Mathematics 431, Fall 2017

Advanced Calculus I

Instructor: Lenny Ng
Meeting time: Tuesdays, Thursdays 11:45am-1:00pm
Location: Physics 047

Office hours:
Mondays 10:30-12:00 (priority to this class)
Tuesdays 2:45-3:45 (priority to my Math 411 class)
Fridays 1:00-2:00
and by appointment.

The textbook for this course is Fundamental Ideas of Analysis by Michael Reed.

Course information sheet (please note: the second midterm is on November 7, not November 2 as stated in the syllabus)

Course schedule and homework assignments are shown below. Homework listings will be updated as they are assigned. Dates of midterms and lists of sections to be covered weekly are tentative and will be confirmed as we go. Other material for this course (e.g., solutions to quizzes) will be posted on Sakai.


Date Sections (by week) In-class Quizzes/Exams Assignments due
August 29
1.1, 1.3, 1.4
(please read 1.2 on your own)


August 31



September 5
2.1, 2.2, 2.4 Quiz 1 HW 1:
1.1 (p. 5): 6, 8, 9, 10
1.3 (p. 19): 1, 3*
1.4 (p. 24): 4, 5, 6, 7, 8, 9
*For 1.3 #3(abc): you may assume that the two sets are disjoint.
September 7



September 12 2.5, 2.6 Quiz 2 HW 2:
2.1 (p. 33): 2(a), 3(a), 4(d), 7, 9
2.2 (p. 39): 1(d), 4, 5, 7, 8
2.4 (p. 50): 1, 3, 5, 11
September 14


September 19
3.1, 3.2 Quiz 3 HW 3:
2.4 (p. 50): 12, 13
2.5 (p. 54): 1, 3, 4, 5, 9
2.6 (p. 59): 1, 2, 3, 7, 9
September 21



September 26 3.3, review Quiz 4 HW 4:
3.1 (p. 79): 3, 7, 8, 9, 11  
3.2 (p. 86): 1, 3, 6, 8, 9, 10  
September 28



October 3

Midterm 1 HW 5:
3.3 (p. 93): 1, 2, 3, 4, 9, 14, 15
October 5
4.1

October 10 Fall break: no class


October 12 4.2


October 17 4.3, 3.4
Quiz 5
HW 6:
4.1 (p. 127): 2, 8 (see p. 85 for the definition of Lipschitz continuous), 10, 11, 12
4.2 (p. 133): 3, 4, 5, 8, 11, 13, 14
October 19



October 24 5.1, 5.2, 5.3 Quiz 6
HW 7:
4.3 (p. 139): 3, 4, 7, 8, 11 (for this problem, you may assume the result of 10(b) from this section), 12
3.4 (p. 101): 1, 3, 5
chapter 3 projects (p. 120): 3
October 26


October 31
5.4, 5.6, review Quiz 7
HW 8:
5.1 (p. 168): 2, 6, 7, 9, 12
5.2 (p. 173): 1, 6, 9
5.3 (p. 181): 1, 3, 10* (see note below this calendar)
For #3, you can assume the result of 5.3 #2.
November 2



November 7

Midterm 2 HW 9:
5.4 (p. 186): 3, 5, 8, 9
5.6 (p. 202): 6, 8
November 9
5.7


November 14 6.1, 6.2 No quiz! HW 10: download here (updated 11/13)
November 16


November 21
No class!


November 23 Thanksgiving: no class

November 28
6.3, 6.4
Quiz 8
HW 11:
6.1 (p. 227): 1(a,b,c), 2, 7, 8, 9
6.2 (p. 236): 1, 4, 8, 9, 15
November 30



December 5
Space-filling curves, review
Quiz 9
HW 12:
6.3 (p. 242): 2, 3, 4, 5, 7
6.4 (p. 250): 1, 2, 3, 8, 9
December 7



December 17
Final exam, 2pm-5pm


* For HW 8, 5.3 #10: what it means for the limit of f(x) to be L as x goes to +∞ is: for any ϵ>0, there is an M such that for all xM, |f(x)-L|ϵ. There's an analogous definition for limits at -∞.