MATH 151:152
CALCULUS AND ANALYTIC GEOMETRY

1. Catalog Entry

MATH 151:152. Calculus and Analytic Geometry I & II. (3:3)
Three hours lecture, one hour lab, three hours credit for each course.

Prerequisite: MATH 140 or four years of high school mathematics, including some trigonometry.

A unified course dealing with the basic principles of Calculus and Analytic Geometry. The basic ideas of analytic geometry in the plane and analysis of functions of a single real variable are discussed, including limits, differentiation, integration, and applications thereof.  Mathematical software packages and graphing calculators will be used as illustrative and problem-solving devices.

Students who earn credit for MATH 151 or MATH 152 may not also earn credit for MATH 155.  General Education Credit - Mathematical Sciences.

2. Detailed Description of Content of Course

The following topics will be covered in MATH 151:

• The real number system including the necessary algebraic and analytic properties.
• Introduction to plane geometry including coordinates, distance measure, graphs of equations.
• Functions including those of the trigonometric, exponential and logarithmic variety, the algebra of functions, inverses.
• Limits, including properties, techniques of evaluation, definition of continuity, limits involving infinity.
• Derivatives, including the basic rule for differentiating sums, products, quotients and compositions of differentiable functions, differentiability and continuity, implicit differentiation, methods for locating extreme values, increasing/decreasing behavior of functions, concavity, Mean Value Theorem, applications to optimization, related rates, approximation, physical problems.
• History of the main results of the course.

The following topics will be covered in MATH 152:

• Fundamental properties of the Riemann integral and its relation to area, Riemann sums, properties of definite integrals, the Fundamental Theorem of Calculus.
• Basic techniques of integration including the integration of polynomials, basic substitutions, integration of exponential and simple trigonometric functions, integration by parts, basic numerical integration methods and the use of tables and formulas.
• Applications of the definite integral to calculating area, volume, arc length, certain applications to the physical sciences.
• 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 solve equations, plot, differentiate and integrate.

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