UNIVERSITY OF MINNESOTA 
SCHOOL OF MATHEMATICS

WARNING!

This is a different text from the one by Stewart being used by all of the other Fall 2009 Math 1271 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.
A syllabus for the lecture given by the Math 1271 course coordinator, Prof. Willard Miller is here.

Prerequisites:

• The explicit prerequisites are a placement exam, or C- or better in either Math 1151 or Math 1155. No prior calculus needs to have been taken, however...
• Math 1271 requires good understanding of algebra and trigonometry. Students without this may not notice much difficulty at the beginning of the course, but then if difficulty is encountered later it may be too late to switch to Math 1151. To help you self-diagnose this problem, try taking this little gateway exam (except that I recommend skipping Exam Problem 1) developed by some of our neighbors at SDSU, and check your answers at their site.
• Beware a common pitfall: students with some calculus background sometimes, after breezing through the early part of the course, develop poor study habits inadequate for later in the course.

• In general, a "calculus" is a method for computing something. But "The calculus" got its name as one of the major human intellectual achievements of all time, and a pinnacle of The Age of Enlightenment. Few other techniques in science even come close to its successes.
• Philosophically it is very satisfying: one finally comes to grips with the notion of infinity in ways that actually make sense!
• In the first part of the course, one learns about derivatives of functions, which you could think of as a way for computing tangent lines to curves. But it's a lot more-- the right language for thinking about many basic concepts in other subjects, such as velocity, acceleration, reaction rates, growth, decay, marginal cost, continuous compounding.
• Later, one learns about integrals of functions, which you could think of as a way for computing areas and volumes. But again, it's much more-- the right language for thinking about concepts such as distance, work, energy, probability, averages, center of mass, moment of inertia.
• Throughout, the course emphasizes these two points:
  • there are mechanical skills and methods, such as calculating derivative and integrals, that we must master, and at the same time
  • we must learn to model situations from the world around us, phrased in natural language like "word" or "story" problems, and translate them into the language of mathematics.
  In this way, we develop skills transcending those of our calculators. Partly for this reason, Math 1271 satisfies the University's Liberal Education "Mathematical Thinking" Core Requirement.

Exam schedule and grading scheme 

Exam or homework	Date	Material emphasized	Course grade contribution
Midterm Exam 1	Thursday, Oct. 1, in section	Chapters 1,2 of Whitman Calculus/td>	15%
Midterm Exam 2	Thursday, Oct. 29, in section	Chapters (1,2), 3,4, and Sections 6.1, 6.2, 6.4	15%
Midterm Exam 3	Tuesday, Nov. 24, in section	Chapters (1,2,3,4),5,6,7	15%
Final Exam	Thursday, Dec. 17, 1:30-4:30pm, room to be announced	The whole course	35%
Quizzes, homework	Quizzes administered and homeworks handed in during discussion sections	That week's material	20%

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 grade is determined in equal parts (half-and-half) by

• scores on short quizzes Thursdays in recitations every week without a midterm, dropping the two lowest quiz scores, and
• homework scores

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 Sept. 15	Section 1.1: 8,12,14 Section 1.2: 2(d) Section 1.3: 3,6,14 Section 1.4: 3,14,16
Tues Sept. 22	Section 2.3: 1,3,5,7,9,11,13,15,18,19,20 Section 2.4: 2,4,6,7
Tues Sept. 29	Section 2.1: 3,4,5 Section 2.2: 2,3 Section 2.4: 1,3 Section 2.5: 1,2,3,5,6,7 + Problems 2,3,6,7,8,9,10,11,12 from my handout on horizontal asymptotes
Thur Oct. 1	Here was Midterm Exam 1 with brief solutions, covering Chapters 1,2
Tues Oct. 6	Section 3.1: 1,3,5 Section 3.2: 2,3,9,12,13 Section 3.3: 1,5 Section 3.4: 1,8
Tues Oct. 13	Section 3.5: 3,6,8,15,21 Section 4.1: 1,9 Section 4.4: 1,3 Section 4.5: 1,2,6,8,11,13
Tues Oct. 20	Section 4.6: 1,3,9,10,12 Section 4.7: 1,2,5,7,12,16,17 Section 4.9: 1,4,7,11 Section 4.10: 1,5
Tues Oct. 27	Section 9.11: 16 Section 6.2: 1,3,5,10,14,16 Section 6.4: 2,4 Section 6.1: 3,9,12,19
Thur Oct. 29	Here was Midterm Exam 2 with brief solutions, covering Chapters (1,2,) 3,4, and Sections 6.1, 6.2, 6.4
Tues Nov. 3	Section 6.3: 1,3 Section 6.1: 1 Section 6.5: 1,2,4,6,7,8,9,10
Tues Nov. 10	Section 4.8: 1,2,3,4,6 Section 5.1: 1,8,14 Section 5.2: 1,8,14 Section 5.3: 1,8,12 Section 5.4: 1,8,12 Section 5.5: 1,14
Tues Nov. 17	Section 7.1: 2,3,7 Section 7.2: 1,2,4,7,11,12,14,17,18 Section 7.3: 1,5
Tues Nov. 24	Here was Midterm Exam 3 with brief solutions covering Chapters (1,2,3,4),5,6,7
Tues Dec. 1	Section 7.3: 2,4,6 Section 9.2: 3,6,10 Section 8.1: 1,3,4,7,10,11,16,19
Tues Dec. 8	Section 9.1: 3,7,11 Section 9.3: 5,6,7,10,11
Tues Dec. 15	Section 9.4: 1,2,3,4,5
Thur Dec. 17	Final Exam 1:20pm - 4:30pm, room to be announced, covering whole course

 
 

Further sources of practice problems: Whitman calculus does not contain as many routine practice calculus problems as some other standard calculus texts. Here are some potential sources of more problems, both with and without solutions, that you might try if you feel like you need more practice. None of these are required for the course.

• The calculus page problem list
• Calculus on the web
• Drexel MathForum calculus page
• The practice midterm exams at the bottom of our Math 1271 course coordinator Prof. Willard Miller's syllabus page.
• Any version of Schaum's Outline of calculus, or other books with many worked calclulus problems.
• A copy of any edition, including very old ones, of the more standard calculus texts, such as the ones by
  • Stewart
  • Edwards and Penney
  • Marsden and Weinstein
  • Thomas and Finney
  • Simmons
  • Anton
  • Salas and Hille
• The Wiki Calculus book
• MIT professor Gilbert Strang's freely available calculus text
• An online text by Dan Sloughter called Difference equations and differential equations: an introduction to calculus
• An online text from Brigham Young University called The Calculus Bible
• My colleague Paul Garrett's online Calculus refresher text

And speaking of Paul Garrett, check out some of these nice applets he has developed for graphing and demonstrating various calculus concepts:

• A few simple specialized grapher applets...
  • For any function y=f(x)
  • For y=f(x) with f(x) a polynomials of degree at most 5, as one varies coefficients
  • For y=sin(c*x) as one varies c
• Some secant lines/chords to a curve approaching a tangent line
• Animation of the tangent lines sliding along a curve
• An example where Newton's method for finding roots works well, as opposed to...
• A closely-related example where Newton's method can fail miserably

And speaking of colleagues of mine with nice calculus demos,
check out another colleague, Doug Arnold's calculus demos,

Some video and other resources for calculus

• Calculus lectures by David Jerison from MIT's Math 18.01
• Video calculus from the University of Houston
• Math Help's links to calculus text pages and videos

Free Tutors

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

As of Fall Semester 2009, the SMART Learning Commons smart.umn.edu 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 smart.umn.edu for specific details.

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