MATH 215: ANALYSIS IN A SINGLE VARIABLE  MWF 10-11
Textbook:
Principles of Mathematical Analysis, Walter Rudin

Prof Alice Chang
(chang@math)
Office Hours: Fine Hall 901 - Monday and Friday, 11-12 am; Wednesday 2-3pm
• Midterm: On October 24, 7:00pm--8:30pm, Room Fine 601.
• Final examination on January 17, 1:30pm --3:30 pm, (may be longer) Jadwin A07
• Review sessions on January 13 and 15, 3 --5pm , Fine 110
•  Final exam 40 % Midterm 20 % Homework 40 %

TA: Luca De Sanctis
(lde@math)
Office Hours: Fine Hall 1106, Tuesdays 4-6pm

• Properties of the Riemann integral
•  WEEK DATES MATERIAL COVERED HOMEWORK DUE_______(* optional) 1 Sept. 13, 16, 18, 20 Chapter 1 Sets, Ordered sets Real numbers, sup and inf Completeness, Archimedean property Absolute value, inequalities Sep. 25 Homework will be assigned on Sept. 18 Homework Assignment(dvi file) Solution for HW1, problem 8(dvi file) Solution for HW1, problem 8(pdf file) 2 Sept. 23, 25, 27 Chapters 1 and 2 Neighborhood, open and closed intervals Nested interval property, decimal expansion Open and closed sets, limits Oct. 2 Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 3 Sept. 30 and Oct. 2, 4 Chapters 2 and 3 Properties of open, closed sets Heine-Borel Theorem; Weierstrass Property Covergent sequences Oct. 9 Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) Quiz on Oct. 4 (ps file) Quiz on Oct. 4 (dvi file) Quiz on Oct 4(pdf file) 4 Oct. 7, 9, 11 Chapters 3 Convergent of some special sequences Subsequence, Cauchy sequences Series, geometric series Oct. 16 Solution of HW 3, problem 9(pdf file) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 5 Oct. 14, 16, 18 Chapters 3 and 4 Ratio, Root and integral tests for series Absolute convergence, alternating series, power series limits, limits of functions Oct. 23 Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) Sample midterm(pdf file) 6 Oct. 21, 23, 25 Chapter 4 Continuous functions Property of continuous functions Continuity and connectedness Nov. 6 Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 7 Nov. 4, 6, 8 Chapter 4 and 5 Maximum-Minimum theorem Uniform continuiuty, monotonic functions Derivative of a real function Nov. 13 (Wed) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 8 Nov. 11, 13, 15 Chapter 5 Chain rule, inverse functions Mean value theorem, L'Hospital's rule Taylor's theorem Nov. 20 (Wed) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 9 Nov. 18, 20, 22 Chapter 6 Definition of the Riemann integral Integrability of monotone and continuous functions Nov. 27 (Wed) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 10 Nov. 25, 27 Chapter 6 Fundamental Theorem of Calculus Evaluation of integrals Dec. 4 (Wed) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 11 Dec. 2, 4, 6 Chapter 7 Sequence and series of functions Uniform convergence Uniform convergence and continuity, integration Dec. 11 (Wed) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file) 12 Dec. 9, 11, 13 Chapter 7 and 8 Uniform convergence and differentiation Power series logarithm and exponential functions * January 10, 2003 (Optional) Homework Assignment(ps file) Homework Assignment(dvi file) Homework Assignment(pdf file)