Calculus I - Mathematics 141,   Sections 13 and 14

Frank Thorne - Fall 2011

University of South Carolina

      Instructor     Graduate Assistant     Supplemental Instructor  
      Frank Thorne     Taylor Short     Lauren Huber  
  Office     LeConte 400G          
  E-mail     thornef [at]         huberl [at]  
  Office hours     Mon, 3:30-4:30     Tue, 11:50-12:30, 1:15-1:45      
  Wed, 3:30-4:30     Wed, 11:15-12:15     see below  
  Thu, 2:30-3:30     Thu, 11:50-12:30, 1:15-1:45      

Course information and learning outcomes:

Calculus is a beautiful subject dating back to Newton, Leibniz, and Gauss. A student who completes Math 141 will master concepts and gain skills related to functions and graphs, limits, derivatives, and integrals, and applications related to all of the above. The successful student will also refine his/her abilities in problem solving, abstract reasoning, and mathematical writing. Finally, although this will not be an emphasis of the course, the student will gain introductory exposure to theorems, proofs, and the rigorous side of mathematics.

Calculus is difficult, but we have every confidence in your ability to succeed. You must spend subsantial effort outside of class in order to learn the subject well. We are here to help you. Please come to office hours as often as you wish; no appointment is necessary. I will also hang around before and after class to answer questions. You may also e-mail me at thornef [at], to set up an appointment or to ask questions over e-mail. I will try to respond within 24 hours.

  • Text : James Stewart, Calculus, Early Transcendentals, 6th edition. We will use a custom edition of this book, available in the campus bookstore.

    Unfortunately it is not the official text, but Calculus Made Easy by Silvanus Thompson, published in 1914, is still the best calculus book ever written. Read the epilogue on p. 283 if you don't believe me.

  • Meeting schedule :

          Section 13     Section 14  
      Lecture     MWF     12:20-1:10     LeConte 113     MWF     12:20-1:10     LeConte 113  
      Maple lab     Thur.     11:00-11:50     LeConte 303A     Thur.     12:30-1:20     LeConte 303A  
      Recitation     Tue.     11:00 - 11:50     LeConte 112     Tue.     12:30-1:20     LeConte 112  

  • Exam schedule :

      Exam 1:     W     Sept. 14  
      Exam 2:     W     Oct. 12  
      Exam 3:     F     Nov. 18  
      Final Exam:     (Dec. 9)     (9:00 am - 12:00 pm)     LeConte 113  

    Practice Exam 1, solutions.

    Exam 1, solutions.

    Practice Exam 2, solutions.

    Exam 2, solutions.

    Practice Exam 3, solutions.

    Practice Final: Do any sixteen problems, including one from 1-9, from the bonus homework.

    I will write up solutions to up to sixteen problems by December 7. E-mail me a list of what problems you want to see. If more than sixteen solutions are requested, I will post solutions to the problems requested most often.

  • Homework : Homework is due to your TA by 5:00 p.m. each Friday. (Your TA will tell you where to turn in your homework.) The homework will be graded and returned to you, according to the following scheme. Each homework is worth 10 points. Out of that, three problems will be selected each week (randomly, for the most part) and graded carefully, and each is worth 2 points. The remaining 4 points are for overall quality and completion.

    The homework assignments will all be posted to this website at least a week in advance. The homeworks will be long. Do not start the night before. Doing the homeworks is the most important thing you should do to learn calculus; in particular, this is much more important than my lectures.

    The homework assignments are designed to be a good guide to what is expected of you. Therefore, at least 80% of the questions on all of the exams will be taken verbatim from the homework, for the most part randomly. Homework questions that are recommended but not required are fair game.

  • Grading :

    WARNING. You will be graded both on correctness and on quality of exposition. The standard is that someone who doesn't know the answer should be able to easily follow your work. Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

    You are guaranteed an A for 88%, a B for 76%, a C for 64%, and a D for 50%. These cutoffs may be lowered slightly if I determine (in consultation with other faculty) that the difficulty of the homework and exams merits it, but please do not count on it. These cutoffs are guaranteed not to be raised.
          % of grade  
      Three hour exams:     15% x 3  
      Final exam:     25%  
      Maple lab assignments:     15%  
      Homework:     15%  

  • Make-up policy :

    If you have a legitimate conflict with any of the exams it is your responsibility to inform me at least a week before the exam. Late homework will generally not be accepted; in case of emergency please speak with your TA.

  • Calculators :

    Calculators will not be allowed for the exams. You may use them on the homework if you want, but this is discouraged, as the purpose of the homework is to prepare you for the exams.

  • Supplemental instruction :

    Lauren Huber runs the supplemental instruction sessions. This is a valuable resource and you are strongly encouraged to take advantage of it. Please go to ask questions and meet other students. It is a particularly good place to work on your homework.

    These sessions run Sunday 7:00-7:50, Monday 9:00-9:50, Thursday 4:00-4:50 in Thomas Cooper Library, Supplemental Instruction Room 3. (All times PM.)

    There is also free drop-in tutoring available Monday through Thursday, from 10:00-4:00 in LeConte 105. The tutoring is run by math grad students (most of whom are TAs); please take advantage of this valuable resource as well.

  • Other help resources : Math lab, Private tutors .

  • Homework assignments:

    Homework 1, due August 26, 2011.

    Homework 2, due September 2, 2011.

    Homework 3, due September 9, 2011.

    Homework 4, due September 16, 2011.

    Homework 5, due September 23, 2011.

    Homework 6, due September 30, 2011.

    Homework 7, due October 7, 2011.

    Homework 8, due October 14, 2011.

    Homework 9, due October 19, 2011 (Wednesday!).

    Homework 10, due October 28, 2011.

    Homework 11, due November 4, 2011.

    Homework 12, due November 11, 2011.

    Homework 13, due November 18, 2011.

    Homework 14, due December 2, 2011.

    Bonus Homework, due December 9, 2011 for extra credit (optional!).

    The bonus homework is good for extra credit equivalent to two homeworks. It is extremely long and lets you review virtually everything you have learned in the course. If you do part of it, you will get partial extra credit.

    Doing this assignment thoroughly, without looking at your book or notes except when you really need to, will be the best thing you can do to prepare for the final exam.

    Lectures and Homework :

    As with all things in life, subject to minor changes. No changes will be made within a week before any exam.

      Dates     Sections     Topics  
      Aug     19     F     1.1     Introduction  
      22     M     1.2-3     Cast of Characters I: Trigonometric and composite functions  
      24     W     1.4-5     Cast of Characters II: Exponential and logarithmic functions  
      26     F     2.1     The tangent and velocity problems  
      29     M     2.2-2.3     Introduction to limits  
      31     W     2.4-2.5     The Limits Game (defend against any enemy!)  
      Sept     2     F     2.6     Limits at infinity  
      7     W     2.7     Introduction to the derivative  
      9     F     2.8     The derivative as a function  
      12     M         Review  
      14     W         Exam 1  
      16     F     3.1     Computing Derivatives I  
      19     M     3.2     Computing Derivatives II  
      21     W     3.3     Derivatives of trigonometric functions  
      23     F     3.4     The Chain Rule  
      26     M     3.5     Implicit differentiation  
      28     W     3.6     Derivatives of logarithmic functions  
      30     F         Differentiation rules: review and practice  
      Oct   3     M     3.9     Related rates  
      5     W     4.1     Maxima and minima  
      7     F     4.2     The mean value theorem (and what not to tell a traffic judge)  
      10     M         Review  
      12     W         Exam 2  
      14     F     4.3     Derivatives and the shape of a graph  
      17     M     4.4     Indeterminate forms and l'Hopital's rule  
      19     W     4.5     Calculus and curve sketching  
      24     M     4.5     Curve sketching (cont.)  
      26     W     4.7     Optimization Problems  
      28     F         Optimization Problems II (the dog who mastered calculus)  
      30     M     4.9     Antiderivatives  
    Nov   2     W     5.1     Areas and distances  
      4     F     5.2     The definite integral  
      7     M     5.3     The Fundamental Theorem of Calculus  
      9     W     5.4     Indefinite integrals and the net change theorem  
      11     F     5.5     Integration by substitution  
      14     M         Integration by substitution  
      16     W         Substitution (cont'd)  
      18     F         Exam 3
      21     M         Area between curves  
      28     M     6.2     Volumes: Disks and washers  
      30     W         Volumes (cont'd)  
    Dec   2     F         Review  
      (TBA)     (TBA)         Final Exam     Date, time, and room TBA.