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)
- 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
- Exercises on improper integration, sequences and series)
- Solution to a recursive problem from a quiz in the past. (html file)
- HW for 7.3: page 453: 5,7,11,13,19-25 odd.
- More HW for 7.3: 7-27 odd (Integral Test) 41,43,45,49. 51-61 odd (Limit Comparison Test).
- Exercises for testing for series. (html 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.
- Practice test from an old test 1.
- 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).
- HW for 7.8: page 500, 21-27 odd, 31, 37, 51.
- Practices on 7.6-7.8.
- 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, 1-13 odd, 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.
- Practice Test 2.
- Polar Graphs (Maple file)
- Some nice animations about surface of revolution
- A fish (Maple file)
- A hat (Maple file)
- **Moving fish (added 2014)
- 3d plots
- Vector(A Maple worksheet)
- HW 9.1: page 557, 31-39 odd, 45,47.
- HW 9.2: page 564, 19-23 odd, 29,41,43.
- 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 579: 11,13,15,25,27,29,35.36.
- HW for 9.5, page 589: 15,17,19,25,27,35,37,39,41,43,45,85,87,93.
- Dot and Cross Product with Maple.
- Line and Plane with Maple
- Maple portion for an old test involving Section 9.6: Surfaces in space.
- Quadric Surfaces-from Paul's online) (our text section 9.6). .
- 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).
- A demo of Sperical Coordinate.
- Maple portion for problems involving cylindrical and spherical coordinates.
- HW for 9.7: page 606: 3,7,9,11,21,23,29,33,35,36,37,39.
- A Review sheet for an old test 3.
- HW for 10.1: page 614: 13-21 odd, 41,43.
- HW for 10.2: page 621: 35, 43,45,47,53,55.
- HW for 10.3: page 629: 1-13 odd, 19, 21.
- An old review sheet for test 4.
- Vector Functions (10.1,10.2, and 10.3)
- Visualize the relationship between acceleration and velocity vectors.
- Acceleration, unit tangent, unit principal normal and etc.
- Arc length for a space curve (Maple).
- Visualize the relationship among Tangent, Principle Normal and Binormal Vectors.
- Some materials on Multivariable Calculus.
- 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