UW COLLEGES

DEPARTMENT OF MATHEMATICS

 

COURSE GUIDELINES

 

Course Title:    Calculus and Analytic Geometry III   .

Course No.     MAT 223        No. of Credits    4 or 5  .       Associate Degree Designation  MS  . 

Contact hrs/wk:  Lecture   4 or  5    .       Lecture/Discussion ____       Lab ____        

 

Course Prerequisites:  A grade of  C or better in MAT 222, or equivalent.

 

Catalog Description:  Continuation of MAT 222.  Analytic geometry of three dimensions, functions of several variables, partial differentiation, multiple integration, and introduction to
differential equations.

 

Course Content (list of topics normally covered)

 

      Three-dimensional analytic geometry

 The three-dimensional rectangular coordinate system.  Equations of lines and planes and  related topics.  Graphs of quadric surfaces.  The cylindrical and spherical coordinate systems.

 

        Vectors and vector functions.

 Geometric and algebraic properties of vectors and vector operations.  Algebra and calculus of vector functions.  Arc length along a curve.  The vector analysis of curvilinear motion.

 

         Continuity and differentiation for real functions of several variables.

 

 Limits and Continuity for functions of several variables.  Partial derivatives.  Tangent planes to surfaces.  Relative extrema and saddle points.  The multivariable chain rule.  Directional derivatives and the gradient.  Optimization..

 

          Multiple integration.

 

Multiple integrals for area, volume, surface area, and mass.  Moments and centers of mass for thin plates and solids. 

 

           Vector fields and line integrals.

 

                Vector fields. Divergence and curl.  Line integrals.  Independence of path.  Green’s
                Theorem.  

 

           Differential equations.

 

Differential equations of the following types:  separable, exact, first order linear, and second order linear with constant coefficients.   

 

           Optional topics.  

                  Surface integrals, Stokes’ Theorem, and the Divergence Theorem.

 

 

Content-Based Departmental Proficiencies.

     The successful student will be able to:

 

        Apply vector methods to solve problems involving lines and planes.

       

        Apply vector analysis in the study of space curves and be able to solve practical problems
        via vector functions.

 

        Compute partial derivatives and use partial derivatives to solve practical problems involving
        multi-variable functions.

 

        Set up and evaluate multiple integrals for volume, surface area, mass, and moments , using
        appropriate coordinate systems.

 

        Evaluate line and integrals, using Greene’s Theorem when appropriate.

 

         Solve differential equations of various types.

 

         Apply differential equations to solve practical problems.

 

 

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 Course.  (editions change over time)

 

         Calculus, Larson, Hostetler and Edwards

        Calculus, 4th Edition, Stewart  AND   Elementary Differential Equations and Boundary

        Value Problems, Boyce and Diprima

         Calculus, 6th Edition, Anton

         Multivariable Calculus, 2nd Edition, Bradley and Smith

 

Approved April 22, 2006