Calculus II Projects

1. Taylor series computing using parallel ( see D2L Python code: Taylor_Series_Parallel.ipynb )

Hint: see https://ipyparallel.readthedocs.io/en/latest/index.html

2. Using Numerical Schemes to approximate definite integrals (Midpoint Rule, Trapezoid Rule, Simpson's Rule) and calculate the corresponding errors. Trapezoidal Rule: Matlab and Python,     C,     Maple,  other language.

George Gannon's GitHub code

3. Approximating Pi using series ( faster converge get more points ) 

4. A physics application ( Calculus-based Physics project  )

5. An engineering application ( MakerSpace: Robotic Arms at MTSU Library and more )

6. 3D printing of a three dimensional object ( sphere, batman, and other shapes, if you can use calculus to calculate its volume/surface area/arc length, you get more points )

  Juan's 3D Printing of an art work - Vase and calculate the volume and surface area using integrals;  
   Cameron's 3D printing snowman with 2 colors, designed by TickerCAD 

3D Printing Vase - Juan Collect Data from 3D PrintingCalculate Volume using CalculusCalculate Surface Area using Calculus3D printing snowman with 2 colors by Cameron

7. Maple/Mathematica computation of integrals showing every detail/step ( Sample codes on D2L: mathematica_practice.pdf, practice.nb )

8. Bézier curves investigation, Brachistochrone problem, Tautochrone problem, conchoids of Nicomedes exploration ( section 10.1 PPT )

9. Music and sequences/series: ( e.g. piano the Fibonacci sequence )

Jacob Fawsett is playing a sequence on piano and Jacob is improvising on playing Pi and Jacob's Music Sheet and README and Zakaria Sohrabi playing Fibonacci sequence on violin and Zak's Sheet Music and Zak's README.txt
10. "Sketch by hand" for a parametric curve more complicated than cycloid, repeat the four steps showed in PPT on section 10.2. 

11. Pumpkin Carve - Samples: click for larger view  

Series PumpkinPi PumpkinVan Gogh PumpkinDNA Pumpkin