Analysis II, MTH 421
Tentative Schedule and Homework Assignments
Chapter numbers refer to:
Introduction to Analysis (4th Edition), William Wade, Prentice Hall, ISBN: 9780132296380.
Sections 5.1 and 5.2 of the textbook are available 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: piazza.com/msu/spring2015/mth421/home
| L | Date | Chapter and Topic | HW | Reading Assignment |
| 1 | 1/12 | 5.1 - The Riemann Integral | Due 1/14HW1 | Read the syllabus, Section 5.1 and Confronting Analysis |
| 2 | 1/14 | 5.1 - continued | Start working on problems 5.1.8, 5.1.9 | Concentrate on the proofs of theorems 5.10 and 5.15 and be prepared with questions |
| 3 | 1/16 | 5.1 - continued | Due 1/215.1.2b, 5.1.3, 5.1.4-bonus, 5.1.5, 5.1.8, 5.1.9 | Read the definition of Riemann sum and Th. 5.18. Is every Upper Riemann sum a Riemann sum? |
| 1/19 | Martin Luther King Day - no class | There will be office hours on Tue, 1/20, 11:30 am - 12:30 pm. | ||
| 4 | 1/21 | 5.2 - Riemann Sums | Be prepared to discuss the 2nd part of the proof of Th. 5.18. Y.J. - presents proof of (6); S.G. - presents proof of (7). You should be able to prove 5.21 on your own. | |
| 5 | 1/23 | 5.2 - continued Quiz 2 solution | Due 1/285.2.2, 5.2.6, 5.2.7, 5.2.11 | Hints: 5.2.2 - use the 1st MVT 5.2.6 - use Comparison Th. + Squeeze Th. 5.2.7 - use Th. 5.20 5.2.11 - What does it mean for the function to be unbounded? |
| 6 | 1/26 | 5.2 - continued | ||
| 7 | 1/28 | 5.3 - The Fundamental Theorem of Calculus | Due 2/45.3.0a, 5.3.1b, 5.3.5, 5.3.6, 5.3.7a-d. | Read the proof of Teorem 5.34 (Change of Variables) |
| 8 | 1/30 | 5.3 - continued Quiz 3 | ||
| 9 | 2/2 | MSU has suspended all classes scheduled before noon (including ours). | Office hours today are 2:00-3:00 pm, as usual. | Read the first 4 pages of Section 8.1 (267-270). |
| 10 | 2/4 | 8.1 - Algebraic Structure of R^n | You can start working on the following problems. There will be a few more problems assigned on Friday. | Please read pages 271 through 277, while focusing on Remark 8.7. |
| 11 | 2/6 | 8.1 - continued | Due 2/11These non-textbook problems, as well as 8.1.2(a,b), 8.1.3, 8.1.4. | |
| 2/6 | Last day to drop with refund (8:00pm) | |||
| 12 | 2/9 | 8.2 - Planes and Linear Transformations | Due 2/188.2.2, 8.2.4, 8.2.5a,b, 8.2.10a, 8.2.11-bonusSolution key | Read Section 8.2 |
| 13 | 2/11 | 8.2 - continued | ||
| 14 | 2/13 | 8.3 - Topology of R^n | ||
| 15 | 2/16 | 8.3 - continued | ||
| 16 | 2/18 | Review | Bring questions you have. Here are some problems for review. | Office hours today have been canceled. Office hours tomorrow (2/19) are from 10:30 am to 1:00 pm. |
| M | 2/20 | Midterm Exam I | Covers sections 5.1, 5.2, 5.3, 8.1, 8.2. | |
| 17 | 2/23 | 8.4 - Interior, Closure, Boundary | Due 2/278.3.2, 8.3.3b, 8.3.4, 8.3.7a,c,d, 8.3.8a, 8.3.9Solution key | Focus on the proof of Theorem 8.30 in 8.3; Read Section 8.4 for a "big picture" understanding. Notes on HW 8.3.2 - provide a rigorous proof 8.3.4 - You do not need to prove that E1 is closed and E2 is open. 8.3.7a - provide a rigorous proof 8.3.7d - picture example is sufficient. |
| 18 | 2/25 | 8.3 - continued | ||
| 19 | 2/27 | 8.4 - continued | Due 3/68.4.3, 8.4.7, 8.4.8, 8.4.10a,b | |
| 20 | 3/2 | 8.4 - continued | Read Section 9.1 before Wednesday; focus on the proofs of Th. 9.2 and 9.5. | |
| 21 | 3/4 | 9.1 - Limits of Sequences | Quiz 7 on Section 8.4 is scheduled for today. | Today's office hours are moved to Tuesday, 3/3, 11:30-12:30 |
| 3/4 | Last day to withdraw with no grade reported | |||
| 22 | 3/6 | Metric Spaces and Topologies | Due 3/209.1.3a, 9.1.4, 9.1.5, 9.1.6 | Worksheet 9.1.5(c) - only prove the part about limit of a sum and dot product (Th. 9.4(v) - the first and third equations). |
| Spring Break 3/9 - 3/13 | ||||
| 23 | 3/16 | 9.1 - continued | Read the proof of the Borel Covering Lemma and the Heine-Borel Theorem and be prepared to discuss them on Wednesday. | |
| 24 | 3/18 | 9.2 - Heine-Borel Theorem | ||
| 25 | 3/20 | 9.2 - continued | Due 3/279.2.1, 9.2.4, 9.2.6, 9.2.7 | Quiz 8 covers Section 9.1 |
| 26 | 3/23 | 9.3 - Limits of Functions | ||
| 27 | 3/25 | 9.3 - continued | ||
| 28 | 3/27 | 9.3 - completed | Due 4/39.3.1c, 9.3.2a, 9.3.3a,b, 9.3.5, 9.3.8b | Quiz 9 covers Section 9.2 Read Sect. 9.4 and focus on the proofs of Th. 9.25 and Th. 9.26. |
| 29 | 3/30 | 9.4 - Continuous Functions | ||
| 30 | 4/1 | 9.4 - continued | ||
| 31 | 4/3 | Due 4/109.4.1, 9.4.4, 9.4.6, 9.4.9, 9.4.8-bonus | Read Section 11.1 | |
| 32 | 4/6 | 11.1 - Partial Derivatives and Partial Integrals | ||
| 33 | 4/8 | Review | Bring questions you have. Here is a study guide for Exam 2. | |
| M | 4/10 | Midterm Exam II | Covers sections 8.3, 8.4, 9.1, 9.2, 9.3, 9.4. | Exam 2 Solution Key |
| 34 | 4/13 | 11.1 - continued | Due 4/2011.1.2b, 11.1.3, 11.1.4, 11.1.5 |
Consider 11.1.6, but no need to turn in. Go over the proofs of theorems 11.2, 11.4 and 11.5 once again. for 11.1.3 Th. 4.17 and MVT on p. 385 might be of help. |
| 35 | 4/15 | Today's office hours are moved to tomorrow. Office hours Thursday: 10:30-12:30. | ||
| 36 | 4/17 | 11.2 - The Deffinition of Differentiability | Quiz on Section 11.1. | |
| 37 | 4/20 | 11.2 - completed | Due 4/27HW 14 |
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| 38 | 4/22 | 11.3 - Derivatives and Tangent Planes | ||
| 39 | 4/24 | Directional Derivatives and the Gradient | ||
| 40 | 4/27 | Chain Rule. Convexity. Review 1 | Bring Quizzes 1-5, Review for Exam 1, Exam 1. | Bring any questions you have on the material covered by Exam 1. |
| 41 | 4/29 | Presentations Review of Chapter 11. | These problems will be presented by student volunteers (already assigned). Even if you are not one of them, you should be able to discuss the problems. | Consider these problems a HW, which is not to be turned in: 11.3.2, 11.3.3, 11.4.6, 11.4.7, 11.4.8, 11.4.9 |
| 42 | 5/1 | Review 2 | Bring Quizzes 6-12, Review for Exam 2, Exam 2. Here is a study guide for Chapter 11. |
Bring any questions you have on the material covered by Exam 2 and Chapter 11. |
| E | 5/7 | Final Exam 10:00 am - noon | Thursday | A328 Wells Hall |