MATH 2415 - Calculus & Analytic Geometry III
Spring 2006 Semester
(Required)
Catalog Data 2006-2008:
MATH 2415:
Calculus and Analytic Geometry III. Credit 4. Sequences, series, functions of several variables, vector analysis, partial derivatives, multiple integrals and differential equations.
Prerequisite: MATH 2414 or its equivalent.
Textbook: James Stewart, Calculus (Early Transcendentals), 5th edition, Brooks//Cole
Coordinator: Michael Laidacker, Associate Professor of Mathematics
Course Objective:
The course is the last of a series of three four-hour calculus courses. The basic goal of the course is to introduce the student to series, multiple-variable calculus, vectors and differential equations.
Prerequisites by Topic: Second course in calculus
Topics:
1. Vector functions and space curves
2. Derivatives and integrals of vector functions
3. Arc length and curvature
4. Motion in space; velocity and acceleration
5. Functions of Several Variables
6. Limits and Continuity
7. Partial Derivatives
8. Tangent planes and linear approximations
9. The Chain Rule
10. Directional derivatives and the Gradient Vector
11. Maximum and minimum values
12. Lagrange Multipliers
13. Double integrals over Rectangles
14. Iterated integrals
15. Double integrals over general regions
16. Double integrals in polar coordinates
17. Applications of double integrals
18. Surface area
19. Triple integrals
20. Triple integrals in cylindrical and spherical coordinates
21. Change of variables in multiple integrals
22. Vector fields
23. Line integrals
24. The fundamental theorem for line integrals
25. Green's Theorem
26. Curl and Divergence
27. Parametric surfaces and their areas
28. Surface integrals
29. Stoke's Theorem
30. The Divergence Theorem
Schedule: Three 50-minute lectures per week. One 50-minute lab. Four 50-minute exams and a 2-hour final.