1 / 20

CAS for visualization, unwieldy computation, and “hands-on” learning

CAS for visualization, unwieldy computation, and “hands-on” learning. Judy Holdener Kenyon College July 30, 2008. Small, private liberal arts college in central Ohio (~1600 students). Kenyon at a Glance. 12-15 math majors per year. All calculus courses taught in a

aletta
Télécharger la présentation

CAS for visualization, unwieldy computation, and “hands-on” learning

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CAS for visualization,unwieldy computation,and “hands-on” learning Judy Holdener Kenyon College July 30, 2008

  2. Small, private liberal arts college in • central Ohio (~1600 students) Kenyon at a Glance • 12-15 math majors per year • All calculuscourses taught in a • computer-equipped classroom • All math classes capped at 25 • Profs use Maple in varying degrees

  3. Lessons that introduce ideas • geometrically. Visualization in Calculus III • a CAS can be the medium for creative, hands-on pursuits! • a CAS can produce motivating pictures/animations. • Projects that involve an element of • design and a healthy competition.

  4. Parametric Plots Project • Students work through a MAPLE • tutorial in class; it guides them • through the parameterizations of • lines, circles, ellipses and functions. • The project culminates with a • parametric masterpiece. y(t) x(t)

  5. Dave Handy

  6. Nick Johnson

  7. Andrew Braddock

  8. Chris Fry

  9. AtulVarma

  10. Christopher White Oh, yeah? Define “well-adjusted”.

  11. If x(t), y(t), and f(x,y) are differentiable then f(x(t),y(t)) is differentiable and The Chain Rule for f(x, y) Actually,

  12. Example. Compute at t=1. Let z = f(x, y) = xe2y,x(t) = 2t+1 and y(t) = t2. Solution. Apply the Chain Rule:

  13. What does this number really mean?

  14. t=4 t=3 t=2 t=1 t=0 Here’s the parametric plot of: (x(t), y(t)) = (2t+1, t2).

  15. The curve together with the surface: At time t=1 the particle is here. z = f(x,y) = xe(2y)

  16. Another Example. Compute at t=1. Let f(x, y)= x2+y2 on R2,and let x(t)= cos(t) and y(t) = sin(t). Solution. Apply the Chain Rule:

  17. Note: it’s 0 for all t!!!

  18. f(x, y)=x2+ y2 (cos(t), sin(t), f(cos(t),sin(t))) (x(t), y(t))=(cos(t), sin(t))

  19. Unwieldy Computations Scavenger Hunt!

  20. Holdener J.A. and E.J. Holdener. "A Cryptographic Scavenger Hunt," Cryptologia,31 (2007) 316-323 References J.A. Holdener. "Art and Design in Mathematics," The Journal of Online Mathematics and its Applications, 4 (2004) Holdener J.A. and K. Howard. "Parametric Plots: A Creative Outlet," The Journal of Online Mathematics and its Applications, 4 (2004)

More Related