MATH 2414 - Calculus & Analytical Geometry II
Spring 2006 Semester
(Required)
Catalog Data 2006-2008:
MATH 2414:
Calculus and Analytic Geometry II. Credit 4. Methods of integration, polar coordinates, parametric equations and vectors.
Prerequisite: MATH 2413 or its equivalent.
Textbook: James Stewart, Calculus (Early Transcendentals), 5th edition, Brooks/Cole Harris and Lopez, Discovering Calculus with Maple, 2nd edition
Coordinator: Michael Laidacker, Associate Professor of Mathematics
Course Objective:
This is the second course in the calculus series. It is designed to introduce students to different methods of integration and other topics.
Prerequisites by Topic: MATH 2413 or its equivalent
Topics:
1. Integration by parts
2. Trigonometric integrals
3. Trigonometric substitution
4. Integration of rational functions by partial fractions
5. Strategy for integration
6. Using tables of integrals
7. Approximate integration
8. Improper integrals
9. Arc length
10. Area of a surface of revolution
11. Applications to physics and engineering
12. Curves defined by parametric equations
13 Calculus with parametric curves
14. Polar coordinates
15. Areas and lengths in polar coordinates
16. Sequences
17. Series
18. The integral test and sum estimates
19. The comparison test
20. Alternating series
21. Absolute convergence, ratio, and root tests
22. Strategy for testing series
23. Power series
24. Representation of functions as power series
25. Taylor and Maclaurin series
26. The binomial series
27. Three-dimensional coordinate systems
28. Vectors
29. The dot product
30. The cross product
31. Equations of lines and planes
32. Cylinders and quadric surfaces
33. Cylindrical and spherical coordinates
Laboratory projects:
3 laboratory sessions involving techniques of integration, parametrized curves and polar plots and sequences and series
Schedule: Three 50-minute lectures per week. One 50-minute lab. Four 50-minute exams and a 2-hour final.