WESTERN OKLAHOMA STATE COLLEGE



WESTERN OKLAHOMA STATE COLLEGE

DIVISION OF MATH, SCIENCE AND AGRICULTURE

COURSE MASTER SYLLABUS

COURSE NUMBER: MATH 2273

COURSE TITLE: Calculus III

CREDIT HOURS: 3

PREREQUISITES: MATH 2235

COREQUISITES: none

CATALOG DESCRIPTION:

A continuation of MATH 2235 Calculus II. Includes vectors, infinite series, partial derivatives, and multiple integrations.

TEXTBOOKS:

CALCULUS 8th edition, Larson, Hostetler, and Edwards, Houghton Mifflin Company 2006.

LEARNING OUTCOMES:

After completing this course, the student should be able to demonstrate competency in the following areas:

1. Vectors and the geometry of space

2. Vector-valued functions

3. Functions of several variables

4. Multiple integrations

5. Vector analysis

COURSE REQUIREMENTS:

See the instructor’s information sheet for specific course requirements.

METHOD OF EVALUATION:

Instructors must provide class information sheets (class syllabus) which specify course

requirements. Class information sheets must clearly state the instructor’s method of

evaluation.

ATTENDANCE POLICY:

Although attendance may not be used in the determination of grades, regular attendance is expected. Class information sheets must clearly state the instructor’s attendance policy.

ACADEMIC ETHICS:

Students are expected to comply with the regulations regarding cheating or plagiarism as stated in the Western Oklahoma State College catalog. (See “Student Disciplinary Regulations”)

COURSE COMPETENCIES:

0. To demonstrate competency with vectors and the geometry of space, the student should be able to:

1.1 Perform vector operations.

1. Use vectors to solve real-life problems.

2. Find dot products and cross products of vectors.

3. Analyze vectors in space.

4. Recognize and write equations for cylindrical surfaces, quadratic surfaces, and surfaces of revolution.

2.0 To demonstrate competency with vector-valued functions, the student should be able to:

1. Differentiate and integrate vector-valued functions.

2. Use vector-valued functions to describe velocity, acceleration, and projectile motion.

3. Find tangential and normal components of acceleration.

4. Find and use arc length parameters to describe curves.

3.0 To demonstrate competency with functions of several variables, the student should be able to:

1. Sketch graphs of multivariable functions.

2. Extend the concept of continuity to functions of two or three variables.

3. Find and use a partial derivative of a function of two or three variables.

4. Extend the concept of differentiability to a function of two variables.

5. Find and use the gradients of functions of two or three variables.

6. Find absolute and relative etrema of functions of two variables.

7. Solve optimization problems involving functions of several variables.

8. Use the method of least squares.

9. Use the Method of Lagrange Multipliers.

0. To demonstrate competency with multiple integration, the student should be able to:

1. Evaluate and use integrated integrals.

2. Evaluate and use double integrals in volumes of solid regions, polar coordinates, centers of masses of planar lamina, and areas of surface.

3. Evaluate and use triple integrals to find volumes of solid regions, centers of masses, and moments of inertia of solid regions.

4. Write and evaluate triple integrals in cylindrical and spherical coordinates.

5. Understand and use the concept of a Jacobian.

5.0 To demonstrate competency in vector analysis, the student should be able to:

1. Understand and use the concepts of a vector field.

2. Understand and use the concepts of a piecewise smooth curve.

3. Write and evaluate a line integral of a vector field and in differential form.

4. Use Green’s Theorem to evaluate a line integral.

5. Understand and use parametric equations.

6. Understand the concept of a flux integral.

7. Understand and use Stokes’s Theorem.

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