visualizing partial derivatives without graphs l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Visualizing Partial Derivatives without Graphs. PowerPoint Presentation
Download Presentation
Visualizing Partial Derivatives without Graphs.

Loading in 2 Seconds...

play fullscreen
1 / 13

Visualizing Partial Derivatives without Graphs. - PowerPoint PPT Presentation


  • 211 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Visualizing Partial Derivatives without Graphs.' - jaden


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
visualizing partial derivatives without graphs

Visualizing Partial Derivatives without Graphs.

Martin Flashman.

Humboldt State University and Occidental College.

flashman@humboldt.edu

abstract
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.
foundations mapping transformation figures
FoundationsMapping (Transformation) Figures
  • Visualize functions f : RR

y = f(x)

  • Winplot examples:
    • linear
    • nonlinear
dynamic interpretation
Dynamic interpretation
  • Dynamic interpretation of the derivative visualized using
    • y/x
    • rates
  • Illustrate using Winplot
visualizing multi variable functions
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 for y f x 1 x 2
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 for y f x 1 x 2 x n
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
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)

slide12
Time!
  • Questions?
  • Responses?
  • Further Communication by e-mail:

flashman@humboldt.edu

  • These notes will be available at

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

thanks
Thanks-

The end!