Visualizing Partial Derivatives without Graphs.

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# Visualizing Partial Derivatives without Graphs. - PowerPoint PPT Presentation

Visualizing Partial Derivatives without Graphs. . Martin Flashman. Humboldt State University and Occidental College. flashman@humboldt.edu. Abstract. In this presentation the author will explain and use free graphing technology ( Winplot ) to illustrate

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### Visualizing Partial Derivatives without Graphs.

Martin Flashman.

Humboldt State University and Occidental College.

flashman@humboldt.edu

Abstract
• In this presentation the author will
• explain and use free graphing technology (Winplot) to illustrate
• how to visualize the partial derivative without graphs.
• The treatment is suitable for any introductory treatment of the concept.
• Based on mapping (transformation) figures this approach
• allows students to understand the concepts in an n-dimensional context
• without any change in presentation from that given for the ordinary derivative.
FoundationsMapping (Transformation) Figures
• Visualize functions f : RR

y = f(x)

• Winplot examples:
• linear
• nonlinear
Dynamic interpretation
• Dynamic interpretation of the derivative visualized using
• y/x
• rates
• Illustrate using Winplot
Visualizing Multi-Variable Functions
• Visualize functions f : RnR

y = f(x1,x2,…,xn)

• Visualize f : R2R

y = f(x1,x2)

Visualizing The Partial Derivative fory = f(x1,x2)
• Dynamic interpretation of the partial derivatives for f : R2R

y = f(x1,x2)

visualized using y/x1 and y/x2.

• Static picture next slide.
• Winplot dynamic visualization.
Visualizing The Partial Derivative fory = f(x1,x2,…,xn)
• Dynamic interpretation of the partial derivative for f : RnR

y = f(x1,x2,…,xn)

visualized using y/x1, … , y/xn.

• Static picture here.
• Winplot dynamic visualization.
Conclusion
• Can use this visualization for other aspects of functions
• f : RnRk

f(x1,x2,…,xn)=(y1,y2,…,yk)

where yk = fk(x1,x2,…,xn)

Time!
• Questions?
• Responses?
• Further Communication by e-mail:

flashman@humboldt.edu

• These notes will be available at

http://www.humboldt.edu/~mef2

Thanks-

The end!