MATH 1271 -- Changes

Mon Jun 28 12:22:10 2010

New:  Differential calculus of functions of a single variable, including polynomial, rational, exponential and trig functions.  Applications, including optimization and related rates problems.  Intro to single variable integral calculus, using anti-derivatives and simple substitution. Applications may include area, volume, work problems.
Old:  Differential calculus of functions of a single variable. Integral calculus of single variable, separable differential equations. Applications: max-min, related rates, area, volume, arc-length.
Term(s) most
frequently offered:
New:  Fall, Spring, Summer
Old:  Fall, Spring
for Catalog:
New:  4 yrs high school math including trig or satisfactory score on placement test or grade of at least C- in [1151 or 1155]
Old:  Satisfactory score on placement test or grade of at least C- in [1151 or 1155]
Proposal Changes: New:  Being submitted for certification for the Lib Ed Mathematical Thinking Core.  
Old:  <no text provided>
Sponsor Name:
New:  Mark Feshbach (DUGS)
Old:  David Frank
Sponsor E-mail Address:
Student Learning Outcomes: * Student in the course:

- Can identify, define, and solve problems


Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome.

Problem solving is at the heart of any mathematics course. In this course some problems would involve purely mathematical issues, like finding the derivative of a polynomial or determining the features of the graph of a rational function. Other problems involve taking a real world situation like predicting the trajectory of a projectile or analyzing population growth and decline, requiring students to first identify the mathematically relevant aspects, then define appropriate mathematical variables and relations, and finally solve the resulting mathematics problem.

How will you assess the students' learning related to this outcome? Give brief examples of how class work related to the outcome will be evaluated.

Practically every homework assignment, quiz, and exam requires students to solve problems. Students receive ample feedback about this learning outcome during the semester.

Old: unselected

this course fulfills:
New:  MATH - MATH Mathematical Thinking
Criteria for
Core Courses:
Describe how the course meets the specific bullet points for the proposed core requirement. Give concrete and detailed examples for the course syllabus, detailed outline, laboratory material, student projects, or other instructional materials or method.

Core courses must meet the following requirements:

  • They explicitly help students understand what liberal education is, how the content and the substance of this course enhance a liberal education, and what this means for them as students and as citizens
  • They employ teaching and learning strategies that engage students with doing the work of the field, not just reading about it.
  • They include small group experiences (such as discussion sections or labs) and use writing as appropriate to the discipline to help students learn and reflect on their learning.
  • They do not (except in rare and clearly justified cases) have prerequisites beyond the Universitys entrance requirements.
  • They are offered on a regular schedule.
  • They are taught by regular faculty or under exceptional circumstances by instructors on continuing appointments. Departments proposing instructors other than regular faculty must provide documentation of how such instructors will be trained and supervised to ensure consistency and continuity in courses.

Calculus I (Math 1271) is the first semester in a multi-semester calculus sequence, primarily for students in engineering, science, and economics, but also for other students desiring a full treatment.  

This course requires students to have a real understanding of the symbolic language of mathematics, giving them ample opportunity to see how mathematics is done by mathematicians and to engage in that same work by solving problems for themselves. In this way, they see how abstract mathematical concepts can find applications in the real world.

An important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia, both for aesthetic reasons and to solve concrete problems.  Calculus is one of the pillars of modern mathematics, and it has important applications in science and everyday life. Calculus was first developed by Newton and Leibniz in the 17th century to solve many types of problems.  For example, using calculus, Newton was able to derive the equations of planetary motion from basic physical laws.  Since that time, calculus has touched virtually every part of modern life, through its use in areas like engineering, the stock market, agriculture, psychology, and all the physical and biological sciences.  While it is beyond the scope of a 1-semester course to cover even a small fraction of all these applications, students will be exposed to a variety of simplified versions of them, preparing them for later advanced study in their fields of interest.  In this way, students experience both the fundamental nature of the questions and the usefulness of abstract reasoning in finding elegant and efficient solutions.

Students meet twice a week in TA recitation sections, where they can ask questions, work problems together, and discussion important points in the material.  The prerequisite for the course is equivalent to 4 years of high school mathematics.  Math 1271 is offered every semester.  The course is taught by a combination of regular faculty and adjunct faculty with on-going appointments, or by experienced grad students or postdocs who act under close supervision by regular faculty.  Every semester, the final exam is a departmental exam that is given in common to all sections, in order to ensure consistency.
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Please provide a provisional syllabus for new courses and courses in which changes in content and/or description and/or credits are proposed that include the following information: course goals and description; format/structure of the course (proposed number of instructor contact hours per week, student workload effort per week, etc.); topics to be covered; scope and nature of assigned readings (texts, authors, frequency, amount per week); required course assignments; nature of any student projects; and how students will be evaluated.

The University policy on credits is found under Section 4A of "Standards for Semester Conversion" at . Provisional course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification, This provisional course syllabus information may not correspond to the course as offered in a particular semester.

New:  (This is a copy of an actual syllabus for Math 1271, modified to include a Liberal Education statement)

Math 1271,  Calculus I, Lecture 030, Spring 2007

Credit will not be granted if credit has been received for: ESPM 1145, 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

Liberal Education:  This course fulfills the Mathematical Thinking component of the Liberal Education requirements at the University of Minnesota.  An important part of any liberal education is learning to use abstract thinking and symbolic language to solve practical problems.  Calculus is one of the pillars of modern mathematical thought, and has diverse applications essential to our complex world.  In this course, students will be exposed to theoretical concepts at the heart of calculus and to numerous examples of real-world applications.

Science Classroom Building (SciCB) 375,  11:15-12:05 MWF

Contact Information for the Instructor:

Instructor: Willard Miller
Office: Vincent Hall 513
Office Hours: 13:25-14:15 M, 9:05-9:55 W, 12:20-13:10 F,  or  by appointment
Phone: 612-624-7379,

Discussion Sections:

    -031  11:15 am- 12:05 pm T,TH, PeikH 215,
    Teng Wang,     Office: VinH 526, (612) 624-1824,
    Office hours: 9:00-10:30, T,TH

    -032  11:15 am-12:05 pm T,TH   VinH 311,
    Kuerak Chung,  Office: VinH 557, (612) 331-9256,
    Office Hours: 10:10-11:00 and 13:25-14:15, T, TH

    -033  12:20 pm-01:10 pm T,TH   RapsonH 43,
    Teng Wang,     Office: VinH 526,  (612) 624-1824,
    Office hours: 9:00-10:30, T,TH

    -034  12:20 pm-01:10 pm T,TH   Rapson 54,
    Kuerak Chung,  Office: VinH 557, (612) 331-9256,
    Office Hours: 10:10-11:00 and 13:25-14:15, T, TH

    -035  12:20 pm-01:10 pm T,TH   PeikH 28,
    Fatimah Wang,   Office: VinH 550,  (612) 624-2838,
    Office Hours: 16:30-17:30, M, W

Brief Course Description

   * This is the first semester of a two semester course in one-variable calculus pitched to students not in IT..
   * Textbook: Calculus, 5th edition, by James Stewart.
   *  We will cover roughly chapters 2-6 (and it will be assumed that you are familiar with most of the review topics in chapter 1):
    o 1. Functions and Models
    o 2. Limits and Derivatives
    o 3. Differentiation Rules
    o 4. Applications of Differentiation
    o 5. Integrals
    o 6. Applications of Integration

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:

   * Final exam   35%,
   * Mid-Term I   15%,
   * Mid-Term II  15%
   * Mid-Term III 15%
   * Homework, quizzes and in-class participation 20%

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 David Frank, Vincent Hall 115.

Date     Lecture will cover
W  Jan  17
        Section     1.3  New functions from old functions     
F   Jan 19
        Section     2.1  The tangent and velocity problems
M  Jan 22
        Section     2.2  The limit of a function
W  Jan 24
        Section     2.3  Calculating limits using the limit laws
F   Jan 26
        Section     2.5  Continuity
M  Jan 29
        Section     2.6  Limits at infinity; horizontal asymptotes
W  Jan 31
        Section     2.7  Tangents, velocities, and other rates of change, with applications to trajectories, cooling bodies, population growth
F   Feb 2
        Section     2.8  Derivatives
M  Feb 5
        Section     2.9  The derivative as a function
W  Feb 7
        Section     3.1  Derivatives of polynomials and exponential functions
F   Feb 9
        Section     3.2  The product and quotient rules
M  Feb 12
        Review for Midterm I
W  Feb 14
        Section     3.3  Rates of change in the natural and social sciences
F   Feb 16
        Section     3.4  Derivatives of trigonometric functions, with applications to geometric problems and periodic motion
M  Feb 19
        Section     3.5  The chain rule
W  Feb 21
        Section     3.6  Implicit differentiation
F   Feb 23
        Section     3.7  Higher derivatives
M  Feb 26
        Section     3.8  Derivatives of logarithmic functions
W  Feb 28
        Section     3.10  Related rates, with applications to problems of motion, cooling, and biology
F   Mar 2
        Section     3.11  Linear approximations and differentials
M  Mar 5
        Section     4.1  Maximum and minimum values
W  Mar 7
        Section     4.2  The mean value theorem
F   Mar 9
        Section     4.3  How derivatives affect the shape of a graph
Mar 12  - 16  
        Spring Break!
M  Mar 19
        Section     4.4  Indeterminate forms and L'Hospital's Rule
W Mar 21
        Section     4.5  Summary of curve-sketching
F  Mar 23
        Section     4.7  Optimization problems, with applications in physics, biology, and manufacturing
M  Mar 26
        Review  for Midterm II
W  Mar 28
        Section     4.9  Newton's method
F   Mar 30
        Section     4.10 Anti-derivatives
M  Apr 2
        Section     5.1  Areas and distances
W  Apr 4
        Section     5.2  Definite integral
F   Apr 6
        Section     5.2  Definite integral (continued)
M  Apr 9
        Section     5.3  Fundamental Theorem of Calculus
W  Apr 11
        Section     5.4  Indefinite integrals and the net-change theorem
F   Apr 13
        Section     5.5  Substitution rule
M  Apr 16
        Section     5.6  The logarithm defined as a integral
W  Apr 18
        Section     6.1  Areas between curves
F   Apr 20
        Section     6.2  Volumes
M  Apr 23
        Review for  Midterm III
W  Apr 25
        Section     6.2
F   Apr 27
        Section     6.3  Volumes by cylindrical shells
M  Apr 30
        Section     6.5  Average value of a function, average velocities, average temperatures, etc.
W  May 2
        Review of Chapter 6
F   May 4
        Review of Chapters 2-5
M  May 7
        Final Exam, 1:30-4:30 pm, Smith Hall 100

Homework Assignments and Exam Dates

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

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

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

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

Old:  <no text provided>