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.
The textbook is available in an electronic format through MSU Libraries.
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: piazza.com/msu/spring2017/mth320002/home
| L | Date | Chapter and Topic | HW | Reading Assignment |
| 1 | 1/9 | Sect. 1 - The Set of Natural Numbers | Due 1/181.2, 1.4, 1.6, 1.8b | Read the syllabus, Section 1 and Confronting Analysis |
| 2 | 1/11 | Sect. 2 - The Set of Rational Numbers | Due 1/182.2 (only for cube root of 2), 2.4, 2.7b, 2.8 | Before Wednesday's class, read Sections 1 and 2. |
| 3 | 1/13 | Sect. 2 - continued; | Quiz 1 - Mathematical Induction | |
| 1/16 | Martin Luther King Day - no class | |||
| 4 | 1/18 | Countable and Uncountable Sets | Due 1/25HW on Cardinality of Sets | Before Wednesday's class, read Section 3. |
| 5 | 1/20 | Sect. 3 - The Set of Real Numbers | Due 1/25Turn in: 3.4, 3.6, 3.7a, 3.8Be able to do, but do not turn in 3.1, 3.3, 3.5 | Quiz 2 - proving a number is rational/irrational; Rational Zeros Theorem |
| 6 | 1/23 | Sect. 4 - The Completeness Axiom | Due 2/14.6, 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 Monday's class, read Section 4. |
| 7 | 1/25 | Properties of Sup/Inf - continued | ||
| 8 | 1/27 | Sect. 7 - Limits of Sequences Sect. 8 - A Discussion about Proofs | Due 2/17.4, 8.2a,c,e, 8.6, 8.8a, 8.10,Prove that the sequence (cos(n pi/4)) diverges. | Before Friday's class, read Sections 7 and 8. Quiz 3 - using axioms to prove simple properties of real numbers; properties of sup and inf. |
| 9 | 1/30 | Sect. 8 - continued | ||
| 10 | 2/1 | Sect. 9 - Limit Theorems for Sequences | Due 2/89.4, 9.6 | Before Wednesday's class, read Sect. 9 and focus on Theorems 9.4, 9.5, 9.7, and Definition 9.8. |
| 11 | 2/3 | Sect. 9 - continued | Due 2/89.10, 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 4 - Proofs involving Sup/Inf and Limits of sequences |
| 2/3 | Last day to drop with refund (8:00pm) | |||
| 12 | 2/6 | Sect. 10 - Monotone Sequences and Cauchy Sequences | Due 2/1510.2, 10.5, 10.10 | Read Sect. 10 before Monday's class. |
| 13 | 2/8 | Sect. 10 - continued | Due 2/1510.6, 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 | 2/10 | Quiz 5 - working with sequences going to +infinity and -infinity; applying Th. 10.2 to prove convergence. | ||
| 15 | 2/13 | Review | ||
| 16 | 2/15 | Exam 1 Review | Bring quiz, HW, review questions. | |
| M | 2/17 | Midterm Exam I | ||
| 17 | 2/20 | Sect. 11 - Subsequences | Due 3/111.4, Prove Th. 11.2(iii), 11.7, 11.10, 11.11 | |
| 18 | 2/22 | Sect. 14 - Series Rearrangements of Infinite Series | Due 3/114.2a,d,e, 14.3d,e, 14.4a,c, 14.6, 14.8, 14.13c,d (14.12-bonus). | Before Wednesday's class read Sect. 14 through Th. 14.6. Focus on the definition of Partial Sum and Convergence of a Series. Think about how you'd approach problem 14.5. |
| 19 | 2/24 | Sect. 14 - continued | Quiz - subsequences, basic properties of infinite series, convergence Conditional Convergence and Infinite Series Rearrangments |
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| 20 | 2/27 | Sect. 15 - Alternating Series and Integral Tests | Due 3/1515.2a, 15.4a,b,d, 15.6a,c, 16.4c, 16.9 | |
| 21 | 3/1 | Sect. 15 - continued | ||
| 3/1 | Last day to withdraw with no grade reported | |||
| 22 | 3/3 | Bonus Quiz - converhence/divergence of series, tests for convergence | ||
| Spring Break 3/6 - 3/10 | ||||
| 23 | 3/13 | Sect. 17 - Continuous Function | Due 3/2217.3c,f, 17.4, 17.8, 17.9b,d, 17.10, 17.12, 17.13 | Read Sect. 17 before Wednesday's class. |
| 24 | 3/15 | Sect. 18 - Properties of Continuous Functions | Due 3/2218.2, 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 | 3/17 | Sect. 18 - continued | Quiz - series, continuity of functions | |
| 26 | 3/20 | Sect. 19 - Uniform Continuity | Due 3/2919.2b,c, 19.4 | Before Wednesday's class carefully read Sect. 19. |
| 27 | 3/22 | Sect. 19 - continued | Due 3/2919.5d,f, 19.7 (see hint on back), 19.8 (assume (a)-no need to prove it, and prove (b)), (19.9-bonus) | Be able to do but do not turn in: 19.1, 19.5, 19.7, 19.9, |
| 28 | 3/24 | Discussion on uniform continuity | | Quiz - continuity, uniform continuity |
| 29 | 3/27 | Sect. 20 - Limits of Functions | Read Sect. 20 carefully and be prepared to discuss proofs in class. | |
| 30 | 3/29 | Sect. 20 - continued | Due 4/520.2, 20.4, 20.6, 20.8, 20.11b (provide a rigorous proof), 20.12, 20.16, 20.18, 20.20 | Be able to do, but do not turn in 20.5, 20.13, 20.14, 20.17, 20.19 Quiz - uniform continuity (Sect. 19) |
| 31 | 3/31 | |||
| 32 | 4/3 | Sect. 23 - Power Series | Read Sect. 23 before Monday's class | |
| 33 | 4/5 | Exam 2 Review | Bring quiz, HW, review questions | |
| M | 4/7 | Midterm Exam II | Due 4/1423.1b,d,f,h, 23.2d (see Example 6 in Sect. 23), 23.4, 23.6 | |
| 34 | 4/10 | Sect. 24 - Uniform Convergence | Due 4/1923. 9, 24.2, 24.3, 24.6, 24.8, 24.10, 24.11 |
Read Sect. 24 |
| 35 | 4/12 | Sect. 25 - More on Uniform Convergence | Due 4/1925.2, 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 | 4/14 | Sect. 28 - Basic Properties of the Derivative | Due 4/1928.2d, 28.3a, 28.7 |
Read Sect. 28 carefully before Friday's class. |
| 37 | 4/17 | 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 | 4/19 | Sect. 29 - The Mean Value Theorem | Read Sect. 29 carefully before Wednesday's class. | |
| 39 | 4/21 | 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 | 4/24 | Sect. 30 - L'Hospital's Rule | Do, but do not turn in: 30.1, 30.2, 30.3, 30.5, 30.6 | |
| 41 | 4/26 | Final Exam Review | We will focus on sections 1-20. | |
| 42 | 4/28 | Final Exam Review | Finals week office hours: May 2nd, 1-2pm | We will focus on sections 23-30 |
| E | 5/4 | Final Exam 10:00 am - noon | Thursday | A220 Wells Hall |