Professor Wei-Chi Yang

Calculus IV - Math 252

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.

1. Some materials on Multivariable Calculus.
2. Dot Product ( A java applet)
3. Homework for 1/6 and 1/8: page 674, 7-11 odd, 15, 21-24.
4. Line and Plane with Maple
5. Interesting 3D graphs
   • More 3D graphs.
6. Cylindrical Coordinate; Spherical Coordinate.
   • Cylindrical and Spherical Coordinate Systems (Maple file)
7. Vector Functions and Space Curves (html)
8. Vector Functions (10.1,10.2, and 10.3) (Maple files)
   • Arc length for a space curve.
9. Visualize the relationship among Tangent, Principle Normal and Binormal Vectors.
10. Visualize the relationship between acceleration and velocity vectors.
11. Acceleration.
12. Review for an old test 1.
13. Maple portion for old test 1.
14. Level Curves. (11.1)
15. Limits and continuity.
16. Partial solutions to quiz 2.
17. Partial Derivatives (computation)
18. Partial Derivatives (visualization)
19. Review for test 2.
20. Directional Derivative and applications:
    • Exercises for directional derivatives
    • HTML file.
21. Gradient vector fields and contour map. (Maple file)
22. Gradient Vector, Tangent Plane and etc.
23. Exterma for functions of two variables.
24. Practices on Max and Min for two variables.
    • Maximizing a probability function.
25. Lagrange Multiplier (Maple file)
26. Test 3 Maple portion.
27. Double Integral I (Maple file)
28. Double Integral II (Maple file)
29. Practices on Double Integrals. (html file)
    • Partial solutions to the questions above (Maple file)
30. Double Integrals in Polar Coordinates. (Maple file)
31. **Review for final exam.
32. Visualizing gradients, level curves and etc. with Java applets.
33. About intersections of Cylinders
    • Volume of intersections of two cylinders.
    • Volume of intersections of three cylinders (site 1, site 2, site 3)
34. Surface Area (Maple)
35. Center of gravity, stock car and trigonometry (discovered by  Tommy Dickerson, a student of my Trig Spring 03)
    • It talks about how to find the center of gravity and has a program. 
    • It talks about the center of gravity height and Jeeps, and the danger of them
      flipping.
    • Very informative site about the center of gravity height
36. Vector I.(A Maple worksheet)
37. Vector II.(A Maple worksheet)
    • An exercise (Maple worksheet)
38. Online Multivariable Calculus and Vector Analysis (by Dr. Duane Q. Nykamp)
39. Online Multivariable Calculus (East Tennessee State University)
40. Paul's Online Math Notes
41. Multivariable Calculus from University of South Dakota
42. YouTubes:
    • Green's Theorem
    • Stoke's Theorem
    • Gauss Divergence Theorem