Course Syllabus - Fall 2002

**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:

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

(C) GRADING:

- 90 - 100: A
- 80 - 89: B
- 70 - 79: C
- 60 -69: D
- Below 60: F

**(III) ATTENDANCE**: Roll will be taken daily.

(A) ABSENCES: 0 - 7 Acceptable; 8 EXCESSIVE ( "WF" )

(B) TARDIES: 2 Tardies = 1 Absence