Math 450 - An Introduction to Real Analysis

Credits: 3

Course Description: A rigorous treatment of the calculus of functions of one real variable. Emphasis is on proofs. Includes discussion of topology of real line, limits, continuity, differentiation, integration and series.

Pre-Requisites: [MATH 310 or MATH 354] AND [(effective Spring 2011) MATH 280]

Frequency: Course offered in the spring only.

Current Textbook: Analysis with an Introduction to Proof, 4th Edition, by Steven Lay, published by Prentice Hall, 2004. ISBN: 0-13-148101-0. Check with your instructor to make sure this is the textbook used for your section.

Section 10: Natural Numbers and Induction.

Section 11: Ordered Fields.

Section 12: The Completeness Axiom.

Section 13: Topology of the Reals.

Section 14: Compact Sets.

Section 16: Convergence.

Section 17: Limit Theorems.

Section 18: Monotone Sequences and Cauchy Sequences.

Section 19: Subsequences.

Section 20: Limits of Functions.

Section 21: Continuous Functions.

Section 22: Properties of Continuous Functions.

Section 23: Uniform Continuity.

Section 25: The Derivative.

Section 26: The Mean Value Theorem.

Section 27: L'Hopital's Rule.

Section 28: Taylor's Theorem.

Section 29: The Riemann Integral.

Section 30: Properties of the Riemann Integral.

Section 31: The Fundamental Theorem of Calculus.

Section 32: Convergence of Infinite Series.

Section 33: Convergence Tests.

Section 34: Power Series.

Section 35: Pointwise and Uniform Convergence.

Section 36: Applications of Uniform Convergence.

Section 37: Uniform Convergence of Power Series.