Fall 19 Classes:

252, 430

Courses taught in the past: Pre-Calculus and Calculus Sequences:151, 251,126, 140,  Linear algebra (460) Advanced Calc. 430.


Be sure to get all your homework done as soon as possible after class as this will lead to better grades.


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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. Link to 251.
  2. (Review) Finding tangent, normal and binormal vectors with Maple.
  3. (Review) Visualize the relationship among Tangent, Principle Normal and Binormal Vectors.
  4. (Review) Arc length for a space curve (Maple file). html file.
  5. (Review) Curvatures (Maple file) (html file)
  6. (Review) Arc length and curvature (html file with a nice java applet)
  7. (Review) Tangent Vector, Curvature and Acceleration (Maple file).An html file.
  8. Acceleration, its tangential and normal components (html-do exercises 13.4.1-13.4.6; Maple). 
  9. (Review) Visualize the relationship between acceleration and velocity vectors.
  10. Equations of Planes.
  11. Quadric Surfaces-from Paul's online)
  12. Level Curves-Maple file. html file.
  13. Limits and continuity-Maplehtml file
  14. Partial solutions to a old quiz.
  15. Partial Derivatives (html): visualization (Maple)
  16. Review for an old test 1.
  17. A nice Java applet for visualizing partial derivatives.
  18. Chain Rule (html)
  19. Directional Derivative and applications-Maple
  20. 2D gradient vector field (Maple); 3D gradient vector field (YouTube)
  21. Application of gradient (YouTube)
  22. Tangent planes and normal lines (reading)
  23. Exterma for functions of two variables (Maple), reading material-html file
  24. Practices on Max and Min for two variables.
  25. Lagrange Multiplier (Maple file)
  26. An old test- 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 (html) (Maple file)
  31. Volume of intersections of two cylinders.
  32. Practices on double integrations using Cylindrical and Spherical Coordinates (html).
  33. Surface Area (Maple) (html)
  34. Volumes using cylindrical and spherical coordinates (Maple).
  35. Practices on change of variables (html).
  36. Vector fields-html; another vector Fields (html).
  37. Idea of Divergence of a vector field.
  38. Idea of the curl of a vector field.
  39. Introduction to conservative vector fields.
  40. How to determine if a vector field is conservative (curl =0).
  41. Line integral (html)
  42. Fundamental Theorem of Line Integrals (html)
  43. Green's theorem
  44. Idea behind the Stokes' Theorem.
  45. Idea behind the divergence theorem.
  46. **Java applet for drawing a vector field. (**You might need to add the URL to your Java security setting).
  47. Online Multivariable Calculus and Vector Analysis (by Dr. Duane Q. Nykamp)
  48. Gradient vector fields and contour map. (Maple file)
  49. Online Multivariable Calculus (East Tennessee State University)
  50. Paul's Online Math Notes
  51. Multivariable Calculus from University of South Dakota.
  52. YouTubes:
  53. **Review for final exam.

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