Real Analysis I
Revised: September, 2014
Course Description
Sequences of real numbers, continuous functions, and differentiation. Prerequisite:
MATH 250 and MATH 255. Three Semester Hours.
Prerequisites
Math250 and Math255.
Student Learning Objectives
By the end of the course students will be able to:
- Use the definitions of convergence as they apply to sequences, series, and functions;
- Determine the continuity, differentiability, and integrability of functions defined
on subsets of the real line;
- Produce rigorous proofs of results that arise in the context of real analysis; and
- Write proofs of theorems that meet rigorous standards based on content, precision,
and style.
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)鈥�Completeness; countable and uncountable sets; real valued functions
-
Chapter 2: Sequences (10 days)鈥–onvergent monotone and Cauchy sequences; subsequences; Bolzano-Weierstrass
-
Chapter 3: Limits and Continuity (14 days)鈥↙imit theorems; one-sided and infinite limits; continuous functions; intermediate
and extreme values; uniform continuity; monotone functions
-
Chapter 4: Differentiation (10 days)鈥═he definition and rules of differentiation; mean value and L'Hopital
-
Chapter 5: Integration (5 days, if time allows)鈥≧iemann Integral; conditions for Riemann integrability
Times above include review and testing.