UW COLLEGES

DEPARTMENT OF MATHEMATICS

COURSE GUIDELINES

Course Title: Calculus of Several Variables

Course No. _MAT 234 No. of Credits __3__

Contact hrs/wk: Lecture ___3____ Lecture/Discussion_____3____ Lab____0____

Course Prerequisites: A grade of C or better in MAT 222. Students may not receive credit for both MAT 223 and MAT 234

Catalog Description:

Continuation of MAT 222. Analytic geometry of three dimensions, functions of several variables, and multiple integration. This course is equivalent to MAT 223 without differential equations. (MS)

Course description for transfer evaluation:

The study of the calculus of several variables includes coordinate systems, vectors and their applications, functions of several variables, partial differentiation, multiple integration, vector-valued functions and applications. This course does not include the study of differential equations.

Complete list of topics normally covered:

· Three-dimensional coordinate systems and vectors

· Dot product and cross product

· Lines, planes, and quadric surfaces

· Vector functions and space curves

· Arc length and curvature

· Velocity and acceleration in space

· Cylindrical and spherical coordinates

· Functions of several variables

· Limits and continuity

· Partial derivatives and the Chain Rule

· Tangent planes and differentials

· Directional derivatives and gradient vectors

· Maximum and minimum on surfaces

· Lagrange multipliers

· Iterated integrals

· Applications of double integrals and surface area

· Triple integrals

· Vector fields

· Line integrals

· Green's Theorem and Stroke' Theorem

Content-based department proficiencies for the course:

· Analyze and interpret various algebraic and geometric aspects of vector representations.

· Understand how vectors can be combined with calculus to study motion in space and other applications through the use of vector-valued functions.

· Extend the methods of single-variable differential calculus to functions of several variables and solve rate and optimization problems in several variables.

· Learn the concept of multiple integration and its use to define and compute surface area, moments, centroids, and other applications.

· Synthesize the concepts of vectors and multiple integration and employ the results to examine applications vector-valued functions and line and surface integrals.

Colleges-wide proficiencies assigned to course:

Students should be able to demonstrate the following:

A. Analytical skills Performance Indicators: Students should be able to:

1. Interpret and synthesize information and ideas.

4. Select and apply scientific and other appropriate methodologies.

B. Quantitative skills Performance Indicators: Students should be able to:

1. Solve quantitative and mathematical problems.

2. Interpret graphs, tables, and diagrams.

Representative textbooks used for the courses:

Calculus-Early Transcendentals – Stewart

Calculus: Concepts and Contexts - Stewart

Approved April 22, 2006