MATH 251:252
CALCULUS AND ANALYTICAL GEOMETRY

1. 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 or MATH 155.

A unified course dealing with the basic principles of Calculus and Analytic Geometry. Inverse trigonometric functions, techniques of integration, infinite sequences and series are discussed. Also includes an introduction to the geometry of higher dimensions and functions of several variables, partial differentiation and multiple integration. Mathematical software packages and graphing calculators 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 of MATH 255. Students who earned credit for MATH 251 or MATH 252 may not also earn credit for MATH 255 or for MATH 162. Students who have earned credit for MATH 153:154 may not subsequently earn credit 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, ratio test, 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, extreme values 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

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.

4. 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.

5. 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.

6. 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.

7. Review and Approval

DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair