Math 1271,  Calculus I, Lecture 030, Fall 2009

Credit will not be granted if credit has been received for:  MATH 1371, MATH 1571H, MATH 1142, or MATH 1281; prerequisites 4 years high school mathematics including trigonometry or placement test or grade of at least C- in 1151 or 1155;  4 credits, meets Liberal Education requirement of Mathematical Thinking Core

Electrical Engineering/Computer Science  Building ( EE/CSci ) 3-210,  02:30 P.M. - 03:20 P.M. MWF

Contact Information for the Instructor:

Instructor: Willard Miller
Office: Vincent Hall 513     VinH
Office Hours:
01:25 P.M.-02:15 P.M. (M,F) , 11:15 A.M.-12:05 P.M. (W),  or  by appointment
Phone: 612-624-7379,
Course web page
The Math Library 1271 Lecture 030 CourseLib page

 Discussion Sections:

                 -031  01:25 P.M.- 02:15 P.M. T,TH,  ApH  219
                 Hao Yu                           Office: Vincent Hall   526

            Office hours: 01:25 P.M. - 02:15 P.M. (M,W,F), 03:35 P.M. - 04:25 P.M. (T)

                 -032  01:25 P.M. - 02:15 P.M. T,TH   LindH  203 ,
Teng Wang                      Office: Vincent Hall  526
            Office hours: 09:05  A.M. - 11:05 A.M. (T,TH)

                 -033  01:25 P.M. -02:15 P.M.  T,TH   FordH  B29 ,
Hsi-Wei Shih                   Office: Vincent Hall 557
              Office hours: 10:00  A.M. - 12:00 P.M. (T,TH)

                 -034  02:30 P.M. - 03:20 P.M. T,TH   FordH  115
Hao Yu                           Office:  Vincent Hall 526
            Office hours: 01:25 P.M. - 02:15 P.M. (M,W,F), 03:35 P.M. - 04:25 P.M. (T)

                 -035  02:30 P.M. - 03:20 P.M. T,TH    ApH  319 ,
Teng Wang                      Office: Vincent Hall 526
            Office hours: 09:05  A.M. - 11:05 A.M. (T,TH)

                 -036  02:30 P.M. - 03:20 P.M.  T,TH  BlegH  425 ,
                     Hsi-Wei Shih                  Office: Vincent Hall 557
            Office hours: 10:00  A.M. - 12:00 P.M. (T,TH)

Brief Course Description

      The invention  of differential and integral calculus in the 17th and early 18th centuries was a milestone in human intellectual development. Calculus provides us with tools and a language to describe precisely and to analyse systems that are dynamic, that change in time and space. Modern science and technolgy would be impossible without calculus. The emphasis in this two semester course will be to provide tools for problem solving, that is, in using calculus to solve or find approximate solutions to problems that arise in the  physical, biological and social sciences  as well as mathematics itself. However, we will also try to impart some of the exciting intellectual history of the subject.

Mathematical Prerequisites: 4 years high school math including trigonometry, or C- in Math 1151 or 1155, or placement exam. You should review your knowledge of algebra and trigonometry. Some students do poorly in this class due to poor understanding of basic arithmetical operations.


(1) Students should not take Math 1271 unless they have a good understanding of trigonometry, both in terms of its relation to geometry and as a source of important functions to which calculus can be applied. Students without an adequate background in trigonometry might not notice much difficulty at the beginning of the course, and then, when serious later difficulty is encountered, it will be too late to switch to Math 1151.
(2) Students with some calculus background might, on the basis of easily understanding the early part of the course, develop bad study habits that will lead to disaster later in the course. 

Grading and Exams: There will be 3 midterm exams and a final exam. Your grade will be determined by the following weights:

Typically, the distribution of final grades is about 15% A, 25% B, 35% C and 25% D and F, but the exact distribution depends on class performance. I would be pleased to give more A's and B's if the class performs especially well.

Homework    The homework assignments are given on the course web page, and are due in discussion session on Tuesday of the week following when the corresponding section was treated by me. You may work together on the homework problems, but must write up your solutions in your own words.

The midterm exams and  the final exam are closed book and without notes. You are expected to attend lectures and recitations.  You should prepare for class in advance by reading the material for that day. If you have a borderline grade, the final exam takes precedent.

Absence from exams: Missing an exam is permitted only for the most compelling reasons. You should obtain my permission in advance to miss an exam. Otherwise you will be given a 0. If you are excused from taking an exam, you will be given an oral exam, or your other exam scores will be prorated.

Calculators and other electronic devices: A basic calculator will be useful for homework problems, but no calculators or computers will be allowed on the midterm exams or the final. 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.

Official University Statement on Academic Dishonesty: Academic dishonesty in any portion of the academic work for a course shall be grounds for awarding a grade of F or N for the entire course.

Official University Statement on Credits and Workload Expectations: For undergraduate courses, one credit is defined as equivalent to an average of three hours of learning effort per week (over a full semester) necessary for an average student to achieve an average grade in the course. For example, a student taking a three credit course that meets for three hours a week should expect to spend an additional six hours a week on coursework outside the classroom.

Statement on Incompletes, S/N: The grade "I'' is assigned only when a student has satisfactorily (a C grade or better) completed all but a small portion of the work for the course, and has made prior arrangements to complete the work. This means, for example, if you quit attending class after the second exam, and then request an "I" in the tenth week, your request will be denied. You will fail the course. To obtain an S, you need at least a C- grade.

Scholastic Conduct: Each student should read his/her college bulletin for the definitions and possible penalties for cheating. During the exams you must do your own work. Students suspected of cheating will be reported to the Scholastic Conduct Committee for appropriate action.

Complaints: You can address any complaints about your TA to me. You can address complaints about your lecturer to the Undergraduate Head, Professor Larry Gray, Vincent Hall 115.

Date                        Lecture will cover

W  Sep  09
Section      1.3    New functions from old                                                                                      
F   Sep 11
Section      2.1    Tangent and velocity
M  Sep 14
Section      2.2    Limit of a function
W  Sep 16
Section      2.3    Calculating limits
F   Sep 18
Section      2.5    Continuity
M  Sep 21
Section      2.6    Limits at infinity, Asymptotes
W  Sep 23
Section      2.7    Derivatives and rates of change
F   Sep 25
Section      2.8    Derivatives as functions
M  Sep 28
Section      3.1   Derivatives of polynomials and exponentials
W  Sep 30
Review for Midterm I
TH Oct 01
Midterm I (in discussion section)
F   Oct 02
Section      3.2   Product and quotient rules
M  Oct 05
Section       3.3   Derivatives of trig functions
W  Oct 07
Section       3.4   Chain rule
F   Oct 09
Section      3.5   Implicit differentiation
M  Oct 12
Section      3.6   Derivatives of log functions
W  Oct 14
Section       3.7   Derivatives in the natural and social sciences
F   Oct 16
Section       3.8   Exponential growth and decay
M  Oct 19
Section       3.9   Related rates
W  Oct 21
Section       3.10 Linear approximations, Differentials
F   Oct 23
Section       4.1   Extreme values
M  Oct 26
Section       4.2   Mean Value Theorem
W  Oct 28
Review  for Midterm II
TH Oct 29
Midterm II (in discussion section)
F   Oct 30
Section       4.3    Use of derivatives in graphing
M  Nov 02
Section       4.4    L'Hospital's rule
W  Nov 04
Section       4.5    Curve sketching
F   Nov 06
Section       4.7    Optimization problems
M  Nov 09
Section       4.8     Newton's method
W  Nov 11
Section       4.9     Antiderivatives
F   Nov 13
Section       5.1     Areas and distances
M  Nov 16
Section       5.2     Definite integral
W  Nov 18
Section       5.3     Fundamental Theorem Of Calculus!
F   Nov 20
Section       5.4     Indefinite integrals, Net change
M  Nov 23
Section       5.5     Substitution rule for integrals
W  Nov 25
Section       6.1     Areas between curves
F   Nov 27
University Holiday
M  Nov 30
Review for  Midterm III
TU Dec 01
Midterm III (in discussion section) Covers sections 4.1 - 5.3
W  Dec 02
Section       6.2     Volumes
F   Dec 04
Section       6.3     Shell method
M  Dec 07
Section      6.5     Average value of a function
W  Dec 09
Review of Chapter 6
F   Dec 11
Review of Chapters 2-3
M  Dec 14
Review of Chapters 4-5
W  Dec 16
Final review
TH Dec 17
Final Exam, 1:30-4:30 pm,  Physics 150

IMPORTANT: You will need to bring your official University I.D. card with you at the time of the final exam and must show it to one of the proctors when handing in your exam. The proctor will NOT accept a final exam from a student without an I.D. Card.

Be sure to know your recitation teacher's name in lecture/recitation courses, and your course and section numbers. You should bring identification to the final examination and should use #1 or #2 pencils for any machine graded portion of the examination.

Homework Assignments and Exam Dates

Practice Midterm  Exam 1 (for  Fall 2009) with (very brief)  answers  (pdf file)

Practice old Midterm Exam 1 (covering different material from Fall 2009) with (very brief)  answers  (pdf file)

Practice Midterm  Exam 2 (for  Fall 2009) with (very brief)  answers  (pdf file)

Practice old Midterm Exam 2 (covering different material from Fall 2009) with (very brief)  answers  (pdf file)

Practice Midterm  Exam 3 (for  Fall 2009) with (very brief)  answers  (pdf file)

Practice old Midterm Exam 3 (covering different material from Fall 2009) with (very brief)  answers  (pdf file)

Practice actual Final Exam  2003  (pdf file)        Very brief answers  (courtesy of Alex Voronov) (pdf file) 

Practice actual Final Exam  F2004 (pdf file)   Solutions (courtesy of Tsevtanka Sendova) (pdf file)

Practice actual Final Exam  S2005  (pdf file)  Solutions (courtesy of Tsevtanka Sendova) (pdf file)

Practice actual Final Exam   F2005  (pdf file)  Answer key (pdf file) and solutions (pdf file)(courtesy of Multicultural Center for Academic Excellence)

Supplementary materials:

Rules for Limits and Derivatives

The Mean Value Theorem, Extended Mean Value Theorem and L'Hospital's Rule

Newton's Method and the Mean Value Theorem

Mathematics Tutoring Services for Math 1271: Fall 2009

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.