Advanced Calculus I

Revised: November 2006 (Julia Barnes)

Course Description

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

Objectives

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

Text

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

Grading Procedure

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

Attendance Policy

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

Course Outline

• 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.