Analysis I, MTH 320
Tentative Schedule and Homework Assignments
Chapter numbers refer to:
Elementary Analysis, The Theory of Calculus(2nd Edition), Kenneth Ross, Springer, ISBN: 978-1-4614-6270-5.
If you do not have the book yet, you can access the first few sections here.
Piazza Forum:
This is a question-and-answer platform created for our class, where we can discuss solutions to class assignments. You can access it using the following link: https://piazza.com/msu/fall2016/mth320001/home
| L | Date | Chapter and Topic | HW | Reading Assignment |
| 1 | 8/31 | Sect. 1 - The Set of Natural Numbers | Due 9/71.2, 1.4, 1.6, 1.8b | Read the syllabus, Section 1 and Confronting Analysis |
| 2 | 9/2 | Sect. 2 - The Set of Rational Numbers | Due 9/72.2 (only for seventh root of 5), 2.4, 2.7b, 2.8 | Before Friday's class, read Sections 1 and 2. Quiz 1 - Mathematical Induction |
| 9/5 | Labor Day - no class | |||
| 3 | 9/7 | Sect. 2 - continued; Countable and Uncountable Sets | Due 9/14Problems on countable sets (click here) | Supplementary reading on cardinality of sets. |
| 4 | 9/9 | Sect. 3 - The Set of Real Numbers | Due 9/14Turn in: 3.4, 3.6, 3.7a, 3.8Be able to do, but do not turn in 3.1, 3.3, 3.5 | Before Friday's class, read Section 3. |
| 5 | 9/12 | Sect. 3 - continued | Quiz 2 - proving a number is rational/irrational; To prepare, make sure you can prove the Rational Zeros Theorem on your own. | 6 | 9/14 | Sect. 4 - The Completeness Axiom | Due 9/214.6, 4.8, 4.10, 4.14, 4.16Be able to do, but do not turn in: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.11, 4.13 | Before Wednesday's class, read Sect. 4. |
| 7 | 9/16 | Sect. 4 - continued | Quiz 4 - using axioms to prove simple properties of real numbers; cardinallity of sets Before Friday's class read Sect. 5. |
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| 8 | 9/19 | Sect. 7 - Limits of Sequences Sect. 8 - A Discussion about Proofs | Due 9/287.4, 8.2a,c,e, 8.6, 8.8a | Before Wednesday's class, read Section 8 again and Sect. 9 up to p. 48. |
| 9 | 9/21 | Sect. 8 - continued | Due 9/288.10, 9.4, 9.6,Prove that the sequence cos(n pi/4) diverges. | |
| 10 | 9/23 | Sect. 9 - Limit Theorems for Sequences | Due 9/289.10, 9.12Be able to do, but do not turn in: 9.8, 9.9, 9.11 | Quiz 5 - infimum and supremum of a set. |
| 9/26 | Last day to drop with refund (8:00pm) | |||
| 11 | 9/26 | Sect. 9 - continued | Before Wednesday's class carefully go through the proof of Th. 9.7 and bring concrete questions regarding it. | |
| 12 | 9/28 | Sect. 10 - Monotone Sequences and Cauchy Sequences | ||
| 13 | 9/30 | Sect. 10 - continued | Due 10/59.9, 10.2, 10.5, 10.7, 10.10, 10.12. | Quiz 6 - convergence of sequences, proving properties of limits |
| 14 | 10/3 | Limsup, liminf, Cauchy sequences | Read Sect. 10 before Monday's class. Focus on the definitions of limsup and liminf, and the proofs of 10.5, 10.7, and 10.11 | |
| 15 | 10/5 | Exam 1 Review | Bring quiz, HW, review questions. Exam 1 covers through Sect. 10 (up to and including Cor. 10.5). | |
| M | 10/7 | Midterm Exam I | ||
| 16 | 10/10 | Sect. 10 - continued | Due 10/1410.6, 12.3, 12.4, | Before Wednesday's class read Sect. 11 and focus on Th. 11.4 and 11.5. |
| 17 | 10/12 | Sect. 11 - Subsequences | Due 10/1911.4, 11.8, 11.10, 11.11, Prove Th. 11.2(iii) | Read Sect. 14 before Friday's class. In addition, we will discuss rearrangements of series using the following: Conditional Convergence and Infinite Series Rearrangments |
| 18 | 10/14 | Sect. 14 - Series Rearrangements of Infinite Series | Quiz 7 - Cauchy sequences, limsup, liminf | |
| 19 | 10/17 | Sect. 14 - continued | Due 10/1914.2a,b,c, 14.4a,c, 14.5, 14.6 | |
| 20 | 10/19 | Sect. 15 - Alternating Series and Integral Tests | ||
| 10/19 | Last day to withdraw with no grade reported | |||
| 21 | 10/21 | Sect. 15 - continued | Due 10/2614.3d, e, 14.4b, 14.13a,b, 15.2a, 15.4a,b,d, 15.6a,c | Quiz 8 - converhence/divergence of series, tests for convergence Read Sect. 17 before Monday's class. |
| 22 | 10/24 | Sect. 17 - Continuous Function | Due 10/2617.12, 17.13. | |
| 23 | 10/26 | Sect. 17 - continued | Due 11/217.3d,g, 17.5, 17.9b,d, 17.10a,b, (17.14-bonus). | Before Friday's class read Sect. 18 carefully and focus on the proof of the Intermediate Value Th. |
| 24 | 10/28 | Sect. 18 - Properties of Continuous Functions | Due 11/218.2, 18.4, 18.6, 18.8, 18.10. | Quiz 9 - convergence of infitite series and continuity of functions |
| 25 | 10/31 | Sect. 19 - Uniform Continuity | ||
| 26 | 11/2 | Sect. 19 - continued | Due 11/919.2b,c, 19.4, 19.5d,f, 19.8 (assume (a)-no need to prove it, and prove (b)), 19.10 | Be able to do, but do not turn in: 19.1, 19.3, 19.5, 19.7, 19.9 Worksheet on Uniform Coninuity |
| 27 | 11/4 | Sect. 19 - continued | | Quiz 10 - continutiy of functions |
| 28 | 11/7 | Sect. 19 - continued | Read Sect. 20 carefully and be prepared to discuss proofs in class. | |
| 29 | 11/9 | Sect. 20 - Limits of Functions | Due 11/1620.2, 20.4, 20.6, 20.8, 20.11b (provide a rigorous proof), 20.12, 20.16, 20.18, 20.20 | Be able to do 20.5, 20.13, 20.14, 20.17, 20.19 |
| 30 | 11/11 | |||
| 31 | 11/14 | |||
| 32 | 11/16 | Exam 2 Review | Bring quiz, HW, review questions | |
| M | 11/18 | Midterm Exam II | ||
| 33 | 11/21 | Sect. 23 - Power Series | Due 11/3023.1b,d,f,h, 23.2d, 23.4, 23.6 |
For 23.2d, Be careful! See Example 6 in sect. 23. Read Sect. 24 before Wednesday's class |
| 34 | 11/23 | Sect. 24 - Uniform Convergence | Due 11/3023. 9, 24.2, 24.3, 24.6, 24.8, 24.10, 24.11 |
Read Sect. 25, focusing on theorems 25.4, 25.5, 25.6, 25.7 |
| 11/25 | Thanksgiving Holiday - no class | |||
| 35 | 11/28 | Sect. 25 - More on Uniform Convergence | Due 11/3025.2, 25.6, 25.8, |
Be able to do, but do not turn in 25.3a, 25.7, 25.9, |
| 36 | 11/30 | Sect. 28 - Basic Properties of the Derivative | Do, but do not turn in: 28.2, 28.3, 28.4, 28.5, 28.6, 28.7 28.8, 28.14 |
Make sure you are able to do all these problems - be sure to ask questions if you are stuck. |
| 37 | 12/2 | Sect. 29 - The Mean Value Theorem | Read Sect. 29 carefully before Friday's class. | |
| 38 | 12/5 | Sect. 29 - continued | Do, but do not turn in: 29.1, 29.2, 29.4, 29.5, 29.7, 29.9, 29.11, |
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| 39 | 12/7 | Sect. 30 - L'Hospital's Rule | Do, but do not turn in: 30.1, 30.2, 30.3, 30.5, 30.6 | |
| 40 | 12/9 | Final Exam Review | ||
| E | 12/14 | Final Exam | Wednesday, 12:45 pm - 2:45 pm | A126 Wells Hall |