Corequisite

64112 Precalculus I, or 64113 Precalculus II, or 64211 Foundations of Calculus. This course must be taken in conjunction with one of the three corequisite courses.

Description

This course is designed as an honors component to supplement existing course at the precalculus level. The course is intended to provide students with exposure to relevant ideas for future courses in Calculus and/or Statistics. Topics include intuitive concept of the limit of a function, introduction to the delta epsilon definiton, limits at infinity, continuity and the Intermediate Value Theorem.

Statement of Course Need

Honors courses in mathematics have been developed to provide mathematically talented students the opportunity to obtain a level of rigor not currently available in existing courses. Topics in these courses have been selected to help students develop an appreciation of the origin and evolutionary growth of mathematical ideas from antiquity to the present. These courses have been designed as one-credit components to existing courses. They are intended to both supplement and complement the ideas and topics presented in courses at the level of precalculus, calculus, and statistics.

Place of Course in College Curriculum

1. Satisfies general education requirements in mathematics and science.
2. Serves as one credit of a mathematics elective for all programs.
3. Serves as one credit of an honors elective in mathematics.

1. Display an intuitive understanding of the concept of a limit.
2. Distinquish between one sided limits, two sided limits and limits at infinity.
3. Evaluate limits algebraically and geometrically.
4. Demonstrate an understanding of the relationship between continuity and limit.

1. Limits of a Function
   1. Informal definition
   2. Properties
   3. Polynomial functions
   4. Infinite limits
2. One-sided Limits
   1. Right-handed limits
   2. Left-handed limits
   3. Two-sided limits
   4. Infinite limits
3. Formal Definition of Limits
4. Continuity
   1. Continuity at a point
   2. Continuity on open and closed intervals
   3. Properties of continuous functions
   4. Continuity of composite functions
   5. The Intermediate Value Theorem
5. Limits at infinity
   1. Limits at positive and negative infinity
   2. Properties of limits at infinity

   Methods for Student Evaluation
   Will vary according to the instructional style of the teaching faculty.
   Lab Fees--None; Date: Jan, 1997, Sponsoring Dept: Mathematics