Course Syllabus - Fall 2002

Course Number: MATH 2654

Course Title: Calculus III

Hours Credit: 4 hours

Prerequisites: MATH 2644

Instructor: Dr. Sharp

Instructor Office Hours: M,W,F: 10:00-11:00 AM; T: 8:50-9:30 AM , 10:20-11:00 AM,12:00 NOON - 1:00 PM; M,W: 12:00 NOON - 1:30 PM AND BY APPOINTMENT

Course Description: A continuation of MATH 2644. Topics include functions of two, three, and more variables, multiple integrals and topics in vector calculus.

Topics: Applications of the definite integral, derivatives and integrals of exponential, logarithmic, and inverse trigonometric functions, indeterminate forms and l´Hospital's Rule, hyperbolic and inverse hyperbolic functions, techniques of integration, polar coordinates and plane curves, and infinite series.

Text:Calculus, Early Transcendentals, by James Stewart, Fourth Edition, Brooks/Cole Publishing Company, 1999

Learning Outcomes: The student will be able to:

1. Compute vector sums, difference, and scalar products (L1).
2. Compute dot products and cross products of vectors (L1).
3. Compute equations of lines and planes in space (L1).
4. Compute the unit tangent vector, the unit normal vector, the unit binormal vector, the curvature, and the torsion of a space curve (L1).
5. Compute the tangential and normal components of acceleration (L1).
6. Convert between Cartesian, cylindrical, and spherical coordinates in space (L1).
7. Compute the limit of a function of two or three variables (L1).
8. Determine if a function of two or three variables is continuous at a points (L1).
9. Compute partial derivatives, gradients, and directional derivatives of functions of two and three variables (L1).
10. Compute using the Chain Rule for functions of several variables (L1).
11. Demonstrate understanding of the significance of the gradient vector (L1).
12. Solve theoretical and applied max-min problems using either direct methods or the method of Lagrange multipliers (L1).
13. Find and classify critical points of functions of two and three variables (L1).
14. Set up and evaluate double and triple integrals as iterated integrals in Cartesian, polar, cylindrical, and spherical coordinates (L1).
15. Set up and evaluate double and triple integrals as iterated integrals in Cartesian, polar, cylindrical, and spherical coordinates (L1).
16. Solve applied problems involving areas, volumes, centers of mass, first, second and polar moments of inertia (L1).
17. Evaluate line integrals, including applying the Fundamental Theorem of Line Integrals (L1).
18. Demonstrate an understanding of the concepts of conservative vector fields and independence of path (L1).
19. Compute using Green's Theorem, Stokes' Theorem and the Divergence Theorem (L1).

MATH 2654-01-(FA 2002)

(I) HOMEWORK: Specifically assigned homework problems will be discussed in class and simulated on exams. There will be no memorized problems, and homework will not be taken up for a grade. However, occasionally selected homework problems may be taken up to check format and notation only--not for a grade. IT IS VIRTUALLY IMPOSSIBLE TO BE SUCCESSFUL IN THE COURSE WITHOUT DOING HOMEWORK ON A DAILY BASIS. PLEASE TURN OFF ALL CELL PHONES DURING CLASS!!

(II) TESTS: ( NO MAKE-UP TESTS !!! )
(A) EXAMS: There will be three or four 100 point exams (USUALLY ON TUESDAYS [MAY OVERLAP MONDAYS OR WEDNESDAYS]).
(B) FINAL EXAM: A comprehensive final exam will be given on Monday (12/09/02) at 11:00 AM-1:00 PM.