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Playing with Multivariable Calculus with 3D Glasses

Playing with Multivariable Calculus with 3D Glasses. Presented by Paul Seeburger of Monroe Community College, Rochester, NY The multivariable calculus content has been developed with support from the National Science Foundation : NSF-DUE-CCLI #0736968. Project Main Goal:.

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Playing with Multivariable Calculus with 3D Glasses

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  1. Playing with Multivariable Calculus with 3D Glasses Presented by Paul Seeburger of Monroe Community College, Rochester, NY The multivariable calculus content has been developed with support from the National Science Foundation: NSF-DUE-CCLI #0736968

  2. Project Main Goal: The main goal of this project is to improve student understanding of the geometric nature of multivariable calculusconcepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.

  3. Theprojectincludesfourparts: • Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF • Creating focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way. • Developing guided exploration/assessments to be used by students to explore calculus concepts visually on their own. • Dissemination of these materials

  4. Why use Visualization in Calculus? • Calculus is the mathematics of change. Limits are defined in terms of change, Derivatives represent rates of change, and Definite Integrals represent total change in an antiderivative function. To see calculus clearly, we need to see motion and change occurring.

  5. Why use Visualization in Calculus? • Calculus is the mathematics of change. Limits are defined in terms of change, Derivatives represent rates of change, and Definite Integrals represent total change in an antiderivative function. To see calculus clearly, we need to see motion and change occurring. • Visualization helps make the geometric and motion-related connections become clearer and much easier to remember. It is especially when the concepts are in 3D.

  6. Why use Visualization in Calculus? • Calculus is the mathematics of change. Limits are defined in terms of change, Derivatives represent rates of change, and Definite Integrals represent total change in an antiderivative function. To see calculus clearly, we need to see motion and change occurring. • Visualization helps make the geometric and motion-related connections become clearer and much easier to remember. It is especially when the concepts are in 3D. • When students “play” with the concepts, they will remember them better.

  7. Why use Visualization in Calculus? • Calculus is the mathematics of change. Limits are defined in terms of change, Derivatives represent rates of change, and Definite Integrals represent total change in an antiderivative function. To see calculus clearly, we need to see motion and change occurring. • Visualization helps make the geometric and motion-related connections become clearer and much easier to remember. It is especially when the concepts are in 3D. • When students “play” with the concepts, they will remember them better. • Using visualizations during a lecture helps not only to develop geometric understanding, but also varies the format of the lecture enough to maintain student attention and involvement in the lecture.

  8. Why use Visualization in Calculus? • Calculus is the mathematics of change. Limits are defined in terms of change, Derivatives represent rates of change, and Definite Integrals represent total change in an antiderivative function. To see calculus clearly, we need to see motion and change occurring. • Visualization helps make the geometric and motion-related connections become clearer and much easier to remember. It is especially when the concepts are in 3D. • When students “play” with the concepts, they will remember them better. • Using visualizations during a lecture helps not only to develop geometric understanding, but also varies the format of the lecture enough to maintain student attention and involvement in the lecture. • Visualizations can help students to become engaged in the concepts and begin asking “what if…” questions.

  9. New Features of CalcPlot3D: • Implicit Equations can now be graphed in Spherical and Cylindrical coordinates as well as in Cartesian coordinates. • STL files can now be saved from the applet for use with 3D printers. See two surfaces I printed below, a saddle and a knot.

  10. Ways to use CalcPlot3D: • Instructors can use them to visually demonstrate concepts and verify results during lectures. Also “What if…?” scenarios can be explored.

  11. Ways to use CalcPlot3D: • Instructors can use them to visually demonstrate concepts and verify results during lectures. Also “What if…?” scenarios can be explored. • Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.

  12. Ways to use CalcPlot3D: • Instructors can use them to visually demonstrate concepts and verify results during lectures. Also “What if…?” scenarios can be explored. • Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own. • Instructors can use CalcPlot3D to create graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 2D and 3D Graphs and vector fields can be copied from the applet and pasted into a word processor like Microsoft Word.

  13. Ways to use CalcPlot3D: • Instructors can use them to visually demonstrate concepts and verify results during lectures. Also “What if…?” scenarios can be explored. • Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own. • Instructors can use CalcPlot3D to create graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 2D and 3D Graphs and vector fields can be copied from the applet and pasted into a word processor like Microsoft Word. • Instructors can also use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.

  14. Ways to use CalcPlot3D: • Instructors can use them to visually demonstrate concepts and verify results during lectures. Also “What if…?” scenarios can be explored. • Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own. • Instructors can use CalcPlot3D to create graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 2D and 3D Graphs and vector fields can be copied from the applet and pasted into a word processor like Microsoft Word. • Instructors can also use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet. Look for my 2-hour workshop on using CalcPlot3D in teaching multivariable calculus, as well as creating these scripts at AMATYC 2011 in Austin!

  15. Contact Info: Paul Seeburger, Associate Professor of Mathematics at Monroe Community College Email: pseeburger@monroecc.edu NSF Project Website: http://web.monroecc.edu/calcNSF/

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