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.
 

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Lab Schedule:
4/29/2009     Walker_216 (Final Exam-Part 1)
2:45 p.m. Tuesday, May 5 (Final Exam-Part 2)

1. Improper Integrals (Maple file)
   • page 422: 1,5,7,15,17,19
   • Drill Practices
   • Table of integration techniques
2. Sequence and Series 
   • A sequence/series plot. (A Maple file)
   • Another exploration Maple file
   • Additional materials
   • Drills on Series. (html file)
   • Solution to a recursive problem from a quiz . (html file)
   • HW for 7.1: page 435: 1,5,11,14,25,27,31,33,35,37,39,43,45, 63-71 odd. Exploration: 96,97.
   • HW for 7.2: page 444: 1-13 odd;  (Feb 4) 31,33,35,37,66
3. Lab 1 (improper integration, sequences and series)
4. Exercises for testing for series. (html file)
   • HW for 7.3:  (Feb 4) page 453: 6,7,11,13,19,20.
5. A Fixed Point Algorithm-Feb 6. (Maple file)
6. HW for Feb 6: page 453: 7-27 odd (Integral Test) , 41-49 odd (Comparison Test), 51-61 odd (Limit Comparison Test).
7. Lab 2 Feb 6: The smallest positive integer N, partial sum and a convergent series-Maple.
8. A summary of all types of tests for series.
9. HW for Feb 11 (Alternating Series and Ratio Test): page 463: 1-13 odd; 31-39 odd; 43-55 odd.
10. Power Series and Taylor's Series (Maple file).
    • Error Estimate for sin(1) (Maple file).
11. More on Power Series (html)
12. (March 6) Integration and derivatives of a power series.
13. Taylor polynomials (html)
    • Maple for Quiz 4.
14. **An old test (Do #1(a), 3, 4,5,6,7, 9,10).
15. Parametric, Polar plots and arc lengths with Maple. (pdf file).
16. Famous Curves (html)
17. Polar Graphs (Maple file)
    • Polar Gallery (html)
18. A fish (Maple file)
19. A hat (Maple file)
20. 3d plots
21. Dot Product ( A java applet) 
22. Maple portion of test 1.
23. Dot and Cross Product with Maple.
24. Line and Plane with Maple
25. Interesting 3D graphs
    • Cross sections.
26. A fish (Maple file)
27. An interesting site on plotting using Java applets.
28. Cylindrical and Spherical Coordinate Systems.
29. Review for an old test 1 of math 252.
30. Maple portion for test 1.
31. Vector Functions (10.1,10.2, and 10.3)
    • Arc length for a space curve.
32. Visualize the relationship among Tangent, Principle Normal and Binormal Vectors.
33. Visualize the relationship between acceleration and velocity vectors.
34. Acceleration.
35. An old Quiz 3
36. Some materials on Multivariable Calculus.
37. Something from Math 151
38. Something from Math 152.

Some topics from Math 152:

1. Some Antiderivatives (Maple file)
2. Partial Fractions (Maple file)
3. Numerical Integrations (Maple file)
4. Integration by parts (Maple file)
   • A java applet
   • Drill Practices.
5. Substitution
   • A java applet
   • Drill Practices
6. Finding area between curves (html)
   • Maple file-Solid of Revolution (A Java applet)
   • Finding the volume step by step
7. Solid of Revolution (A Maple file)
8. Arc Lengths
   • (Maple file)
   • Cycloid (Java Applet)
9. Average value of a function
   • Exercises.
10. Moment and center of mass.
    • A Maple file.
    • More on center of mass which requires knowledge of double integrals.