ANALYSIS I
Math 554
Fall 1997
Instructor:
- Professor: Bob Sharpley
Office: 313D LeConte
Office Hours: MWF 11:00 a.m. or by appointment.
Course Materials:
- General Reference
- Real Analysis, A First Course, by Russell A. Gordon, Addision-Wesley
Higher Mathematics Series, Reading, MA, 1997.
- Supplementary materials
- Principles of Real Analysis (3 rd ed.),
by Walter Rudin, McGraw-Hill, 1976.
- Lectures
Grading:
Course Content
The course will cover the topics contained in the first six chapters
of the text. Several additional topics will also be covered and the presentation
will not necessarily follow the text. Attendence is required and the exams
will be over the lectures and homework. The topics will include:
- Countable and uncountable sets, principle of induction, the real numbers,
order, least upper bounds, the Archimedian property and completeness.
- Sequences of real numbers, monotone sequences, 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, intermediate and extreme
value theorems, uniform continuity, monotone functions and inverses.
- Differentiation, the chain rule, Rolle's theorem and the Mean Value
Theorem, L'Hospital's rule.
- The Riemann integral, its properties, and the Fundamental Theorem of
Calculus.