Mathematics and Computer Science at Western Carolina University

Revised: November 2006 (Julia Barnes)

Sequences of real numbers, continuous functions, and differentiation. Prerequisite: Math 250 and 255. Three semester hours.

To build an understanding of the basic principles of real analysis through the use of mathematical proof.

Gordon. Real Analysis, A First Course, Second Edition. Addison-Wesley, 2002.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Chapter 1: Real Numbers (6 days)
Completeness; countable and uncountable sets; real valued functions
Chapter 2: Sequences (10 days)
Convergent monotone and Cauchy sequences; subsequences; Bolzano-Weierstrass
Chapter 3: Limits and Continuity (14 days)
Limit theorems; one-sided and infinite limits; continuous functions; intermediate and extreme values; uniform continuity; monotone functions
Chapter 4: Differentiation (10 days)
The definition and rules of differentiation; mean value and L'Hopital
Chapter 5: Integration (5 days, if time allows)
Riemann Integral; conditions for Riemann integrability
Times include review and testing.