### Calculus III - Math 251

Course ContractTopics:

**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.*

- Useful online Calculus textbook.
- 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; 31,33,35,37,66 plus 57,59,63,65 and 67

- Lab 1 (improper integration, sequences and series)
- Exercises for testing for series. (html file)
- HW for 7.3: page 453: 5,7,11,13,19-25 odd.

- A Fixed Point Algorithm
**:**(Maple file) - Lab 2: The smallest positive integer N, partial sum and a convergent series-Maple.
- A summary of all types of tests for series.
- HW for 7.4 Alternating Series and Ratio Test: page 463: 1-13 odd; 31-39 odd; 43-53 odd.
- HW for 7.5: page 474, #7-15 odd and 19-23 odd.
- HW for 7.6: page 483, #7-17 odd. Power Series and Taylor's Series (Maple file).
- HW for 7.7: page 489, #1-9 odd; 15-21 odd.
- Error Estimate for sin(1) (Maple file).

- More on Power Series (html)
- Integration and derivatives of a power series.
- Taylor polynomials (html)
- Power Series (Paul's Online Calculus).
- **An old test (Do #1(a), 3, 4,5,6,7, 9,10).
- Parametric, Polar plots and arc lengths with Maple. (pdf file).
- Maple file (arc length and surface area)
- Famous Curves (html)
- HW 8.1: page 511, 17-27 odd.
- HW 8.2: page 519, 45-53 odd, 63,65.
- HW 8.3: page 529, 19-33 odd, 53,54.
- HW 8.4, page 537, 27, 29, 33, 35, 43, 45.
- Polar Graphs (Maple
file)
- Polar Gallery (html)

- A fish (Maple file)
- A hat (Maple file)
- 3d plots
- Vector I.(A Maple worksheet)
- Vector II.(A
Maple worksheet)
- An exercise (Maple worksheet)

- Dot Product ( A java applet)
- HW for 9.3, page 573: 25-35 odd
- Java applet on the Cross Product and the area of a parallelogram.
- Java applet on the Volume of a parallelepiped spanned by three vectors.
- HW for 9.4, page 574: 11,13,15,25,27,29,35.
- HW for 9.5, page 589: 15,17,19,25,27,35,37,39,41,43,45,85,87,93.
- Maple portion for an old test 1.
- Dot and Cross Product with Maple.
- Line and Plane with Maple
- Quadric Surfaces. (Paul's online).
- HW for 9.6, page 599, 1-5, 11-17, 31,33,35.
- Basic 3D surfaces. (Maple)
- Interesting 3D graphs
- An interesting site on plotting using Java applets.
- Cylindrical and Spherical Coordinate Systems (Maple).
- Cylindrical and Spherical Coordinate Systems (Paul's online).
- HW for 9.7: page 606: 3,7,9,11,21,23,29,33,35,36,37,39.
- Review for an old test 1 of math 252.
- Maple portion for test 1.
- Vector Functions (10.1,10.2, and 10.3)
- Visualize the relationship among Tangent, Principle Normal and Binormal Vectors.
- Visualize the relationship between acceleration and velocity vectors.
- Acceleration.
- An old Quiz 3
- Some materials on Multivariable Calculus.
- Dot Product ( A java applet)
- Homework for 1/6 and 1/8: page 674, 7-11 odd, 15, 21-24.
- Line and Plane with Maple
- Interesting 3D graphs.
- Cylindrical Coordinate; Spherical Coordinate.
- Something from Math 151
- Something from Math 152.

Some topics from Math 152:

- Some Antiderivatives (Maple file)
- Partial Fractions (Maple file)
- Numerical Integrations (Maple file)
- Integration by parts (Maple file)
- Substitution
- Finding area between curves (html)
- Solid of Revolution (A Maple file)
- Arc
Lengths
- (Maple file)
- Cycloid (Java Applet)

- Average value of a function
- Moment and center of mass.
- Improper Integrals (Maple file)
- page 422: 1,5,7,15,17,19
- Drill Practices
- Table of integration techniques