Syllabus Math 313 Summer 2017XD

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Calculus III (MATH 313) Summer 2017XD Section 002

[Course Materials] [Homework]

Instructor: Sean Carver, Ph.D., Professorial Lecturer, American University.


  • office location: 107 Gray Hall (before July 17, 2017)
  • office location: Myers 208F (after July 17, 2017)
  • email:
  • office phone: 202-885-6629

Course Description (from department website): Vectors, functions of several variables, partial differentiation, and multiple integrals.

Prerequisite: MATH-222, or permission of department.

Required Text: Calculus: Early Transcendentals, Third Edition, by Jon Rogawski and Colin Adams. W.H. Freeman and Company, New York, NY.

You will need to bring the textbook to class every day, so I recommend buying or renting an e-Textbook from Amazon or Barnes and Noble. The electronic option is also less expensive. In addition to reading the text, you will need the book for homework problems, which we will work in class.

Recommended Text for Optional Projects: CalcLabs with Mathematica: Multivariable Calculus, Fifth Edition, by Selwyn Hollis. Brooks/Cole Cengage Learning, Belmont CA.

Software for Optional Project: Mathematica. Free to American University students and faculty. See me for help installing this software.

Learning Outcomes: At the end of the course, a student will be able to:

  • Graph functions in three dimensions.
  • Compute the dot product and cross product of vectors.
  • Convert from Cartesian coordinates to cylindrical and spherical coordinates.
  • Take partial derivatives, and use these to examine optimization problems.
  • Integrate in two and three variables.
  • Find the line and surface integrals for multivariable functions and vector fields.
  • Apply Green’s, Stokes’ and Gauss’ Theorems.

Rough Outline of Topics:

  • Vectors 12.1–12.2
  • Vector Operations 12.3–12.4
  • Planes and Surfaces 12.5–12.6
  • Three-Dimensional Coordinate Systems 12.7
  • Vector Functions 13.1
  • Calculus of Vector Functions 13.2
  • Arc Length and Speed 13.3
  • Curvature 13.4
  • Functions of Several Variables, Limits and Continuity 14.1–14.2
  • Partial Derivatives, Tangent Planes, and the Gradient 14.3–14.5
  • The Chain Rule 14.6
  • Optimization and Lagrange Multipliers with Applications 14.7–14.8
  • Double and Triple Integrals in Different Coordinate Systems 15.1–15.6
  • Vector Fields 16.1
  • Line Integrals and the Fundamental Theorem for Line Integrals 16.2–16.3
  • Surfaces and Surface Integrals 16.4–16.5
  • Green’s and Stokes’ Theorem with Applications 17.1–17.2

Office Hours: Students are strongly encouraged to come to office hours if they need or want help.

  • Until July 17, 2017, my office is Gray Hall, Room 107.
  • After July 17, 2017, my office is Myers, Room 208F.

Office hours are TENTATIVELY scheduled as follows: (may be adjusted throughout the semester)

  • Monday, Tuesday, Thursday: 12:30 PM TO 1:30 PM.
  • Saturday: 12:30 PM TO 3:30 PM

NOTE: If you would like to come to office hours on a regular or irregular basis and you have a compelling reason why you cannot make it during the hours listed above, please send me an email. I cannot guarantee that I will be able to find a time that works (this summer will be a very busy one for me), but I will try.

Class times and locations:

  • Section 002: Monday, Tuesday, Thursday: 5:30 PM TO 8:10 PM, East Quad Building, Room 14.

Important Dates:

  • Monday, July 3, First Day of Class
  • Tuesday, July 4, Independence Day, no class, university offices closed.
  • Thursday, July 13 (tentative), Optional Project Proposal Due
  • Thursday, July 27 (tentative), Optional Project Update Due
  • Tuesday, August 1, Substitute Instructor, while Dr. Carver presents at the Joint Statistical Meetings in Baltimore.
  • Thursday August 10, Final Exam, Optional Projects Due, and Last Day of Class

Optional Extra-credit Projects: These will be done in Mathematica. Details to follow.

Tentative grading scheme:

Homework 50%
Final Exam 50%
Extra Credit Project + 0-3%

Class Etiquette: Please give the class your full attention and refrain from talking, texting, surfing the web, and similar distractions. If it is clear to other students that you are not paying attention, it will be harder for them to pay attention to me. This statement is true in general, but it is especially true if you are talking. Also, it can also be harder for me to give good lectures, when it is clear that not everyone is paying attention. Like you, your classmates are paying a lot of money to be here. Have some respect for your fellow students! Otherwise you are negatively impacting their educational experience, which isn't fair to them. If you need to attend to something urgently, it is OK to excuse yourself from the classroom. Please be warned that if people are not following this request, I may reread this statement to the class.

This summer, as classes are 2 hours and 40 minutes long, expect a 5-10 minute break about mid-way through the evening.

Please participate in class by asking questions when you do not understand something. Invariably other students benefit from these questions. Please engage in discussions, and please engage with the class, generally. I find it easier to give good lectures when students are asking questions, and engaging with the material.

Academic Integrity: Cheating is not acceptable and will not be tolerated. Consider this: in subtle ways, cheating to get a better grade on an exam can result in lowering the grades of some of your classmates. Certainly this is true when a specific curve is used to assign grades. Even when I don't use curves explicitly, they can be implicit in decisions about writing and grading exams. As required by the policy of American University, I will report all suspected cases of cheating to the Dean's office who will proceed to investigate and adjudicate the issues. Cheating is giving or receiving unauthorized assistance on homework or exams, from other students or other people, from notes, from books, or from the web. When inappropriate copying between students is caught, both parties may be culpable. You may work together on homework, but you must write up the work you turn in, and the work you turn in must reflect your own understanding of the material.

Public Service Announcement: A representative of AU's Students Against Sexual Violence (SASV) approached me and asked me to include on my syllabi a list of resources available for survivors of sexual assault and their friends. While sexual violence is by no means the only challenge faced by students, I agree that this issue merits particular attention, so I am honoring her request by attaching the list she gave me:

Sexual Assault Resources

  • It’s never the survivor’s fault. There are many people you can talk to if you or someone you care about has been sexually assaulted:
  • AU's Sexual Assault Prevention Coordinator Daniel Rappaport (
  • AU's Coordinator for Victim Advocacy Sara Yzaguirre (
  • DC SANE Program (Sexual Assault Nurse Examiner) 1-800-641-4028
  • The only hospital in DC area that gives Physical Evidence Recover Kits (rape kits) is Medstar Washington Hospital
  • DC Rape Crisis Center: 202-333-7273
  • Students found responsible for sexual misconduct can be sanctioned with penalties that include suspension or expulsion from American University, and they may be subject to criminal charges
  • If you want to submit a formal complaint against someone who has sexually assaulted you, harassed you, or discriminated against you based on your gender identity or sexual orientation, you can do so online at, or contact the Dean of Students at or 202-885-3300. These are Title IX violations, and universities are legally required to prohibit these actions.
  • Resources on campus that are required to keep what you tell them confidential are Daniel Rappaport, Sara Yzaguirre, ordained chaplains in Kay, and counselors at the counseling center. (OASIS may also belong here but it didn't exist when this list was created.)