Fall 2016
General Information
Syllabus and Homeworks
Exams
Syllabus and Homeworks
Homeworks
Homework sets will be typically assigned weekly on Thursday
and due next Th in class. They will be posted on this web site (NOT on blackboard site!).
Late homework will not be accepted. However, grades for homework assignments
may be dropped in cases of documented medical problems or similar difficulties.
| Week | Dates | Notes | Topics | HW | Due date |
|---|---|---|---|---|---|
| 1 | 8/29 - 9/2 | 1-3: Introduction: what are real numbers? Integer numbers and induction; rational numbers and idea of a field; basic properties of real numbers. | Read carefully section 3 of the textbook and subsections 4.1-4.4 of section 4. In particular, work out proofs of Theorems 3.1, 3.2 and 3.5. Write down solutions for exercises 3.2, 3.4, 3.8, 4.6. |
9/8 | |
| 2 | 9/5 - 9/9 | 9/5, 9/6: No classes - Labor day | 4: The completeness axiom. Archimedean property | HW 2; solutions | 9/15 |
| 3 | 9/12-9/16 | 5: Infinity, boundedness and unboundedness. 7: Sequences; limit of a sequence. | 5.2, 5.6, 7.3 (a- j), 7.4, 8.1 | 9/22 | |
| 4 | 9/19 - 9/23 | 8-9: Limit laws for sequences and formal proofs. | 8.3, 8.7, 9.1, 9.4, 9.12*, 9.15, 9.16. Problem 9.12 is optional (worth extra credit); even if you do not solve it, you are allowed to use results of this problem to solve other problems. | ||
| 5 | 9/26 - 9/30 | Midterm 1 on Th, 9/29 | |||
| 6 | 10/3 - 10/7 | This is the last week MAT 319/320 meet together | 10: Monotone and Cauchy sequences; 11: Subsequences | HW 5 for MAT 319 only | 10/13 |
| 7 | 10/10 - 10/14 | 11. Subsequences continued; 12:lim inf and lim sup. 14: series | HW 6 (for MAT 319 only): 11.4, 11.10, 12.4, 14.2, 14.6 | 10/20 | |
| 8 | 10/17 - 10/21 | 14:series; 15: integral test and alternating series | HW 7 for MAT 319 only | postponed to 11/1 | |
| 9 | 10/24 - 10/28 | 17, 18: continuous functions | |||
| 10 | 10/31 - 11/4 | Midterm 2: 11/3 | |||
| 11 | 11/7 - 11/11 | 20: limits of functions | HW 8: 17.8, 17.10 (a), 17.12, 18.6, 18.10, 20.4, 20.8, 20.14, 20.20 | ||
| 12 | 11/14 - 11/18 | 28: derivatives | |||
| 13 | 11/21 - 11/25 | No classes on Nov 23-25: Thanksgiving break | 29 Mean value theorem | ||
| 14 | 11/28 - 12/2 | 32 The Riemann integral (up to Th. 32.5); 33 Properties of Reimann integral | HW 9: 28.6; 28.8, 29.2, 29.12, 29.14, 32.2, 32.6, 33.4 | 12/8 | |
| 15 | 12/5 - 12/9 | ||||
| 12/16 | Final exam |