MATH 554 and 703-I Real Analysis I  - Spring 2004 Professor Robert Sharpley Meets: MWF  10:10 - 11:00 in LeConte 405 Instructor Information  Office:   LeConte 313 D  Office Hours:   MWF 11-11:50

Course Information

Description:   This course is a rigorous treatment of analysis required for a fuller understanding of the calculus, as well as preparation for graduate school in mathematics and other disciplines requiring analytical and numerical solution of equations arising from mathematical modeling. Standard topics of an introductory analysis course will be covered, along with additional concepts which do not necessarily follow the text. Attendence is required and the exams will be over the lectures and homework. The course topics include:

• Countable and uncountable sets, the real numbers, order, least upper bounds, and the Archimedean property.
• Metric spaces: topology, open and closed sets, convergent sequences, completeness, compactness and the Heine-Borel Theorem for the real line, connectedness.
• Limits; Continuous functions and their properties, limits, continuous functions on a compact metric space, continuous functions on a connected metric space; intermediate and extreme value theorems, uniform continuity, monotone functions and inverses.
• Derivatives and their properties, the chain rule, Rolle's theorem and the Mean Value Theorem, Taylor's theorem, L'Hospital's rule.
• The Riemann integral, its properties, and the Fundamental Theorem of Calculus.

Text:  Introduction to Analysis, by Maxwell Rosenlicht, Dover Pub., New York, 1968.
   ISBN 0-486-65038-3 (pbk.)

Grading scheme: Three tests, each counting 20% of the final grade. The homework, turned in on a regular basis, counts 15%, with the comprehensive final exam counting 25%. Make-up tests are not normally given. Graduate Students will be required to complete additional homework and problems on Tests and the Final Exam.

Attendance: Classroom attendance is required according to official university 10% policy. Make-up tests are not normally given for missed examinations.

Important Course Dates:

January 12   (Monday) January 16   (Friday) January 19   (Monday) February 6   (Friday) February 23   (Monday) March 5   (Friday) March 7-14   (Sun.-Sun.) April 12   (Monday) April 14   (Wednesday) Classes Begin Last Day for Withdrawal w/o penalty Dr. Martin Luther King, Jr. Service Day (no classes) Test 1 Last Day for Withdrawal w/o WF grade Test 2 Spring Break - no classes Review Session Test 3 April 28   (Wednesday) May 5   (9 am, Wednesday)   Classses End Final Exam

Prerequisites: Qualification through placement, or a grade of C or better in MATH 241 or its equivalent.

  Lectures Notes

  Homework Assignments

  Tests and Samples

This page maintained by Robert Sharpley (sharpley@math.sc.edu) and last updated November 2, 2003.  This page ©2003-2004, The Board of Trustees of the University of South Carolina.  URL: http://www.math.sc.edu/~sharpley/math554