relationship between the input and output values, typically plotted on a Cartesian coordinate system.
• Lissajous Pattern: Also known as Lissajous curve or Bowditch curve, the graph of a system of parametric equations: x = A sin(at + δ), y = B sin(bt), which describes complex harmonic motion. The shape of the curve is determined by the ratio of the frequencies (a/b), the phase difference (δ), and the amplitudes (A, B).
• Parametric Equation: A set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." In this case, the x and y coordinates are functions of a parameter 't'.
• Open Educational Resources (OER): Teaching, learning, and research materials in any medium – digital or otherwise – that reside in the public domain or have been released under an open license, permitting no-cost access, use, adaptation, and redistribution by others with no or limited restrictions.
• Open Source Physics (OSP): A project focused on creating and disseminating open-source computational tools and resources for physics education.
• Simulation: A computer program that models a real-world system or phenomenon, often allowing users to interact with and explore different parameters.
• Noise (in this context): An additional signal or component added to a primary signal, in this case, affecting the generation of the Lissajous pattern.
• Executable File (.jar): A Java Archive file that contains the compiled Java code and resources needed to run a Java application or applet.
• Source Code (.zip): The human-readable programming instructions that make up a software application, often compressed into a zip file for distribution.