MTH 236 Calculus  IV Project Semester 082

Project Grade Sheet

Previous Projects

Three Nice Maple Worksheets from Projects from Previous Years:

Mike Koscielny: Puma Lettering with space curves

Stephanie and Danny Witch of Agnessi

Kyle Rush: Clothoids

Useful Links for Ideas, Reference

Project Description

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 individually

Choose your partner
Choose a topic -- Some suggestions below give you some ideas
Then get to work.

• Tell me your partner  and potential topic by Friday Feb 26th
• Submit your Colloquium form abstract to me by Wed March 3rd via email to me.   The abstract should be a paragraph giving the title of your topic and several sentences describing what your exploration covers. Submit approved colloquium application via Moodle by March 19th
• Project (Maple worksheet and Poster -- or PowerPoint if doing a presentation) due Wednesday April 7th  -- we will preview in class that day.
• Colloquium is Tuesday April 13th

 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.

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)

Here is a nice project done by

7.  Applications of Multivariable Calculus to Probability. Since some of you just finished probability, you could do some applications of computing joint probabilities whose density is represented by a function of two variables -- graph joint densities and use double integrals to compute various probabilities.

8.  Exploration of surfaces and their contour plots (level curves) and gradient fields.     

9.  Modeling planetary motion.    (See section 10.6)

Interesting Links for Possible Project Ideas

Dynamic Visualization Tools for Multivariable Calculus -- Might give you some ideas for a Maple project.

http://web.monroecc.edu/calcNSF/

MAA Digital Journal: Relative motion with Maple examples

http://mathdl.maa.org/mathDL//?pa=content&sa=viewDocument&nodeId=451&pf=1

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

Web sites for Prof. Matthias Kawski, Arizona St with Maple project ideas, examples.

http://math.asu.edu/~kawski/MAPLE/MAPLE.html

http://math.asu.edu/~kawski/classes/mat272/projects/projects.html

Student Projects in Multivariable Calculus

Instructor: David Arnold

http://math.asu.edu/~kawski/classes/mat272/projects/projects.html

Professor Judy Holenerj’s Calculus Projects

http://www2.kenyon.edu/personal/holdenerj/Projects/CalculusProjects.htm

Collection of Multiple Choice (for clickers in class) questions that investigate ideas in Multivariable Calculus -- Could inspire some interesting project explorations.

http://mathquest.carroll.edu/mvcalc.html

Blog for a professor’s Multivariable Calculus projects

http://samjshah.com/2009/05/29/the-mv-calc-final-projects/

This is at Mathematica site (Wolfram.com) – Maple’s main competitor.

http://demonstrations.wolfram.com/topic.html?topic=Multivariable+Calculus&limit=20

Maple worksheets (older versions) of Multivariable Calculus

http://www.math.cornell.edu/~projcalc/

In the article below are some links to Multivariable Calculus Projects

http://faculty.uca.edu/clarenceb/HP_Tablet_PC/UCA_HP_Tablet_PC.html

Mike Penna, Indiana University - Purdue University Maple projects for Calculus

http://www.brookscole.com/math_d/special_features/maplelabs05/maple_9-5_revisions_penna/stewartc5index.html