Northeastern State University

College of Mathematics, Science and Nursing

Department of Mathematics

Syllabus for Math 2633 Calculus III

PREREQUISITES: Math 2624 Calculus II

CATALOG DESCRIPTION OF COURSE: Polar coordinates, parametric equations, vector-valued functions, partial derivatives, and multiple integrals.

COURSE PURPOSE: This course completes the calculus sequence, and gives the student an opportunity to extend their differentiation and integrations skills to different types of functions, functions with vector inputs and functions with vector outputs. Differentiation and integrations with respect to one variable or more variables is covered under the topics of partial derivatives and multiple integrals. A wide variety of real-life applications are chosen to illustrate the usefulness and universality of these techniques.

EXPECTED COURSE OUTCOMES:

The student will be expected to achieve the following objectives:
1. Communicate with appropriate mathematical symbols.
2. Manipulate vectors algebraically, solve application problems using vectors, and perform techniques of calculus of functions with vector inputs and outputs.

3. Use the techniques and concepts of differential calculus in the computation, interpretation , applications, and graphical representation of partial derivatives.

4. Use the techniques and concepts of integral calculus in the computation, interpretation, graphical representation, and applications of multiple integrals.

5. Use polar, cylindrical and spherical coordinates as well as rectangular coordinates in problem solving.

6. Compute efficiently using the appropriate method - calculator, paper/pencil algorithms, or mental calculation

INSTRUCTIONAL MATERIALS: (Required Textbook) Calculus, 2^nd ed., Finney and Thomas.,Addison-Wesley Publication Co., 1994

Recommended: Graphing calculator TI -83

INSTRUCTIONAL PROCEDURES: The expected course outcomes will be realized through a variety of instructional strategies to aid the students' construction of cognitive schemas . Those strategies include, but are not limited to, the following: expository-discussion, demonstration, inquiry, and group activities. The instructor also will integrate appropriate multi-media technology and invite guest speakers, for the purpose of enriching the students total experience.

Calculus III

I. Vectors and Analytic Geometry in Space

A. Vectors in the Plane and in Space

B. Dot and Cross Products

C. Lines, Planes, and Surfaces in Space

D. Polar, Cylindrical, Spherical Coordinates

II. Vector-Valued Functions

A. Definition/ Space Curves

B. Modeling Projectile Motion

C. Arc Length/ Unit Tangent Vectors

D. Curvature/Torsion/ TNB Frame

E. Planetary Motion/ Satellites

III. Partial Derivatives

A. Functions of Several Independent Variables

B. Limits and Continuity

C. Definition of Partial Derivative

D. Differentiability/Linearization/Differentials

E. Directional Derivatives/Gradient Vectors/Tangent Planes

F. Maxima, Minima, Saddle points

IV. Multiple Integrals

A. Double Integrals

B. Areas/Moments/Centers of Mass

C. Double Integrals in Polar Form

D. Triple Integrals in Rectangular, Cylindrical and Spherical Coordinates

ADA COMPLIANCE: If any member of the class feels that he/she has a disability and needs special accommodations of any nature whatsoever, the instructor will work with you and the University's Office of Student Affairs to provide reasonable accommodations to ensure that you have a fair opportunity to perform in this class. Please advise the instructor of such disability and the desired accommodations at the first class attended.

INCLEMENT WEATHER / DISASTER POLICY: The following are basic premises for the inclement weather policy at Northeastern State University:

1. Classes are expected to be held if at all possible.

2. It is the student's responsibility to receive the information when weather is questionable.

3. Neither students nor faculty are expected to risk life or limb.

4. Faculty members are obligated to hold classes if the University is not closed, unless the faculty member is unable to get to campus.

Policy: During times of inclement weather, decisions concerning day classes will be made by 6:00 a.m. in order for the media to be notified and for students to receive the announcement before they leave home. Decisions concerning night classes will be made by 3:00 p.m.

The following media will be notified regarding closing of the campus:

Radio Stations: Television Stations:

KRMG 740 AM Tulsa KJRH Channel 2 Tulsa

KAYI 107 FM Tulsa KOTV Channel 6 Tulsa

KTLQ 1350 AM Tahlequah KTUL Channel 8 Tulsa

KEOK 102 FM Tahlequah KFSM Channel 5 Fort Smith

KBIX 1490 AM Muskogee Cable Channel 96 Tahlequah

KMMY 97 FM Muskogee

KVOO 1170 AM Tulsa

The automated attendant message on 918-456-5511 will be modified to include information concerning campus operations during inclement weather.