MTH 311: ADVANCED CALCULUS

LECTURE: MWF 1300 - 1450 STAG 160 CRN 26817
RECITATION: W 1200 - 1250 STAG 160
Instructor: R.E. Showalter Kidder 286 show@math.oregonstate.edu
HW Grader: Alireza Hosseinkhan Kidder 330
Office Hours: Alireza Hosseinkhan: Mon 10-12, Tu 1-2pm in Kidder 330 and Tu 2-3pm, Th 1-3pm in MLC (Kidder 108).
R.E. Showalter: Wed 9-11, after class and by appointment.
Rigorous development of calculus: axiomatic properties and topology of the real line, convergence of sequences and series, limits and continuity of functions, derivatives and Riemann integration. Rigorous mathematical writing will be emphasized.
Prerequisites: MTH 255 or MTH 255H, and MTH 355, both courses completed with grade of C- or better.
Text: Fitzpatrick, Advanced Calculus, 2nd edition, 2009, ISBN 9780821847916
Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you believe you are eligible for accommodations but have not obtained approval, contact DAS immediately at 541-737-4098 or at their website. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.
Grading: Homework (HW) = 50%, Quizzes (QU) = 10%, Midterm & Final Exams = 20% each.
Homework will be assigned Wednesdays and collected in class Fridays. Late Homework will not be accepted; the lowest HW score will be dropped.
The Quiz and Midterm dates will be announced, usually on Wednesdays. Check the website for current information. The lowest Quiz score will be dropped.
Midterm Exam: Wed 10/18 Final Exam: Wed 12/6 1200 - 1400
Extra Office Hours: Alireza Hosseinkhan: Monday 12/4 & Tuesday 12/5 1300-1500 in Kidder 330 and R. Showalter: Monday 12/4 1100-1200 & Tuesday 12/5 1200-1330 in Kidder 286.
Schedule:
1. Preliminaries & Appendix A, pp. 1-4, 559-564; HW#1 p. 564: 1, 2, 3, 4 due Friday.
2. 1.1 Induction, pp. 5-8.
3. 1.1 Completeness, pp. 9-10 (9/25).
Quiz #1 on Ch 1.1: 1,2,13,14.
4. 1.2 Integers & Rationals. HW#2: 1.1: 1, 2, 15, 19 due Friday.
5. 1.3 Inequalities.
6. 2.1 Convergent Sequences. (10/02)
Quiz #2 on 1.2: 1, 5, 7 and 1.3: 4, 6, 8 and 2.1: 1, 6.
7. 2.2, 2.3 Closed sets, monotone sequences, pp. 35 - 40. HW#3: 1.3: 12, 2.1: 2, 2.2: 1, 2.3: 3 due Friday.
8. 2.4 & Prop. 2.37. Compactness.
9. 3.1, 3.2 Continuity, Max & min on [a,b]. (10/09)
Quiz #3 on Chap 2 and 3.1.
10. 3.2, 3.3 Intermediate-value theorem
11. 3.5 pp. 70-72. No HW today.
12. REVIEW Ch 2 to Proposition 2.37; Ch 3 to 3.3 and 3.5 to Theorem 3.20. (10/16)
13. MidTerm Exam: 2.1: 1-3,6; 2.2: 1-5; 2.3: 1-6; 2.4: 1,2,8,10; 2.5: 1-7 (not 3b), 3.1: 1-13; 3.2: 1,4,7; 3.3: 1-6; 3.5: 1-6.
14. 3.4. Uniform continuity and Thm 3.22.
15. 3.6: Monotone & Inverse functions. (10/23)
16. 3.7: Limits.
17. No class today.
18. 4.1, 4.2: pp. 87-98, Derivative & Inverse function. (10/30)
Quiz #4 from 4.1: 1-5, 9, 11, 13 and Definition of Derivative.
19. 4.2: Characterizations of derivative & Chain Rule. HW#4: 4.1: 4a, 11, and `Characterize derivative with epsilon-delta criterion'.
20. 4.3: Mean Value theorem.
21. 6.1: Upper & lower integrals. (11/06)
Quiz #5: from 4.2: 3-8 and 4.3: 1,3,5.
22. 6.2: Riemann theorem: monotone or step functions. (11/13)
23. No Class Friday.
24. Problems from 6.1 & 6.2. (11/13)
Quiz #6: from 6.1 (all problems) and 6.2: 1-3, 7,8.
25. 6.3, 6.4: Properties of the integral, continuous => integrable.
26. 6.5: integrating derivatives
27. 6.6: differentiating integrals(11/20)
28. REVIEW Ch 2: see `13. MidTerm Exam' above.(11/27)
29. REVIEW Chs 3, 4: `13. MidTerm Exam' and 3.4: 1, 11; 3.7: all; 4/1: 1-11; 4/2: 3-8; 4/3: 1, 3, 5.
30. REVIEW Ch 6: 6.1 (all problems); 6.2: 1-3, 7, 8; 6.3: 6; 6.4: 1-3, 5; 6.5: 4; 6.6: 1, 3-5.