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Mathematics 251

MATH 251:252

Catalog Entry

MATH 251:252. Calculus and Analytic Geometry III & IV
Three hours lecture, three hours credit for each course (3:3).

Prerequisite: MATH 152, MATH 251 is prerequisite for MATH 252.

The first part of this course covers sequences and series, Taylor and power series, parametric curves, geometry higher dimensional spaces, vector-valued functions.  The second part deals with functions of several variables, discussion of limits, continuity, and differentiability, multivariable optimization, iterated integrals and applications to volumes, line integrals and Green's Theorem.

Mathematical software packages and graphing calculators will be used as illustrative and problem solving devices.


Detailed Description of Content of Course

The following topics will be covered in MATH 251:

    -Sequences, convergence

    -Series, geometric series and telescoping series

    -Convergence tests for series

    -Taylor and power series

    -Parametric Curves, polar coordinates

    -Vectors in two and three dimensions, dot and cross products

    -Lines planes and surfaces

    -Cylindrical and spherical coordinates

    Vector-valued functions, tangent and normal vectors, arc length.


The following topics will be covered in MATH 252:

    -Functions of several real variables, graphs, continuity and limits

    -Partial derivatives, directional derivatives and gradient, differentiability

    -Tangent and normal planes, extrema, optimization problems, Lagrange multipliers

    -Iterated integrals, volumes, surface areas, change of variables, integration in polar, cylindrical and spherical coordinates

    -Line integrals, Green's theorem, divergence and Stokes theorem.


Detailed Description of Conduct of Course

Instructors will use a combination of lectures, group work and computer laboratory sessions.  Some may require students to present homework problems to the rest of the class on a regular basis.  Software packages and graphing utilities will be used in solving problems and as illustrative aids.


Goals and Objectives of the Course

Students are expected to learn the basic principles of Calculus and Analytic Geometry and to demonstrate the use of these principles in problem solving.  In addition to paper and pencil problem solving, students will use appropriate graphing calculator and computer algebra system technology to analyze parametric representations, conic sections, sequences, series and features of multivariable calculus.


Assessment Measures

Graded tasks may include tests, quizzes, homework exercises, papers, class participation and attendance.  Students will be required to demonstrate literacy in the use of mathematical software packages and/or graphing calculators as effective tools in problem-solving.


Other Course Information

This course is primarily intended for freshman and sophomore students, especially those majoring in mathematics, computer science, the sciences, psychology, or economics.


Review and Approval

October 2007