Math 20
Autumn 2019

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Course Description and Prerequisites

Math 20 is a 3 credit course in introductory calculus, second in the Math 19-20-21 sequence. The class provides an introduction to single variable integration, including many integration techniques and applications to geometry. We will also explore differential equations and parametric equations. A one-page summary of the important information from this webpage can be found here, and a more detailed breakdown of the schedule and homework can be found at the Course Schedule page.

Students are expected to have a strong foundation in precalculus, such as comfort with the concept of functions, equations of lines, trig and inverse trig, ability to manipulate algebraic expressions, factoring polynomials, etc. Further, students are expected to be familiar with the material of Math 19. In particular, students should be comfortable with the idea of a limit, the idea of the derivative, and taking derivatives of a wide range of functions. Further, students should know (and know when to apply) the product rule and chain rule. Students who are unsure of their background should see Dr. Lucianovic as early as possible. Students who want to brush up on their precalculus skills can find more resources on this page.


  • Dr. Mark Lucianovic
    Office: 380-382S
    Email: mark.lucianovic(at)stanford(dot)edu
    Lectures: MWF 10:30-11:20, 11:30-12:20 (both in 380-380W)

Course Assistants

  • Shintaro Fushida-Hardy
    Office: 380-381B
    Email: sfh(at)stanford(dot)edu

  • Juan Carlos Ortiz
    Office: 380-381H
    Email: jcortiz(at)stanford(dot)edu

Office Hours and Tutoring

You are encouraged to attend the office hours provided by any of the teaching staff. No appointment is necessary, just drop in at the scheduled office hours with your questions!

The scheduled office hours for any given week can be found on the Office Hours page. Note that they might change slightly from week to week so it's always a good idea to check both the time and location before walking all the way across campus.

The Stanford University Mathematics Organization (SUMO) works with the Stanford Math department to provide free drop-in tutoring services for Math 20. The tutors are Stanford undergraduates available to answer any questions you have about the material and homework in Math 20. Just show up and the tutors will help you out. Starting the second week of each quarter, SUMO tutoring for Math 20 is on Tuesdays and Thursdays from 6pm-10pm in Room 380-381T on the first floor of the Math department. Tutoring continues through Dead Week but excludes university holidays.

The Office of the Vice Provost for Teaching and Learning offers free drop-in and individual appointment tutoring in the following Math courses: Math 19, 20, 21, 51, 52, 53. To schedule an individual appointment, visit To view our drop-in schedule and to view information about tutoring for other courses, visit


The textbook for this course is Calculus: Single Variable, 7th edition, by Hughes-Hallett, Gleason, McCallum, et al. (This is the text for Math 19 and Math 21 as well.) This course mainly focus on topics from chapters 5, 6, 7, 8, and 11. Most homework exercises and suggested reading are taken from the book, so you should have a copy.

For your convenience the textbook is available for purchase at the Stanford bookstore. However, the Stanford bookstore is charging a very high price for the textbook. Please read the following advice on how to obtain the textbook at a fair price.

Affordability of Course Materials

All students should retain receipts for books and other course-related expenses, as these may be qualified educational expenses for tax purposes. If you are an undergraduate receiving financial aid, you may be eligible for additional financial aid for required books and course materials if these expenses exceed the aid amount in your award letter. For more information, review your award letter or visit the Student Budget website.

Attending lecture

Attendance is not required, yet regular attendance is important to your success in this class. A student who misses class is responsible for finding out what was discussed and learning the material that was covered on that day. The teaching team is not responsible for re-teaching material missed by a student who did not attend class regardless of the reason for the absence, though we are willing to address any points of confusion in office hours (whether you were in class or not).

Students are strongly encouraged to attend the lecture they are registered for. We recognize that schedules can vary week-to-week, so you are invited to attend whichever lecture works.


Your grade will be based on the following components:

  • Homework: 15%
  • Midterm Exam 1: 25%
  • Midterm Exam 2: 25%
  • Final Exam: 35%

There are no predetermined numerical cutoffs for letter grades.


There will be weekly homework posted on the homework page.

Your solutions to the assigned homework will be graded and returned to you.

Homework will be due every week on Wednesday at 10am, starting on October 2. For details about handing in your homework, see the homework page.

Late homework will be not be accepted under any circumstances; however, you will be provided an opportunity to have your lowest homework score dropped at the end of the quarter.

Homework and the Honor Code

You are bound by the Stanford Honor Code for all work submitted for Math 20, including the homework assignments. For homework, we encourage you to use your book and all your notes, come to office hours, talk with any tutor(s) you have, and collaborate with your peers. We believe that thinking about math and conversing about math is an important part of the learning process.

However, we expect that the work you submit reflects your understanding of the problem and how to solve it. If you work on a problem with someone else, DO NOT copy their solution and instead, write it up on your own.

Finding a solution off of the internet, copying it without thought onto your homework, and then submitting it for credit is a violation of the Stanford Honor Code and will be addressed as such.


There will be two EVENING midterm exams and a university scheduled final exam. Most of the problems on the exams will be similar to the problems in the weekly homework, but there will always be some harder problems. The material covered by each exam is given by the suggested reading and homework, including the practice problems.

All exams for Math 20 this quarter are closed-book, closed-notes, with no calculators or other electronic aids permitted. Individual exams will be neither curved nor scaled.

The evening midterm dates are given below; it is your responsibility to verify right now that you can attend these exams. Please contact Dr. Lucianovic as soon as possible if you have a permissible schedule conflict (e.g., course or competition) with a midterm. In any case, if you need to reschedule the exam to an alternate sitting (which by department policy must be slightly earlier on the same day), you must do so no later than two weeks before the exam. The date and time of the final exam are set by the University and cannot be changed.

You will have assigned seating for exams. The seating chart will be posted in the exam classroom on the day of the exam; you are responsible for arriving a few minutes early to find your seat before the exam starts. Failure to sit in your assigned seat will be considered a breach of the Stanford Honor Code and be handled accordingly.

  • Midterm 1: Wednesday, October 16, approximately 7:00pm
  • Midterm 2: Wednesday, November 6, approximately 7:00pm
  • Final exam: Tuesday, December 10, 12:15pm-3:15pm

For more information, see the Exams page. See also the exam-studying advice in Tips for a Successful Calculus Course.

Office of Accessible Education accommodations

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, URL:

Once you have done so, please let Dr. Lucianovic know as soon as possible so that proper accommodations can be made. For accommodations on exams, Dr. Lucianovic must have your letter from OAE no later than two weeks prior to the exam. Otherwise, we may not have sufficient time to make the accommodations.

Student Athletes

If you are involved in a sport which may require you to travel this quarter, and especially if you will miss either of the midterms, please let Dr. Lucianovic know as soon as possible so that appropriate accommodations can be made. If you do not let Dr. Lucianovic know at least two weeks in advance of a missed exam, you may be denied the opportunity to take it at an alternate time or on the road. You are also responsible for homework while traveling. See the homework for information about turning in homework.

ACE program

ACE (Additional Calculus for Engineers) is a program run by the School of Engineering for all students (not just prospective engineering majors). More info on ACE is available here, including a link to the application (due Friday of Week 1 at 11:59pm). Only students who have applied and been accepted should attend these sessions, starting Week 3.

Other important policies

  • Extra credit assignments: Occasionally students ask for extra credit in order to improve their grade. While we can recommend additional practice problems, we cannot offer them for credit as it would be unfair to the entire class if only a small number of students were allowed a chance to improve their grade. If you become worried about your understanding and grade in the course, please see Dr. Lucianovic as soon as possible for advice.
  • Calculator policy: Calculators are not used in a systematic way in the Math 19-20-21 sequence. Calculators are not allowed or needed on any of the exams. Occasionally, homework problems may call for the use of a scientific or graphing calculator, and it is fine to use them for this purpose.
  • Honor code policy: 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.

Autumn 2019 -- Department of Mathematics, Stanford University
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