Department of Mathematics
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MATH 450 : 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 [MATH 280]

Comments: Course offered in the spring only.

Topics:
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.
Fall 2017 Schedule:

Section Meetings Instructor Comments
001
TuTh 02:00pm - 03:15pm
Wortman, Dennis


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