NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

TITLE OF COURSE: Calculus III (MTH 227)

DIVISION: Mathematics, Science, and Technology

COURSE DESCRIPTION: This is the third of three courses in the basic calculus sequence. Topics include vector functions, functions of two or more variables, partial derivatives(including applications), quadric surfaces, multiple integration, and vector calculus(including Green’s Theorem, Curl and Divergence, surface integrals, and Stoke’s Theorem).

HOURS:

Credit: 4 Contact: 4 Lecture: 4 Clinical: 0 Lab: 0

PREREQUISITE(S): MTH 126

COREQUISITE(S): None

REQUIRED TEXTBOOK(S): Calculus, Eighth Edition, by Larson, Hostetler, and Edwards, Houghton-Mifflin Co., 2006.

SUPPLIES: Recommended supplies include graph paper (rectangular and polar) and a graphing paper.

GENERAL EDUCATION OBJECTIVE: All associate degree graduates should be able to use the mathematical concepts, notations, and manipulations needed in their field of study or occupation. (3)

COURSE OBJECTIVE(S): Upon successfully completing Calculus III, the student should be able to:

1. Recognize and write equations for surfaces in space (cylindrical, quadric, and surfaces of revolution) and use conversions between the rectangular, cylindrical and spherical coordinate systems to represent surfaces in space.

2. Differentiate, integrate, and find limits of vector-valued functions as related to velocity and acceleration vectors; find tangent and normal vectors; and calculate arc length and curvature for a space curve.

3. Interpret graphs involving level curves and level surfaces; define continuity; and find limits of functions of two or three variables.

4. Find and interpret partial derivatives, higher-order partial derivatives, total differential, directional derivatives and gradients, and extrema for functions of two or three variables.

5. Evaluate double and triple integrals, and use multiple integration to solve application problems.

6. Do mathematical operations on vector fields in the plane and space: sketch representative vectors and find orientation; define curl and divergence; define, integrate, and evaluate line integrals using Green’s and Stoke’s Theorems; and evaluate surface integrals.

METHODS OF EVALUATION:

1. Course Grade Evaluation: (Minimum of 4 measurements)

A comprehensive final exam will be given and counted toward the student’s final average. Make-up examinations, as such, will not generally be given.

2. Evaluation of General Educational Objectives: Student success on the General Educational Objective (3) is measured by student performance on each of the course objectives, which require use of mathematical concepts, notations, and manipulations. Performance on each course objective will be evaluated using appropriate problems from the final exam. Results will be tallied for each course objective.

3. Use of Findings: Instructors will analyze data gathered from the assessment(s) for each course objective and changes will be made based on identified weaknesses. The math department will meet once every three years to discuss findings and implement strategies to improve department and student performance.
   

OUTLINE OF COURSE TOPICS:

I. Surfaces in Space

A. Cylindrical Surfaces

B. Quadric Surfaces

C. Surfaces of Revolution

D. Cylindrical Coordinates

E. Spherical Coordinates

II. Vector-Valued Functions

A. Definition and Space Curve

B. Continuity and Limits

C. Differentiation and Integration

D. Velocity and Acceleration

E. Tangent and Normal Vectors

F. Arc Length and Curvature

III. Functions of Several Variables

A. Level Surfaces and Level Curves

B. Definition

C. Limits and Continuity

D. Partial Derivatives

E. Differentials

E. Chain Rules for Several Variables

F. Directional Derivatives and Gradients

G. Tangent Planes and Normal Lines

H. Extrema of Functions of Two Variables

IV. Multiple Integration

A. Iterated Integrals and Area in the Plane

B. Double Integrals and Volume

C. Surface Area

D. Triple Integrals and Applications

V. Vector Analysis

A. Vector Fields, including Curl and Divergence

B. Line Integrals

C. Conservative Vector Fields and Independence of Path

D. Green’s Theorem

E. Surface Integrals

F. Stoke’s Theorem

AMERICANS WITH DISABILITIES ACT POLICY: It is the policy of Northwest-Shoals Community College to comply with the Americans with Disabilities (ADA) Act. Any student covered under this act needing and desiring reasonable accommodations for this class should notify Linda Waide at 331-5321. See NWSCC catalog for additional details.

ATTENDANCE POLICY: Because class attendance is considered to be essential to the accomplishment of course objectives, excessive absences are discouraged. At no time should a student miss more than 20% of the class meetings for a course. These absences also include any absences accrued during late registration. Failure to adhere to the 20% policy may result in a failing grade based on academic performance. Students should discuss with the instructor what is considered “excessive” for a particular course. Any variation of this policy must be approved through the Chief Instructional Officer. A student who is absent due to required participation in a school activity must be allowed to make up work, according to guidelines issued by individual instructors.

WITHDRAWAL POLICY: A student who is unable to complete a course is expected to withdraw from that course by the end of 60% of class meetings. A student who withdraws by the date published in the schedule will receive a grade of “W” for the course. This withdrawal is done only by student request. The grade of “W” is allowed regardless of the student’s grades to the point of withdrawal.

After the designated date of class withdrawal, the approval of the Chief Instructional Officer is required prior to allowing a student to withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal failing) will be made by the instructor for the course and is based on the student’s grades to the point of withdrawal.