Professor Wei-Chi Yang

Calculus III - Math 251

Course Contract
Topics: *Many Maple files are modified from the department of math at North Carolina State University, my colleagues from Australia, U.S. and others. Some of the Maple files are created by myself.

Labs: Feb 1, 8 (WR 225); Feb 13 (WR 216).

1. Some Antiderivatives (Maple file)
2. Partial Fractions (Maple file)
3. Numerical Integrations (Maple file)
4. Improper Integrals (Maple file)
5. Integration by parts (Maple file)
   • A java applet
   • Drill Practices.
6. Substitution
   • A java applet
   • Drill Practices
7. Finding area between curves (html)
   • Maple file-Solid of Revolution (A Java applet)
   • Finding the volume step by step
8. Solid of Revolution (A Maple file)
9. Arc Lengths
   • (Maple file)
   • Cycloid (Java Applet)
10. Average value of a function
    • Exercises.
11. Moment and center of mass.
    • A Maple file.
    • **More on center of mass which requires knowledge of double integrals.
12. Sequence and Series 
    • Reading materials.
      • For what x is 2^x> x^10? Using Fixed point or Newton's method?
      • Continuous Function and Limit of a Sequence.
    • A sequence/series plot.
    • Another exploration Maple file
    • Fun animation (html file)
    • Additional materials
    • A simple animation (Maple file)
    • ** Drills on Series. (html file)
    • Solution to a recursive problem from a quiz . (html file)
13. Exercises for testing for series. (html file)
14. A summary of all types of tests for series.
15. More exercises on series
16. Power Series and Taylor's Series (Maple file).
    • Error Estimate for sin(1) (Maple file).
17. More on Power Series
18. Integration and derivatives of a power series.
19. Taylor polynomials.
    • Maple for Quiz 4.
20. ** An old test
21. 3d plots
22. Dot Product ( A java applet)
23. Polar Graphs (Maple file)
24. Maple portion of test 1.
25. Dot and Cross Product with Maple.
26. Line and Plane with Maple
27. Interesting 3D graphs
    • Cross sections.
28. A fish (Maple file)
29. An interesting site on plotting using Java applets.
30. Cylindrical and Spherical Coordinate Systems.
31. Review for an old test 1 of math 252.
32. Maple portion for test 1.
33. Vector Functions (10.1,10.2, and 10.3)
    • Arc length for a space curve.
34. Visualize the relationship among Tangent, Principle Normal and Binormall Vectors.
35. Visualize the relationship between acceleration and velocity vectors.
36. Acceleration.
37. An old Quiz 3
38. Some materials on Multivariable Calculus.
39. Something from Math 151
40. Something from Math 152.