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21-355 Principles of Real Analysis I

Department:Mathematical Sciences
Prerequisites:21-122 and 21-127
Related URLs:

The Real Number System: Field and order axioms, sups and infs, completeness, integers and rational numbers. Real Sequences: Limits, cluster points, limsup and liminf, subsequences, monotonic sequences, Cauchy's criterion, Bolzano-Weierstrass Theorem. Topology of the Real Line: Open sets, closed sets, density, compactness, Heine-Borel Theorem. Continuity: attainment of extrema, Intermediate Value Theorem, uniform continuity. Differentiation: Chain Rule, local extrema, Mean-Value Theorems, L'Hospital's Rule, Taylor's Theorem. Riemann Integration: Partitions, upper and lower integrals, sufficient conditions for integrability, Fundamental Theorem of Calculus. Sequences of Functions: Pointwise convergence, uniform convergence, interchanging the order of limits. 3 hours lecture.

  Popularity index
Rank for this semester:#169
Rank in this department:#21

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  Spring 2005 times

Sec Time Day Instructor Location  
A 11:30 am - 12:20 pm M Leoni DH A310 Add course to my schedule
W Leoni DH A310
F Leoni DH A310

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