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ANALYSIS I
Math 554
  Spring 1996

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Instructor Information:

 

Professor: Bob Sharpley
    Office: 313D LeConte
    Office Hours: MWF 2:30-3:30   or   by appointment.
 

General Reference Text:

Introduction to Mathematical Analysis, by W.R Parzynski and P.W. Zipse, McGraw-Hill, New York, 1982.

Grading:

The course grade is computed from 3 Test grades (20% each), Homework (10%) and the Final Exam (30%).
 

Course Content:

The text will only be used as a general reference, with lecture notes provided. The lecture notes were designed so that proofs of most theorems are fairly short and build progressively on the ideas developed. The few more difficult proofs necessary to complete our development are presented in detail in these notes. Using these lectures as an outline and filling in the proofs from in-class notes, provides the student with a full set of lecture notes for the course. Classroom participation is extremely important and regular attendence is required.
The topics will include:
• Sets and set operations, principle of induction, the real numbers, order, least upper bounds, the Archimedian property and completeness.
• Sequences of real numbers, convergence, subsequences, the Bolzanno-Weierstrass property and compactness.
• Topology of the real numbers: open and closed sets, the Heine-Borel theorem and compactness, connectedness.
• Continuous functions and their properties, uniform continuity, monotone functions.
• Differentiation, Rolle's theorem and the Mean Value Theorem, L'Hospital's rule.
• The Riemann integral, its properties, and the Fundamental Theorem of Calculus.

 

Make-up Policy:

Make-up exams are not normally given.
 

Important Dates:

 

Classes Begin	Monday, Jan. 8
Last Drop Date (no record)	Fri., Jan. 12
Test 1	Mon., Feb. 5
Last Drop Date (without penalty)   ...	Fri., Feb. 16
Test 2	Fri., March 1
Spring Break	March 3-10
Test 3	Fri., April 5
Easter	Mon., April 8
Last Day of Classes	Mon., April 22
Reading Day	Tue., April 23
Cumulative Final Exam	Wed., May 1
	[2 PM]

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