# Lecture Schedule / Homework Assignments

**Tues 12/15: Final exam 1-3pm in 411 Ell Hall.**You may bring a single sided, 8.5x11 sheet of notes with theorems, definitions, etc. (but not fully worked problems)

**Wed 12/9: Review and evaluations.****Homework 6 due in class.****Mon 12/7: No class or office hours.**Extra office hours will be held on Tuesday from 10-12.

**Wed 12/2:**Section 26. Differentiation and integration of power series.**Homework 6: Due Wed 12/9 in class**Exercises 26.2, 26.6, 28.4, 28.8, 29.14, 32.8, 33.4.**Mon 11/30:**Section 32 (through Thm 32.5), 33, 34. Integration and properties thereof.**Mon 11/23:**Section 29. Mean Value Theorem.**Homework 5 due in class, or tomorrow by email.****Wed 11/18:**Section 25, 28. More uniform convergence (esp. for series), Differentiation.**Homework 5: Due Mon 11/23 in class, or Tue 11/24 by email:**Exercises 23.2, 23.6, 24.2, 24.6, 25.6.**Mon 11/16:**Sections 23, 24. Power series, uniform convergence.**Homework 4 due in class.****Wed 11/11: Veteran's Day. No classes.****Mon 11/9:**Section 19/21 continued, 20: Uniform continuity. Limits of functions on R.**Wed 11/4:**Section 19, 21: Uniform continuity in R and in abstract metric spaces.**Homework 4: Due Mon 11/16:**Exercises 17.9, 17.14, 18.10, 19.6, 19.9, 21.6, 22.2.**Mon 11/2:**Section 18, 22: Properties of continuous functions (extreme and intermediate value theorems); connectedness in metric spaces.**Wed 10/28: Midterm exam, in class.****Mon 10/26: No class or office hours.**You may attend Prof. Suciu's section in Snell 119 at the usual time.Here are some (optional) practice problems from the book, which may help you prepare for the exam (they are all odd-numbered problems, with the answers in the back of the book): 4.3, 4.7, 8.3, 8.7, 10.9, 11.3, 13.9, 13.13, 14.11, 14.5, 15.7.

Homework 3 solutions have been updated with solutions to 14.4, 15.6.

**Wed 10/21:**Section 17: Continuous functions.**Homework 3 addendum:**14.4, 15.6, due Monday 10/26 by email to c.kottke@neu.edu or turned in to Prof. Suciu's section.**Mon 10/19:**Section 14, 15: Series continued: ratio test, examples. Alternating test.**Wed 10/14:**Section 13 continued: more on limsup/liminf, Section 14: Series.**Homework 3 due in class.**The midterm has been moved from Wed 10/21 to Wed 10/28.

Solutions to Homework 3. Mean score 21.6/30

**Mon 10/12: Columbus Day, no classes or office hours.**Extra office hours on Tuesday 10/13 from 10:30-12.

**Wed 10/7:**Section 13, Section 12. Compactness in metric spaces, more on limsup/liminf.**Homework 3: Due Wed 10/14:**Exercises 12.4, 12.8, 13.3, 13.6, and 13.12.Solutions to Homework 1. Mean score 27.7/36.

Solutions to Homework 2. Mean score 36.9/42.

**Mon 10/5:**Section 13 continued, Metric space topology.**Homework 2 due in class.****Wed 9/30:**Section 11 continued, Section 13 (pp. 83-88): Subsequences, Metric space topology.**Mon 9/28:**Sections 10, 11: Cauchy sequences, subsequences**Homework 2: Due Mon 10/5:**Exercises 8.9, 9.6, 9.12, 10.6, 10.10, and 11.10.**Wed 9/23:**Sections 9, 10: Limit theorems, monotone~~and Cauchy sequences~~**Homework 1 due in class.****Mon 9/21:**Sections 8, 9: More limits, and limit theorems.**Wed 9/16:**Sections 5, 7, 8: Sequences and limits.Here is a proof that nth roots of positive numbers always exist in R. The proof, which uses the completeness axiom for R, is a bit technical, and will not be covered in class.

**Update to Homework 1:**I am adding a limit problem, #8.1 to the homework set, and also extending the deadline to Wednesday.**Mon 9/14:**Sections 2, 4: Completeness of the real numbers.**Homework 1: Due**Exercises 1.2, 3.3, 3.4, 3.8, 4.8, 4.10,~~Mon 9/21~~Wed 9/23:**8.1**. (In the textbook).**Wed 9/9:**Sections 1-3: Natural, rational and real numbers, and the axioms for an ordered field.Here are some notes about proofs by induction and contradiction, including a proof that N is well-ordered.