Math 1272: Calculus II

Lecture 010, Vic Reiner
Spring 2010

CourseLib page


This is the only lecture of Math 1272 Calculus I being taught from this free text, Whitman Calculus, available for both browsing and printing. Note that this is the version that also contains some multivariable calculus, in addition to the sections used last semester in my lecture of Math 1271.

This is a different text from the one by Stewart being used by all of the other Spring 2010 Math 1272 lectures. Therefore if you are in my lecture, you should not buy any book, and just use the above link.
We will be taking the same common final exam as the other Math 1271 lectures. I will do my best to ensure that we cover exactly the same topics.

Here is a rough correspondence between sections in Whitman calculus versus those in Stewart's Calculus: early transcendentals, Vol. 1.

NEW! We've given you access to online practice problems through something called WeBWorK.
Check out the WeBWorK intro, which explains your username and password, and then go to WeBWorK problems themselves.

The Math 1272 course coordinator will be Prof. Karel Prikry.
You can find some interesting course materials at the downloads page for Prof. Greg Ruffa, one of our co-lecturers this semester.

Prerequisites: a grade of C- in Math 1271 or the equivalent.

What is this course about? Mainly, we continue learning the methods, techniques, and applications of single variable calculus that we began in Math 1271, such as

Instructor and class data 
Lecture or discussion section Time Location Lecturer or teaching assistant E-mail, office, phone, office hours
Lecture 010 9:05 A.M. - 9:55 A.M. , Mon,Wed,Fri 101 Fraser Hall Vic Reiner
256 Vincent Hall,
(612) 625-6682
Office hours:
Mon and Fri at 10:10-11:00,
Thurs at 11:15,
and by appointment
Discussion section 011 09:05 A.M. - 09:55 A.M. , Tues,Thur 1 Vincent Hall Weiwei Wu
550 Vincent Hall
(612) 624-2838
Office hours:
Tues 2:30-4:30,
Fri 3:30-5:30
Discussion section 014 10:10 A.M. - 11:00 A.M. , Tues,Thur 116 Armory building Weiwei Wu (see info above)
Discussion section 012 09:05 A.M. - 09:55 A.M. , Tues,Thur 103 Appleby Hall Liping Li
504 Vincent Hall
(612) 624-1543
Office hours:
Mon 2:30-4:30,
Thur 12:00-2:00
Discussion section 016 10:10 A.M. - 11:00 A.M. , Tues,Thur 103 Appleby Hall Liping Li (see info above)
Discussion section 013 09:05 A.M. - 09:55 A.M. , Tues,Thur 207 Vincent Hall Adil Ali
550 Vincent Hall
(612) 624-2838
Office hours:
Monday 4:40-5:30
Tuesday 2:30-4:20,
Wednesday 4:40-5:30,
Thursday 11:15-12:05.
Discussion section 015 10:10 A.M. - 11:00 A.M. , Tues,Thur 211 Vincent Hall Adil Ali (see info above)
Complaints: Address me if you have complaints about your TA. Complaints about me should go to our Mathematics Director of Undergraduate Studies: Prof. Larry Gray, in Vincent Hall 115.

Exam schedule and grading scheme 
Exam or homework Date Material emphasized Course grade contribution
Midterm Exam 1 Thursday, February 18 in section Whitman Calculus Sections 8.2, 8.3, 8.4, 8.5, 8.6, 9.7, 9.9, 9.10
+ numerical integration from Calc Text Pages Section 8.7
Midterm Exam 2 Thursday, March 11 in section Whitman Calculus Sections 9.6, 9.11,
+ direction fields, Euler's method, conic sections, polar coordinates
from Calc Text Pages Chapters 9 and 10
Midterm Exam 3 Thursday, April 22 in section Whitman Calculus Chapter 10 and Sections 11.1,11.2,11.3 15%
Final Exam Monday, May 10, 1:30-4:30pm
Dis 11,12,14,16-- AndersonHall 310
Dis 13,15-- AndersonHall 330
The whole course -
sample finals available here,
using "math1272" as search term and as password.
Weekly quizzes generally during Thursday section;
two lowest quiz scores dropped
That week's material 15%
Homework generally handed in at beginning
of Tuesday sections
That week's material 10%
The midterm exams and the final exam are closed book, with no notes allowed, and no consultation of other sources.

There will be no make-up exams for any of the midterms nor for the final exam.

Calculators and electronic devices: If you don't already have one here is a nice online basic scientific calculator, that might be useful for homework problems, although no calculators or computers will be allowed on the midterm exams or the final. As a companion to the above calculator, here is a nice online, grapher. No electronic devices may be accessible to any student during an exam. This includes cell phones and sufficiently sophisticated watches in addition to calculators and other machines. The instructor or proctor reserves the right to require, at the instructor's or proctor's discretion, that any electronic device be put away. Failure to comply is considered cheating by Institute of Technology policy.

Homework: The weekly homework assignments and due dates are given below, to be handed in at the beginning of discussion sections on Tuesdays. Beyond the homework problems assigned, it is strongly encouraged that you get further practice by trying non-assigned problems from the book, or from some of the other source materials listed far below.

Collaboration on the homework is encouraged. However, each student must understand the solutions, write them up in their own handwriting, and also write down with whom they have collaborated on the homework sheet.

The recitation component (25%) of the grade is determined

Incompletes: The grade I ("incomplete") shall be assigned at the lecturer's discretion when, due to extraordinary circumstances, the student was prevented from completing the entire course. It is my policy to assign incompletes only rarely, and only when almost all of the course has already been completed in a satisfactory fashion prior to the extraordinary circumstances. See me (Vic) if something occurs which makes you think you should receive an incomplete.
Homework assignments and exams 
Due date (handed in at beginning of section) Homework problems from Whitman Calculus
Tues Jan. 26 Section 8.2: 2,3,4,8,10
Tues Feb. 2 Section 8.3: 5,8,10 (problem 4 removed!)
Section 8.4: 3,4,7,8,10
Tues Feb. 9 Section 8.5: 2,3,10
Section 8.6: 1,3,7,11,12,17,27
Calc text pages exercises for Section 8.7: 3,17,33
Tues Feb. 16 Section 9.7: 2,4,5,8,13
Section 9.9: 1,4,6
Section 9.10: 2,3,4,6
Thur Feb. 18 This was Midterm Exam 1 with solutions
given in discussion section,
covering Whitman Calculus Sections 8.2, 8.3, 8.4, 8.5, 8.6, 9.7, 9.9, 9.10
+ numerical integration from Calc Text Pages Section 8.7
Tues Feb. 23 Section 9.6: 1,2,5,9
Section 9.11: 1,3,5,7,10,12,19
Tues Mar. 2 Calc text pages exercises for Section 9.1:19,20,21,22,23,24,26
Calc text pages exercises for Section 9.3:2,7,8
Calc text pages exercises for Section 10.1:1,2,3,4,5,6,7,8,19,22,27 (yes, 5,6,7,8, got added!)
Tues Mar. 9 Calc text pages exercises for Section 10.5:1,3ad,5,10,16,19,24,34,
Calc text pages exercises for Section 10.6:7,9,19,21a,22a,23a,24a
(and do get help from an online polar plotter, such as this one)
Calc text pages
exercises for Section 10.7:1,3,21
Thur Mar. 11 This was Midterm Exam 2 with solutions
given in discussion section
covering Whitman Sections 9.6 (center of mass, centroids),
9.11 (differential equations), direction fields, Euler's method,
conic sections, polar coordinates
including tangent slopes, arc-lengths, and areas in polar coordinates.
Tues Mar. 29 Section 10.1: 1,2,4,5
Section 10.2: 2,3,4,5
Section 10.3: 1,4,6,10
Section 10.4: 2,3
(Sections 10.5,10.6 got shifted to the next HW)
Tues Apr. 6 Section 10.5: 1,2,6,7,9,10
Section 10.6: 1,3,4,5,6,7
Section 10.7: 1,2,3,4,5,7,8
Section 10.8: 1,3,5,6
Section 10.9: 1,4,5
Tues Apr. 13 Section 10.10: 3,5,6,7,8,10
Section 10.11: 1,2,4
Section 10.12: 1,7,8,13,14,19,23,28,29
Need help? Try a convergence/divergence testing
flow chart or another flow chart,
Tues Apr. 20 Section 11.1: 1,3,5,7,10
Section 11.2: 1,2,5,7,11
Section 11.3: 4,9,11,13,14,18
Thur Apr. 22 This was Midterm Exam 3 with solutions
given in discussion section
covering Whitman Chapter 10 (sequences, series, Taylor series/polynomials)
and Sections 11.1,11.2,11.3 (coordinates, vectors, dot products in the plane and 3-space)
Tues Apr. 27 Section 11.4:1,4,5,8,9
Section 11.5:1,4,7,9,10,12,13,14
Tues May 4 Section 12.1: 8
Section 12.2: 2,5,6,8,10
Section 12.3: 2,3,5
Section 12.4: 5,8
Monday May 10 Final Exam 1:30pm - 4:30pm,
Dis 11,12,14,16-- AndersonHall 310
Dis 13,15-- AndersonHall 330,
covering whole course


More resources!

None of these are required for the course. However, I highly recommend that you consult them for more practice problems, more examples, more exposition and different perspectives, beyond those provided by our lectures and our text.

Free Tutors

(for U of M Students Currently Enrolled in Day or Evening Math Classes)

As of Fall Semester 2009, the SMART Learning Commons will be the only source of free tutoring for Mathematics courses. The SMART Commons offers both workshop and tutorial options for students. Tutorials are available for most lower division Math courses (1xxx-2xxx level) plus a selected few upper division (4xxx, 5xxx level) Math courses - see SMART Commons Consultant Schedules.

The SMART Commons is not only offering tutorials at its three regular locations - Walter Library (East Bank), Wilson Library (West Bank), and the Magrath Library (St. Paul campus) - but also in selected dorms during selected evening and weekend time slots! Tutoring at the four SMART Learning Commons locations began Monday, September 14, 2009. Please check for specific details.

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