Professor Wei-Chi Yang

Calculus IV - Math 252

1. Vector Functions and Space Curves (html)
2. Vector Functions (10.1,10.2, and 10.3) (Maple files)
   • Arc length for a space curve.
3. Finding tangent, normal and binormal vectors with Maple.
4. Visualize the relationship among Tangent, Principle Normal and Binormal Vectors.
5. Visualize the relationship between acceleration and velocity vectors.
6. Tangent Vector, Curvature and Acceleration.
7. Level Curves. (11.1)
8. Limits and continuity.
9. Partial solutions to quiz 2.
10. Partial Derivatives (computation)
11. Partial Derivatives (visualization)
12. Review for test 2.
13. Directional Derivative and applications:
    • Exercises for directional derivatives
    • HTML file.
14. Gradient vector fields and contour map. (Maple file)
• Gradient vector field in 2D-relationship with level curves. (Video by khanacademy.org)
• Gradient of a scalar field (Video by khanacademy.org).
15. Gradient Vector, Tangent Plane and etc.
16. Exterma for functions of two variables.
17. Practices on Max and Min for two variables.
    • Interactive Geometry and Critical Points by Professor Thomas F. Banchoff at eJMT.
    • Maximizing a probability function by Dr. Yang et al..
18. Lagrange Multiplier (Maple file)
• Application to Lagrange Multipliers by Dr. Yang at eJMT.
19. Test 3 Maple portion.
20. Double Integral I (Maple file)
21. Double Integral II (Maple file)
22. Practices on Double Integrals. (html file)
    • Partial solutions to the questions above (Maple file)
23. Double Integrals in Polar Coordinates. (Maple file)
24. **Review for final exam.
25. Visualizing gradients, level curves and etc. with Java applets.
26. About intersections of Cylinders
    • Volume of intersections of two cylinders.
    • Volume of intersections of three cylinders (site 1, site 2, site 3)
27. Surface Area (Maple)
28. Online Multivariable Calculus and Vector Analysis (by Dr. Duane Q. Nykamp)
29. *Conservative or non-conservative vector fields in 2D (html)
• 3D case. (html)
30. Online Multivariable Calculus (East Tennessee State University)
31. Paul's Online Math Notes
32. Multivariable Calculus from University of South Dakota.
33. YouTubes:
    • Green's Theorem
    • Stoke's Theorem
    • Gauss Divergence Theorem