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.
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/spring2016/mth320001
| L | Date | Chapter and Topic | HW | Reading Assignment | |
| 1 | 1/11 | Sect. 1 - The Set of Natural Numbers | Due 1/201.2, 1.4, 1.6, 1.8b | Read the syllabus, Section 1 and Confronting Analysis | |
| 2 | 1/13 | Sect. 2 - The Set of Rational Numbers | Due 1/202.2 (only for cube root of 2), 2.4, 2.7b, 2.8 | Before Wednesday's class, read Sections 1 and 2. | |
| 3 | 1/15 | Sect. 2 - continued; Countable and Uncountable Sets | Quiz 1 - Mathematical Induction | ||
| 1/18 | Martin Luther King Day - no class | ||||
| 4 | 1/20 | Sect. 3 - The Set of Real Numbers | Due 1/27Turn in: 3.4, 3.6, 3.7a, 3.8Be able to do, but do not turn in 3.1, 3.3, 3.5, | Before Wednesday's class, read Section 3. | |
| 5 | 1/22 | Quiz 2 - proving a number is rational/irrational; Rational Zeros Theorem | |||
| 6 | 1/25 | Sect. 4 - The Completeness Axiom | Due 1/274.6, 4.8Due 2/34.10, 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 Monday's class, read Section 4. | |
| 7 | 1/27 | Sect. 7 - Limits of Sequences Sect. 8 - A Discussion about Proofs | Due 2/37.4, 8.2a,c,e, 8.6, 8.8a | Before Wednesday's class, read Sections 5 and 7. | |
| 8 | 1/29 | Sect. 8 - continued | Due 2/38.10, Prove that the sequence cos(n pi/4) diverges. | Before Friday's class, read Section 8. Quiz 4 - using axioms to prove simple properties of real numbers; properties of sup and inf. |
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| 9 | 2/1 | Sect. 9 - Limit Theorems for Sequences | |||
| 10 | 2/3 | Sect. 9 - continued | Due 2/109.4, 9.6, | Before Wednesday's class, read Sect. 9 and focus on Theorems 9.4, 9.5, 9.7, and Definition 9.8. | |
| 11 | 2/5 | Sect. 9 - continued | Due 2/109.10, 9.12, 9.14Be able to do 9.8, 9.9, 9.11 | Before Friday's class carefully go through the proof of Th. 9.7 and bring concrete questions regarding it. Quiz 5 - Limits of sequences |
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| 2/5 | Last day to drop with refund (8:00pm) | ||||
| 12 | 2/8 | Sect. 10 - Monotone Sequences and Cauchy Sequences | Due 2/1010.2, 10.5, 10.10 | Read Sect. 10 before Monday's class. | |
| 13 | 2/10 | Sect. 10 - continued | Due 2/1710.6, 10.7, 10.12, 12.3, 12.4 | Focus on the definitions of limsup and liminf, and the proofs of 10.5, 10.7, and 10.11 | |
| 14 | 2/12 | Quiz 7 - working with sequences going to +infinity and -infinity; applying Th. 10.2 to prove convergence. | |||
| 15 | 2/15 | Sect. 11 - Subsequences | Due 2/2411.4, Prove Th. 11.2(iii) | ||
| 16 | 2/17 | Exam 1 Review | Bring quiz, HW, review questions. | ||
| M | 2/19 | Midterm Exam I | |||
| 17 | 2/22 | Sect. 11 - continued Sect. 14 - Series | Due 2/2411.10,11.11, 14.5, 14.12 | Before Monday's class read Sect. 11 and focus on Th. 11.4 and 11.5. Read Sect. 14. | |
| 18 | 2/24 | Sect. 14 - continued Rearrangements of Infinite Series | Due 3/214.2a,d,e, 14.3d,e, 14.4a,c, 14.6, 14.8, 14.13c,d. | Conditional Convergence and Infinite Series Reaeeangments | |
| 19 | 2/26 | Sect. 14 - continued | Quiz 8 - subsequences, basic properties of infinite series, convergence | ||
| 20 | 2/29 | Sect. 15 - Alternating Series and Integral Tests | Due 3/215.2a, 15.4a,b,d, 15.6a,c, | Read the proof of Th 14.8 carefully, then close the book and be sure you can prove it on your own. Read Sect. 15 before Monday's class. | |
| 21 | 3/2 | Sect. 17 - Continuous Function | Due 3/1617.9b,d, 17.10, 17.12, 17.13 | Read Sect. 17 before Wednesday's class. | |
| 3/2 | Last day to withdraw with no grade reported | ||||
| 22 | 3/4 | Quiz 10 - converhence/divergence of series, tests for convergence | |||
| Spring Break 3/7 - 3/11 | |||||
| 23 | 3/14 | Sect. 17 - continued Sect. 18 - Properties of Continuous Functions | Due 3/2317.3c,f, 17.4, 17.8, | ||
| 24 | 3/16 | Sect. 18 - continued | Due 3/2318.2, 18.4, 18.6, 18.8, 18.10, | Before Wednesday's class read Sect. 18 carefully and focus on the proof of the Intermediate Value Th. | |
| 25 | 3/18 | Sect. 19 - Uniform Continuity | Quiz 11 - continuity of functions | ||
| 26 | 3/21 | Sect. 19 - continued | Due 3/2319.2b,c, 19.4 | Before Monday's class carefully read Sect. 19. | |
| 27 | 3/23 | Sect. 19 - continued | Due 3/3019.5d,f, 19.8 (assume (a)-no need to prove it, and prove (b)), 19.10 | Be able to do 19.1, 19.5, 19.7, 19.9 | |
| 28 | 3/25 | Discussion on uniform continuity | | Quiz 12 - univorm continuity | |
| 29 | 3/28 | Sect. 20 - Limits of Functions | Read Sect. 20 carefully and be prepared to discuss proofs in class. | ||
| 30 | 3/30 | Sect. 20 - continued | Due 4/620.2, 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 | |
| 31 | 4/1 | Read Sect. 23 | |||
| 32 | 4/4 | Sect. 23 - Power Series | |||
| 33 | 4/6 | Exam 2 Review | Bring quiz, HW, review questions | ||
| M | 4/8 | Midterm Exam II | Due 4/1323.1b,d,f,h, 23.2d, 23.4, 23.6 | For 23.2d, Be careful! See Example 6 in sect. 23. | |
| 34 | 4/11 | Sect. 24 - Uniform Convergence | Due 4/2223. 9, 24.2, 24.3, 24.6, 24.8, 24.10, 24.11 |
Read Sect. 24 | |
| 35 | 4/13 | Sect. 25 - More on Uniform Convergence | Due 4/2225.2, 25.6, 25.8, |
Read Sect. 25, focusing on theorems 25.4, 25.5, 25.6, 25.7 Be able to do, but do not turn in 25.3a, 25.7, 25.9, | |
| 36 | 4/15 | Sect. 28 - Basic Properties of the Derivative | Due 4/2228.2d, 28.3a, 28.7 |
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| 37 | 4/18 | Sect. 28 - continued | Do, but do not turn in: 28.4, 28.5, 28.6, 28.8, 28.14 |
Make sure you are able to do all these problems - be sure to ask questions if you are stuck. | |
| 38 | 4/20 | Sect. 29 - The Mean Value Theorem | Read Sect. 29 carefully before Wednesday's class. | ||
| 39 | 4/22 | 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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| 40 | 4/25 | Sect. 30 - L'Hospital's Rule | Do, but do not turn in: 30.1, 30.2, 30.3, 30.5, 30.6 | ||
| 41 | 4/27 | Final Exam Review | We will focus on sections 1-20. | ||
| 42 | 4/29 | Final Exam Review | Finals week office hours: May 3rd, 3-4pm | We will focus on sections 23-30 | |
| E | 5/4 | Final Exam 10:00 am - noon | Wednesday | A218 Wells Hall |