Visualizing Linearity:
Alternatives to Lines and Planes

Dec. 9, 2013

Martin Flashman
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Humboldt State University
Arcata, CA 95521
flashman@humboldt.edu
users.humboldt.edu/flashman












Descartes  ¤

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Example:  Graph and Mapping Diagram










Go to worksheet.

Exploring with a spreadsheet .


 Example: LF.DA.0  with GeoGebra .

For more on linearity [composition and inverses] go to http://users.humboldt.edu/flashman/MD/section-2.1LF.html.












Example: LF.DFP  with GeoGebra



   





“Linear” Functions with  two variables
$z=f(x,y) = Ax + By + C$ 

Traditional Approaches to visualizing functions of two variables:
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  This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
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A 3D Mapping Diagram for a Linear Function of 2 Variables ¤
Example: MFC.0   with GeoGebra









The End



Questions?

Mapping Diagrams from A(lgebra) B(asics) to C(alculus) and D(ifferential) E(quation)s.
A Reference and Resource Book on Function Visualizations Using Mapping Diagrams

http://users.humboldt.edu/flashman/MD/section-2.1LF.html