21-355 Principles of Real Analysis I

Units: 9.0 Department: Mathematical Sciences Prerequisites: 21-122 and 21-127 Related URLs: http://www.math.cmu.edu 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   Students also scheduled 73-100 Principles of Economics 21-201 Undergrad Colloquium 15-213 Introduction to Computer Systems 21-300 Basic Logic 15-451 Algorithm Design and Analysis 21-320 Symbolic Programming Methods 15-212 Principles of Programming 15-411 Compiler Design 82-334 Structure of Chinese 21-373 Algebraic Structures

Spring 2005 times

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