Math-104 Introduction to Analysis, Spring 2019 Section 1

Lectures: Mon.-Wed.-Fri. 1:00PM-2:00PM (Berkeley Time) at Hearst Mining 310

Professor: Semeon Artamonov

Textbook: K. A. Ross "Elementary Analysis" ISBN 978-1-4614-6271-2 (You can download it for free on campus through UC Library)

Office Hours: Monday 4-5PM, Wednesday 3-4 PM, Friday 3-4PM (or by Appointment) at 1055 Evans Hall

Syllabus

GSI: Theodore Zhu (Information on the GSI office hours is provided by the link)

Homework Assignments

Reading Assignments

Wed, Jan. 23Axioms of Natural Numbers, Principle of Mathematical Induction§1
Fri, Jan. 25Rational and Algebraic Numbers§2
Mon, Jan. 28The set of Real Numbers§3,6
Wed, Jan. 30The Completeness Axiom§4
Fri, Feb. 1Archimedean Property and The Symbols ±∞§4-5
Mon, Feb. 4Limits of Sequences§7
Wed, Feb. 6Proofs in Mathematics§8
Fri, Feb. 8Limit Theorems for Sequences§9
Mon, Feb. 11Monotone Sequences§10
Wed, Feb. 13Cauchy Sequences and Subsequences§10-11
Fri, Feb. 15Bolzano-Weierstrass Theorem§11
Mon, Feb. 18No Class, Holiday
Wed, Feb. 20lim sup and lim inf§12
Fri, Feb. 22Midterm I
Mon, Feb. 25Infinite Series§14
Wed, Feb. 27Infinite Series (continued) and convergence tests§14-15
Fri, Mar. 1Definition of Continuous Functions§17
Mon, Mar. 4Properties of Continuous Functions§17-18
Wed, Mar. 6Intermediate Value Theorem and Uniform Continuity§18-19
Fri, Mar. 8Uniform Continuity (continued)§19
Mon, Mar. 11Limits of Functions§20
Wed, Mar. 13Power Series§23
Fri, Mar. 15Uniform Convergence§24
Mon, Mar. 18Weierstrass M-test§25
Wed, Mar. 20Differentiation and Integration of Power Series§26
Fri, Mar. 22Midterm II
Mon, Mar. 25No Class, Spring Break
Wed, Mar. 27No Class, Spring Break
Fri, Mar. 29No Class, Spring Break
Mon, Apr. 01Derivatives and Basic Properties§28
Wed, Apr. 03The Mean Value Theorem§29
Fri, Apr. 05L'Hopital's Rule§30
Mon, Apr. 08Taylor's Theorem§31
Wed, Apr. 10Applications of Taylor's Theorem§31
Fri, Apr. 12Definition of The Riemann Integral§32
Mon, Apr. 15Basic Properties of The Riemann Integral§32-33
Wed, Apr. 17Intermediate Value Theorem for Integrals§33
Fri, Apr. 19Fundamental Theorem of Calculus§34
Mon, Apr. 22Improper Integrals§35
Wed, Apr. 24Metric Spaces and Metric Topology§13
Fri, Apr. 26Metric Topology (continued)§13
Mon, Apr. 29Continuous Maps of Metric Spaces§21
Wed, May 1Connected Spaces§22
Fri, May 3Exponents and Logarithms§37