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

Prerequisite: MATH 152 or MATH 155.

A unified course dealing with the basic principles of Calculus and Analytic Geometry. Inversetrigonometric functions, techniques of integration, infinite sequences and series are discussed. Alsoincludes an introduction to the geometry of higher dimensions and functions of several variables,partial differentiation and multiple integration. Mathematical software packages and graphingcalculators will be used as illustrative and problem solving devices.

MATH 251 is equivalent to the first half of MATH 255. MATH 252 is equivalent to the second half ofMATH 255. Students who earned credit for MATH 251 or MATH 252 may not also earn credit for MATH255 or for MATH 162. Students who have earned credit for MATH 153:154 may not subsequently earncredit for MATH 251:252.

2. Detailed Description of Content of Course

The following topics will be covered in MATH 251:

Inverse trigonometric functions

Integration techniques, including integrating powers and functions of trigonometric functions,

trigonometric substitutions, method of partial fractions, use of integration tables and formulas

L'Hopital's rule

Analysis of improper integrals

Infinite sequences, including techniques of detecting convergence/divergence, basic

properties, squeeze theorem, absolute value theorem, monotonicity and boundedness

Theory of infinite series, including the definition of convergence, methods of detecting

convergence/divergence (n th term test, integral test, comparison theorem, root test, ratiotest, etc.), Taylor polynomials and approximations with error analysis.

History of the main results of the course.

The following topics will be covered in MATH 252:

Polar coordinates and parametric representations of curves, including differentiation and

integration of functions in polar form

The geometry of 3-space, including the definition of vectors and their basic properties,

equations of lines and planes in 3-space, dot and cross product

Vector-valued functions: graphs, continuity, differentiation and integration

Functions of several real variables, graphs, continuity and limits, use of computers to visualize

surfaces in 3-space

partial differentiation, applications to approximation, chain rules for functions of several

variables

Directional derivatives and gradients, equations of tangent planes and normal lines, extremevalues of functions of several variables, Lagrange multipliers

Multiple and iterated integrals, applications to calculating surface areas and volumes

History of the main results of the course.

3. Detailed Description of Conduct of Course

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Instructors will use a combination of lectures, group work and computer laboratory sessions. Somemay 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.

4. Goals and Objectives of the Course

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

5. Assessment Measures

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

6. Other Course Information

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

7. Review and Approval

DATE ACTION APPROVED BYSept. 2001 Review Stephen Corwin, Chair