Three Nice Maple Worksheets from Projects from Last Year:
Mike Koscielny: Puma Lettering with
space curves
Stephanie and Danny Witch of Agnessi
Kyle Rush: Clothoids
Complete a visual exploration of an application of either
vector-valued functions (space or plane curves) or functions of several
variables (surfaces) in a Maple worksheet. The worksheet should be
well organized, well-documented with text cells that explain the mathematics
and the Maple computations.
Make good use of Maple graphics options. Then construct either:
a poster ( and /
or other visual aids) to submit to our SJC Undergraduate Colloquium if
participating in the Poster session.
OR
a PowerPoint -style
presentation if giving a oral presentation
Worth 120 assignment points.
You may with a partner (or alone).
Choose your partner
Choose a topic -- Some suggestions below give you some ideas
Then get to work.
1. Explore a class of related planar curves in
parametric form or polar form. Create “stunning”
artwork along with mathematical formulas for generation of the curves.
See “A
Visual Dictionary of Special Plane Curves” http://www.xahlee.org/SpecialPlaneCurves_dir/specialPlaneCurves.html
for an abundance of ideas!
Database of
curves: http://curvebank.calstatela.edu/index/index.htm
Database of curves
with Java applets generating them: http://turnbull.mcs.st-and.ac.uk/~history/Java/
Maple examples of
many interesting plots:
http://math.haifa.ac.il/ROVENSKI/rovenski/Birkhauser.html
2. Explore a "class" of related surfaces or solids using Maple
to create a visual display. You might want to focus on the
mathematical properties (continuity, differentiability, level curves, gradient
field, tangent plane,). It might be appropriate to include some
animation.
3. Use one of the Section Projects to motivate an exploration -- e.g. see
the Witch of Agnesi on page 839 or Capillary Action, page 1023.
4. Look at the index of applications A143 forward -- with page numbers
within the bounds of Calc IV (Chapters 12-14) for ideas. You might
want to do some work with velocity and acceleration.
5. Representations of surfaces in coordinate systems other than
rectangular (cylindrical , spherical, and others). (
6. Financial Applications of Multivariable calculus: Optimization
Problems. (Some examples of these types of problems are found at
the end of section 13.9)
7. Applications of Multivariable Calculus to Probability.
8. Exploration
of surfaces and their contour plots (level curves) and gradient
fields.
9. Modeling planetary motion. (See section 10.6)
Some links that may give you further ideas:
Doing a search on
Calc III projects or Multivariable Calculus Projects can be helpful –
Some examples of
results of searches:
Calc III projects
at Georgia Tech
Honors
projects at Chipola College
Calc
III projects at Arizona State
hMultivariable
Calculus Projects at Redwood College