Math 41 Autumn 2014

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About This Class

Math 41 is a 5-unit course in introductory calculus with an accelerated pace -- the class covers limits, derivatives, applications of differentiation, and the basics of integration (up to substitution and integration by parts). It is one of three different single-variable calculus courses taught at Stanford in the autumn quarter, so you should be deciding during the first week whether it's the right calculus class for you.

If you have recently finished a calculus class covering all of the subjects listed above and you feel confident about them, you should consider instead taking Math 41's continuation, Math 42, this fall -- even if you don't have AP credit. If you're undecided about which of Math 41/42 (or any two courses in sequence) to take, keep in mind that it will be easier to drop back than to jump ahead during the second or third week of the quarter.

On the other hand, if it's been a year or more since your last math class or you are taking math just to satisfy a DB-MATH, you should consider instead entering the Math 19-20-21 sequence -- even if you did well in calculus in high school. The sequence Math 19-20-21 covers the same material as Math 41-42, but at the more traditional year-long pace (ending with Math 21 in the spring quarter). By contrast, Math 41 moves very quickly, and leaves you very little time to get back into shape if your math skills are rusty. It is intended to quickly develop the necessary background for students who will need calculus for their further studies, and may be more intense than what students satisfying a disciplinary breadth requirement are looking for.

On Registrar deadlines: Please pay careful attention to all Registrar deadlines, especially the add/drop deadline at the end of the third week of classes. University Advising and Research has recently reaffirmed that it will not allow changes in course registrations from Math 42 to 41 after the drop deadline. However, UAR has a special provision in place to accept petitions for switches from Math 41 to 19 submitted in complete form before Friday, October 24th at 5pm. The instructions for how to properly complete the petition is contained at the bottom of this page. You can also contact your instructor for more information.

Teaching Staff

  • Dr. Zhiyuan Li, Instructor (email)
    Lectures: 01 (MWF 9:00 AM - 9:50 AM at 380-380Y), 02 (MWF 10:00 AM - 10:50 AM at McCullough 115)
    Office: 382-B (2nd floor of Building 380) (office hours)

  • Dr. Daniel Berwick-Evans, Instructor (email)
    Lectures: 03 (MWF 11:00 AM - 11:50 AM at McCullough 115), 04 (MWF 1:15 PM - 2:05 PM at 380-380Y)
    Office: 383-FF (3rd floor of Building 380) (office hours)

  • Jafar Jafarov, Teaching Assistant (email)
    Discussions: 05 (TTh 9-9:50am, Gates B12), 07 (TTh 10-10:50am, Gates B12)
    Office: 380-U1 (1st floor of Building 380) (office hours)

  • Jeremy Leach, Teaching Assistant (email)
    Discussions: 10 (TTh 11-11:50am, McCullough 122), 11 (TTh 1:15-2:05pm, 320-220)
    Office: 381-J (1st floor of Building 380) (office hours)

  • Alex Zamorzaev, Teaching Assistant (email)
    Discussions: 08 (TTh 10-10:50am, 380-381U), 09 (TTh 11-11:50am, 380-380F)
    Office: 380-M (basement of Building 380) (office hours)

  • John Pardon, Teaching Assistant (email)
    Discussions: 06 (TTh 10-10:50am, 380-380D), 12 (TTh 1:15-2:05, Green Earth Sciences 150)
    Office: 381-L (1st floor of Building 380) (office hours)

  • Megan Bernstein, Teaching Assistant (email)
    Discussion: ACE (TTh 1:15-3:05pm, 200-305)
    Office: 380-R (basement of Building 380) (office hours)


The textbook is Single Variable Calculus: Concepts and Contexts, 4th edition, by James Stewart. We will cover most of the material from Chapter 1 through the first half of Chapter 5. Most homework exercises and reading assignments are taken from the book, so you should have access to a copy throughout the quarter. (It is not recommended that you try to use a copy of an older edition: although the text is very similar, some examples, some of the homework problems, and most of the problem numbers will be different.)

This text is also used by Math 19, 20, 21, and 42.

Lectures and Sections

Each week you will attend three lectures and two discussion sections. The lectures are on Monday, Wednesday and Friday, either at 9am, 10am, 11am, or 1:15pm. The discussion sections are on Tuesday and Thursday. See the Section Assignments page to view the choices for times and locations and instructions on the sign-up process. You will sign up for a discussion section via CourseWork, and your available options will depend on your lecture instructor.

The lectures will be used primarily to introduce concepts and develop theory, and serve as a complement to the course textbook. You can get the most out of lecture by having first read the relevant sections in the textbook (as set in the calendar of topics on the course schedule page). In the discussion sections, you meet with your Teaching Assistant in a smaller group. Much of the time in section will be used for example problems based on topics developed in lecture and the textbook; you can get the most out of section by working on the posted daily discussion problems in advance (i.e., immediately after lectures).

Attendance at all lectures and sections is required. If you miss a lecture or a section, it is your responsibility to catch up on the topics that you missed. You should keep in mind that in this course, the material builds on itself; if you miss some of the material, subsequent lectures will be more difficult (or even unintelligible) for you.


There will be weekly homework assignments. For more information and policies, see the Homework page.


Calculators will not be used in a systematic way in Math 41. Calculators will not be allowed on any of the exams, nor should there be any need for one. Occasionally, homework problems may call for the use of a scientific or graphing calculator.


The midterm exams will be held in the evenings on October 14 and November 4. The exact times and locations and other information will be posted on the Exam Information page. If you have a schedule conflict with one of the midterm exams due to another course meeting, you must contact us at least one week before the exam to arrange to take it at an alternate (early) sitting. (The same deadline holds for OAE accomodation requests; see below for details.)

The final exam will be held on Monday, December 8, from 7-10pm. You must take the final exam at this time, which is set by the University.

All of the exams are closed book, closed notes, with no electronic aids. For each exam, if appropriate, you may be provided with a formula sheet, which will be available on the exam materials page prior to the exam, along with other study materials.


Your grade will be based on the following components:
  • Weekly Homework: 10%
  • Total points earned on all exams (midterms and final): 90%

Points available on exams: The total points available on the exams will be in approximate proportion 2:2:3. That is, the first and second midterm exams will have approximately equal numbers of total points available, and the number of points available on the final exam will be approximately 1.5 times those available on a single midterm exam.

There are no predetermined numerical cutoffs for letter grades, and the cutoffs may turn out to be rather different from what you are accustomed to from high school. In general, the grade distribution for the class is usually (roughly) as follows: around 30% of the class receive A's, around 40% receive B's, and most of the rest receive C's.


CourseWork is a web-based program that will be used in Math 41 to allow students to check grades online. It is a secure program, so your grades will be available through CourseWork only to you. Every student must sign into CourseWork and choose a discussion section. CourseWork will be our primary gradekeeping tool; if you do not sign up, you could lose credit for work that you have done. This is completely independent of signing up for the course on Axess -- neither program has any knowledge of the other.

Before you sign into CourseWork, make sure you read the Section Assignments page, which contains instructions on the sign-up process for discussion sections.

Again, remember that Axess and CourseWork are different programs, and you will sign up for different course components on each -- on CourseWork, you sign up for a discussion section based on the table on the Section Assignments page, but on Axess you sign up for a lecture.

Despite its other capabilities, in this class CourseWork will be used only for grades and possibly email announcements.

Links, Getting Help, and Other Resources

  • Tips for Success in Undergraduate Math Courses by Jessica Purcell
    Some very good advice for college calculus students. Read this carefully and do as it suggests.
    Note: Pay particular attention to #3 under "Weekly" and #6 and #7 under "Before the exam". Students who think they're following these tips often overlook those parts, and they're the most important ones!

  • Common Errors in Undergraduate Mathematics by Eric Schechter
    Although this document is a bit on the long side, you should read at least some of it carefully -- you'll do better in your math classes because of it. We encourage you to pay particular attention to the sections: bad handwriting, all of the algebra errors, stream-of-consciousness notations, and going over your work.

  • Math 41 Teaching Staff Office Hours
    Your first resource for help outside of class meetings should be the course instructors and teaching assistants. You are encouraged to attend any of their office-hour sessions, not just those for your lecture or section leader, and no appointment is necessary at the times posted. In office hours we welcome any kind of question; we are here to help you and ready to explain the same thing as many times as necessary. You can also email us, but keep in mind that questions in office hours are answered more quickly and more clearly.

  • Free Tutoring at the Center for Teaching & Learning (runs Sunday, Sep. 29 through dead week)

  • Evening Tutoring by SUMO undergraduate members (free, but priority goes to Math 50-series students)

  • Math Department Web Page

  • Math 41A students are part of the ACE program, short for "Accelerated Calculus for Engineers." More information about the program can be found here.

  • Precalculus at Stanford
    This online learning tool (not for credit) has been developed by the Mathematics Department to help you review and acquire the skills you will need to enter a single variable calculus course sequence. (Remember that due to its accelerated pace, Math 41 demands strong mastery of precalculus material.)

  • Statement from the Registrar concerning students with documented disabilities:
    "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."

  • Honor Code and Fundamental Standard
    By Math Department policy, any student found to be in violation of the Honor Code on any assignment or exam in this course will receive a final course letter grade of NP.

  • Statement from Undergraduate Advising and Research concerning the special provision for fifth-week switch to Math 19:
    "Any student registered for either MATH 41 or MATH 41A who wishes to switch to MATH 19 after the Add/Drop Deadline may do so by submitting a Petition to Change Course Enrollment no later than 5:00 pm on Friday, October 24, 2014. Students will receive full credit for MATH 19 (3 units) upon earning a passing grade for that course. (Students switching from MATH 41A to MATH 19 may also add the 1-unit ACE course EE 191A, before the above date.)
    "Note: Because of the discrepancy in units between either MATH 41 (5 units) or MATH 41A (6 units), and MATH 19 (3 units), students should be advised to consider the possible impact this change may have on their university enrollment requirements. For this reason, students switching from either MATH 41/41A must meet with a UAR Advisor.
    "Specifically, students should complete the Petition to Change Course Enrollment form in the following manner:
    1. Complete the personal information section.
    2. Select 'Section change' and enter the information for both courses in the Change Requested section.
    3. Obtain signature from the instructor of the new course, MATH 19. This may require advance notice of 1-2 days, so prompt attention to this is imperative. [Click to contact Math 19 instructor] (Students switching from MATH 41A may also submit a separate petition form to request a Late Add for EE 191A at 1-unit, signed by Professor Brad Osgood.)
    4. Sign the form(s).
    5. Meet with an Advisor from the office of Undergraduate Advising and Research to discuss the situation and obtain the Advisor's signature.
    6. Submit the form to VPUE in the office of Undergraduate Advising and Research (UAR) by 5:00pm, October 24, 2014.
    "Students will not need to write a statement regarding why they wish to submit the petition. But they will need to obtain the instructor's signature, as well as the signature of a UAR Advisor. The request will be routinely approved and rather than a withdrawal with the notation of 'W,' MATH 41 or MATH 41A will be dropped from the student's record and MATH 19 (and EE 191A, where appropriate) will be added. Students should be directed to speak with their new MATH instructor regarding the grading policy for the MATH Switch."
  • Additional details concerning switch to Math 19:
    When switching to Math 19, all of your grades from Math 41 will be deleted. You will be excused from all work from Math 19 that was due before you enrolled in Math 19; your final grade in Math 19 will be computed using the work turned in during the rest of the quarter. In particular, when necessary, the weight of the first midterm will be made up by increasing the weights of the pre-quizzes, homework, second midterm, and final exam proportionally to their original weight in Math 19. Note that Math 19 does not have a discussion section. Please see the Math 19 course website for more details on that course, and please contact the Math 19 instructors listed there if you have additional questions.
    To ensure that you can receive the signature of the Math 19 instructor in time for the UAR deadline listed above, you must email the Math 19 instructor for permission by 5:00pm on Thursday, October 23rd, 2014. In your email, you must include the following:
    • Your full name
    • The Math 19 lecture you wish to enroll in. To choose your lecture, you can visit the Math 19 course website for a list of lectures offered, along with the lecturer contact information. Please note that by the fifth week some of the lectures might be full; if possible note a second choice in case your first-choice lecture is full and otherwise state clearly that this is the only time slot you are able to attend. Make sure to send your email to the instructor of your first-choice lecture.
    • Your SUNetID (for example "gocard12") and your student ID number (for example "05555555")
  • Autumn 2014 -- Department of Mathematics, Stanford University