Math 451 Winter 2021
Class Schedule:
Section 001: Tuesday-Thursday, 8:30-10:00 AM; on Zoom
Section 002: Tuesday-Thursday, 10:00-11:30 AM; on Zoom
Textbook: Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross, 2nd edition (2013), published by Springer.
Email: neeljp@umich.edu
Office Hours:
Tuesday 7:55am-8:25am (Priority Students In Distant Time Zones)
Tuesday 1:00pm-2:00pm (Priority Math 451)
Tuesday 2:00pm-3:00pm (Priority Math 289)
Saturday 3:00pm-4:00pm (Open)
Course Assistant: The grader for this course is to be determined. For any questions about the grading of your homework, please contact at...
Homework Policy: There will be a weekly problem set with possible exceptions for exam weeks/holidays. You may work on these problem sets together, but you must submit your own original solutions. You are expected to write or type up your homework clearly and to show all relevant steps. Points will be docked for sloppy work.
Homework will be uploaded as a file to Canvas. The file should be in a document reader form (such as PDF) and easy to read for the grader.
Exams: There will be one midterm and one final exam. Both will be take-home with several days to complete.
The midterm will be given on Friday March 5 at 3pm and due Wednesday March 10 at midnight. The topics will be real numbers/sequences/series.
The final will be given on April 15 at 5pm and due April 27 at midnight.
Grading Policy: 40% Homework, 25% take-home Midterm, 35% take-home Final. The lowest homework score will be dropped.
Homework 1: Due Thursday 01/28 and Tuesday 02/02
Read Chapter 1 Sections 1-4.
Sign up by posting your name under one of the problem discussions on Canvas. All problems are referring to Chapter 1. If there are already 2 people signed up for that problem, choose a different problem.
By Thursday on 01/28, please post a neatly written and scanned solution of that problem to that Canvas discussion.
By Tuesday 02/02, please comment on and check for correctness a solution posted to a problem that is not yours. If there are already 2 people checking that problem, please check a different problem.
Homework 2: Due Thursday 02/04
Chapter 1: 2.5, 3.5(b), 3.6, 3.7(c), 4.3(j,m,q), 4.4(j,m,q), 4.7, 4.8, 4.14(a)
Chapter 2: 7.1(a,b,c)
Note: No proofs/explanations needed for problems 4.3(j,m,q), 4.4(j,m,q) or 7.1(a,b,c).
Homework 3: Due Thursday 02/11
Chapter 1: 3.8, 4.10
Notes: Prove the "Fact" at the bottom of page 29 of the notes
Read Chapter 1, Section 5 and Chapter 2, Sections 7 and 8
Chapter 2: 7.3(e,j,o), 7.5, 8.2(a,c)
For 8.2(a,c), you may use the convergence definition in class for sequences in Q or the definition from the book Sections 7,8.
Homework 4: Due Thursday 02/18
Chapter 2: 8.6(a), 8.8(c), 8.9(b,c), 8.10, 9.6, 10.10. For 8.9(c), you may assume 8.9(a).
Read and use example 6 of Section 8 to prove Lemma 9.5 in Section 9.
Prove if a_{n} converges to a, then a_{n+k} converges to a.
Homework 5: Due Thursday 02/25
Prove the Fact on page 46 of the notes.
Chapter 2: 9.15, 10.12, 11.4 (no proof needed), 11.11, 12.3 (no proof needed), 14.5
In a problem, when the book says "show..." it means to prove the statement.
Homework 6: Due Thursday 03/04
Do Case 2 or Case 3 of the proof of pages 61-62.
Chapter 2: 14.1(a,b,c), 14.6(a), 14.7, 14.9, 14.12, 14.14
(Optional) Prove the "homework" part of the proof stated on page 65. The proof starts on page 64 and ends on page 65.
Prepare for the take-home midterm that starts on March 5!
Homework 7: Due Monday 03/22
Do the worksheet on limits attached below. Read Section 20 of the book.
Chapter 3: 17.8 (a,c), 17.9(b,d), 17.13(b), 17.14, 18.6, 18.10, 20.16
Homework 8: Due Thursday 04/01
Chapter 5: 28.3(b), 28.4(a,b), 29.3, 29.5, 29.11, 29.13, 31.1
Homework 9: Due Monday 04/19
Chapter 6: 32.2, 32.8, 33.5, 33.7, 33.8(a), 34.2, 34.5
Math 451 Winter 2021 Final Exam.pdfLimits of Functions.pdfLecture Notes Math 451 Winter 2021.pdfMath 451 Winter 2021 Midterm Solutions.pdfMath 451 Winter 2021 Midterm Exam.pdf