Math 13: Multivariable Calculus

Spring 2019


Instructors and Lectures information
Instructor Rosa Orellana (Section 01) Sara Chari (Section 02) Warren Lord (Section 03)
Lecture MWF 10:10 - 11:15 MWF 12:50 - 1:55 MWF 11:30 - 12:35
x-Hour Thursday, 12:15-1:05 Tuesday, 1:20-2:10 Tuesday, 12:15-1:05
Classroom KH006 KH006 KH120
Email Rosa Orellana Sara Chari Warren Lord
Office Hours T. 11:00 - 12:30,
Th. 1:10 - 2:30
and by appt.
M. 2:00-3:30,
Th. 10:00am-11:30
M. 9-10:30
M 12:45-1:30,
W. 12:45-1:30
Office 319 Kemeny 213 Kemeny 310 Kemeny
Course Description and Prerequisites
  • Prerequisites: Math 8 is a prerequisite.

  • Course Description: Multivariable calculus is the branch of calculus that studies functions of more than one variable, or vector-valued functions. In Math 8 you learned about taking partial derivatives. Now we turn to integration. We will learn the method of iterated integrals to integrate functions in several variables. Partial derivatives and multiple integrals are the generalizations of derivative and integral that are used in one variable calculus. The Fundamental Theorem in one variable calculus relates integrals to derivatives. The main theorems in multivariable calculus are generalizations of this theorem. Green's theorem generalizes the Fundamental theorem to two dimensions. Another important theorem is Stokes's theorem that relates surface integrals to line integras. Multivariable calculus is used in many fields of natural and social science and engineering to model and study high-dimensional systems that exhibit deterministic behavior.
  • "Mathematics is not for spectators; in order to gain in understanding, confidence, and enthusiasm one has to participate." M.A. Armstrong

  • "Calculus Early Transcendentals Multivariable", by Rogawski & Adams, 3rd Edition, ISBN: 978-1464171758

  • Exams
    DateTime Location
    Mid #1 Wed., April 17 5:00-7:00 PM Carpenter 013
    Mid #2 Wed., May 8 5:00-7:00 PM Dartmouth Hall 105
    Final Sat., June 1 11:30 - 2:30 PM Silsby 028

    The course grade will be computed as follows:

    Percent of Final Grade
    WebWork 5
    Midterms 50 (25 each)
    Homework 10
    Participation 5
    Final Exam 30

    Students will be graded on class participation. Unfortunately, coming late to class may disrupt small group discussions, and so this will have to be reflected in the class participation grades of students who habitually come late to class. Of course it is difficult to participate if one does not come to class at all, and so habitual absence will also be reflected in the class participation grade.
    Homework Policy
      Written Homework: Written homework assignments will be assigned once a week and will be posted on the homework page and it will be collected once a week every Wednesday. No late homework will be accepted. However, the lowest homework grade will be dropped, so if you have to miss a homework assignment you can drop that score. Please do not ask for extensions on the homework.
    • Check the homework page for due dates for the written homework.
    • Unexcused late and missing papers count zero. It is your responsibility to keep track of your homework grades.
    • Homework is to be written neatly using both sides of 8 1/2 x 11 inch paper. Do not use paper from a spiral notebook unless you can tear off the ragged edge. All papers are to be stapled.
    • Use English. If you can't read your solutions aloud as fluently as if you were reading a textbook, try using nouns and verbs in your write ups!
    • If you do not follow this guidelines, your written homework will be returned to you ungraded.
      WebWork: The daily web-based problems can be accessed via the WeBWorK homepage. See also the WeBWorK login containing a FAQ and quick start guide.

      It is highly recommended that you keep a notebook in which you write up your WeBWorK homework (including your work as well as the answers). Then when you are studying for exams, you will have a record of your work to which to refer.

      WeBWorK assigned from each class is due at 10:00pm the day of the next class.

    Our graduate teaching assistants Lizzie Buchanan will run tutorials Tuesday, Thursday, and Sunday from 7:00-9:00pm in Kemeny 007, focusing on answering your questions as you work through the homework problems. You can get further explanations about the concepts, or ask for help with specific practice problems. Tutorials are open to all Math 13 students. You don't need an appointment.

    Past students have found these tutorials to be immensely helpful!

    Other Outside Help:

    • Office Hours: Please feel free to meet with us during office hours (or by appointment).
    • Peer Tutoring: The Tutor Clearinghouse of the Academic Skills Center provides one-on-one peer tutoring.
    • Study Group: We encourage you to work with other people in the class. It will be more fun!
    Honor Principle

    Academic integrity is at the core of our mission as mathematicians and educators, and we take it very seriously.

    Students are encouraged to work together to do homework problems. What is important is a student's eventual understanding of homework problems, and not how that is achieved. However, when the student writes the solution to the homework, he/she should write his/her own understanding of the problem. It is not allowed to read someone else's solution to write yours. It is also not allowed to use a computer calculator (such as Wolfram Alpha).

    The honor principle on homework: What a student turns in as a homework solution is to be his or her own understanding of how to do the problem. Students must state what sources they have consulted, with whom they have collaborated, and from whom they have received help. It is a violation of the honor code to copy solutions from problems posted on the web or book or any other source. The solutions you submit must be written by you alone. Any copying (electronic or otherwise) of another person's solutions, in whole or in part, is a violation of the Honor Code. For example, it is a breach of the honor code to read the solutions of someone else in order to write your solution.

    The honor principle on exams: Students may not give or receive assistance of any kind on an exam from any person except for the professor or someone explicitly designated by the professor to answer questions about the exam. The use of electronic devices is forbidden during an exam, in particular students shouldn't be checking their phones during bathroom breaks.

    If you have any questions as to whether some action would be acceptable under the Academic Honor Code, please speak to me I will be glad to help clarify things. It is always easier to ask beforehand than to have trouble later!
    Disabilities, Mental Health and Religious Observances
  • Disabilities: Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Hall, Suite 125, 646-9900). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to their professor. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.
  • Mental Health: The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean (, Counseling and Human Development (, and the Student Wellness Center (

  • Religious Observances: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with your instructor before the end of the second week of the term to discuss appropriate accommodations.

  • Page created and maintained by R. Orellana