index - Math 104 Introduction to Analysis Lectures MWF...

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Math 104 Introduction to Analysis Lectures MWF 13:10-14:00, 71 Evans Hall Office hours WF 14:00-15:00, 821 Evans Hall Table of Contents Course Info (.pdf version here ) Resources (books, notes, more) Academic honesty Assignments Solutions Exams Demos, mfiles, etc Topics covered 08/29: Basic notation and terminology. Integers and rationals. 08/31: Ordered sets. Upper and lower bounds. Suprema and infima. 09/02: Fields. Ordered fields. 09/07: The real number system. 09/09: The complex field. 09/12: Euclidean spaces. Finite and infinite sets. 09/14: Basic set operations. Countable and uncountable sets. 09/16: Metric spaces. Open and closed sets. 09/19: Limit points. Interior and closure. 09/21: Relatively open and closed sets. Compactness. 09/23: More on compactness. 09/26: The Heine-Borel theorem and consequences. 09/28: Perfect sets. Connected sets. 09/30: Convergent sequences. 10/03: Subsequences. 10/05: Cauchy sequences. 10/07: Upper and lower limits. Series. 10/10: Nonnegative series. The dyadic trick. The number e. 10/12: Root and ratio tests. Power series. 10/14: Summation by parts. Absolute convergence. 10/17: Cauchy product of series. Rearrangements. 10/19: Midterm on Chapters 1-3 of the book. 10/21: Discussion of the midterm. 10/24: Continuous maps of metric spaces. 10/26: Continuity and compactness.
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10/31: Continuity and connectedness. Discontinuities. 11/02: Monotonic functions. Infinite limits and limits at infinity. 11/04: The derivative of a real function. 11/07: Mean value theorems. Continuity of derivatives. 11/09: L'Hospital's rule. Taylor's formula. 11/14: Differentiation of vector-valued functions. 11/16: Riemann-Stieltjes integral. 11/18: Riemann sums, refinements, and the integrability criterion. 11/21: Integrating continuous and monotone functions. 11/23: Properties of the integral. Integrating against step functions. 11/28: The fundamental theorem of Calculus (3 versions). 11/30: Integration of vector-valued functions. Rectifiable curves.
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