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Calculus III

MATH 227 Section 004

Spring 2016, Lecture

Dr. Andrew Lewis


UA Course Catalog Prerequisites

Prerequisite(s): MATH 146 or MATH 126 or MATH 132.

Course Description

UA Course Catalog Information


Core Designations:

Required Texts

UA Supply Store Textbook Information


The supply store listing is a bit of a mess, as the textbook is available in numerous forms.  You must have two things for this course:

  • Acess to WebAssign.  You can buy a standalone access code, get one bundled with a physical textbook, or pay directly through the WebAssign website.
  • Either a physical clicker, or a license for ResponseWare, which is an app you can use on your phone instead of having a physical clicker.  

Note that I did not include a physical textbook in this list.  When you pay for WebAssign, you get access to an eBook version of the textbook.  Most students are happy to just use this.  If you would like a physical textbook, the SupeStore has a number of options as you can see above.

Outline of Topics

We will cover chapters 10-13.

Student Learning Outcomes

At the conclusion of this course, students will 

  1. Be able to perform routine operations on vectors and understand how these relate to curves and surfaces.
  2. Be able to perform routine calculations in the differential calculus of functions of several variables (e.g. limits, partial derivatives, etc.).
  3. Be able to compute integrals of functions of several variables.
  4. Understand the basics of vector calculus, including conservative vector fields, computing line and surface integrals, and Green's Theorem and its generalizations.
  5. Be able to apply their multivariable calculus skills to real world problems such as optimization and other science and engineering applications.

Standards Based Grading

This course is graded by a methodology called Standards Based Grading.  There is a list of 26 learning standards for this course (available in Blackboard), divided into core standards and supplementary standards.  Rather than receiving a numerical score on an assessment (e.g. exam or quiz), you will instead be scored as either Mastered or Not yet mastered on each standard that is on that assessment.

Standards will be assessed multiple times throughout the semester.  Unlike most classes, these numbers will not be averaged.  Instead, your grade will be computed in a way that rewards growth and continued mastery of the material.  At the end of the semester, for each standard you will be scored as Not mastered, Mastered, or Continued mastery.  These are defined as having demonstrated mastery on 0, 1, or 2+ assessments, respectively.



One key aspect of this system is constant reassessment.  This can occur in a couple of different ways.  A standard can be reassessed explicitly on another quiz or exam.  Secondly, a standard may be assessed again as part of a problem designed to primarily assess a different standard (for an example from Calculus I, a problem assessing optimization would also necessarily assess your differentiation skills).  Additionally, you can reassess a standard during my office hours.  This reassessment can take several forms, depending on the situation:

  • If possible, I'll make up a problem or two on the spot and have you work it.
  • I might ask you to come back the next day so I can think up a good problem for you to work.
  • I might simply ask you to explain the concept to me on the chalkboard.

A few caveats to office hour reassessments:

  • In order to reassess a standard in my office, you must have completed the WebAssign homework corresponding to that standard.
  • Reassessments are given at the discretion of the instructor, they are not guaranteed opportunities.  
  • If you come in for help on a standard, you should come back at a later time to reassess it after you have practiced it some more on your own.  Most WebAssign problems have a "Practice another version" button which is a great source for extra practice.
  • Reassessments opportunities may be limited by practical considerations like time, particularly towards the end of the semester.  In general, you should not plan on being able to assess more than one or two related standards per visit to my office.
  • You can certainly demonstrate continued mastery of a standard in my office hours; however, to qualify as continued mastery it must be at least a week after you first mastered the standard.

The goal is to view assessments as opportunities for you to demonstrate mastery.



Unfortunately, this grading system is far too sophisticated for Blackboard's gradebook to handle.  So you will periodically receive an automatic email from me detailing your current progress in the course.  If you have any questions about how to interpret where you stand, come to my office hours to discuss.


We will be using WebAssign ( for homework assignments.  If you did not purchase an access code bundled with your textbook, you will need to purchase one from the bookstore or directly from WebAssign.  I have created a WebAssign account for each student; you should be able to log in simply by clicking the link from our course section in Blackboard.

Homework will be due at noon on most Wednesdays and Fridays. You should plan on working on homework every day after class. I have organized the assignments to correspond to the learning standards; for this reason, some assignments are longer than others, and sometimes you might have two assignments due on the same day, depending on how quickly we work through the material.

Grading notes:

  • You will have an unlimited number of attempts on each problem, so your homework grade is merely a function of how much effort you want to put into it.  
  • There is a 5% bonus if you answer correctly on the first attempt.  
  • There is another 5% bonus if you complete the assignment at least 12 hours early.
  • If you do not complete the assignment by the due date, extensions are granted "no questions asked" at a 20% penalty--I'd rather you do your assignments on time, but doing them eventually is better than not doing them at all.  Use the "request an extension" button in WebAssign.  For the first two weeks after an assignment is due, extensions will be automatically granted.  After that, you instead have to hit "manual extension" and I have to manually approve it. The penalty is applied on a per-problem basis, so it only affects problems you did not correctly answer by the deadline; thus the extension can only improve your score.  
  • At the end of the semester, I will drop your four lowest homework scores in computing your homework grade.

It is your responsibility to ensure access to a working computer to complete these assignments.  If your personal computer or network is having problems, it is expected that you will be able to use one of the numerous labs on campus to complete the assignment.  

Exams and Assignments

Most weeks, we will have a short quiz on Friday designed to assess one or two standards.  Additionally, we will have four longer assessments ("exams") tentatively scheduled for the following dates (all Fridays):

Exam 1 February 5
Exam 2 February 26
Exam 3 March 25
Exam 4 April 22
Final Exam May 6, 11:30-2:00

Grading Policy

At the end of the semester, your grade will be computed in the following manner.  Note that for each grade you must meet every criteria listed. 

To earn a letter grade of ... ... you should at least
  • Demonstrate continued mastery on each core standard;
  • master 12-15 supplementary standards
  • demonstrate continued mastery on 10-15 supplementary standards;
  • have a 75% clicker participation score;
  • have a 95% homework grade.
  • Master each core standard;
  • demonstrate continued mastery on 5-10 core standards;
  • master 8-15 supplementary standards;
  • demonstrate continued mastery on  5-15 supplementary standards;
  • have a 75% clicker participation score;
  • have a 85% homework grade.
  • Master 10 core standards;
  • master 8-15 supplementary standards;
  • have a 75% clicker participation score;
  • have a 75% homework grade.
  • Master 8 core standards;
  • have a 50% clicker participation score;
  • have a 50% homework grade.
  • not fit in the above categories.

Within each letter grade, plus and minus will be assigned based on where you fit in the ranges.  A minus will be given for being on the lower end of the ranges, while a plus will be given for being on the upper end of the ranges.


One fundamental aspect of my teaching philosophy is the axiom that mathematics is not a spectator sport.  For this reason, not only is attendance mandatory for this course, but you are also required to actively participate in learning mathematics in the classroom.  Passively observing a lecture and blindly taking notes are not active participation; instead, focus on understanding what is going on, asking questions to clarify misconceptions, and working through the examples in real time with the class.

One tangible way to foster this participation is by working on the clicker questions I scatter through the lectures.  Each student is required to bring a working clicker to class each day.  Most days, you will be asked to use them to respond to some questions.  You will not be graded for correctness, but on if you responded or not.  You will receive full credit for the clicker portion of your grade if you answer 75% of the clicker questions over the semester.  There will be no makeups for clicker questions for any reason except in the case of a long term excused absence (i.e. more than 25% of the class).  Temporary absences for any reason, clicker malfunctions, dead batteries, etc. are accounted for in the "free" 25%.

Policy on Missed Exams & Coursework

Exams and quizzes can only be made up in the event of illness (with a doctor's note), or other emergent situation (with appropriate documentation).  

Attendance Policy

Attendance is required for this course, and is measured implicitly by clicker participation.

Calculator Policy

No calculators will be permitted on the exams (they will not be necessary).  You are free to use whatever calculator you like for the homework, but I encourage you to work without one.

Severe Weather Guidelines

The guiding principle at The University of Alabama is to promote the personal safety of our students, faculty and staff during severe weather events. It is impossible to develop policies which anticipate every weather-related emergency. These guidelines are intended to provide additional assistance for responding to severe weather on campus.

UA is a residential campus with many students living on or near campus. In general classes will remain in session until the National Weather Service issues safety warnings for the city of Tuscaloosa. Clearly, some students and faculty commute from adjacent counties. These counties may experience weather related problems not encountered in Tuscaloosa. Individuals should follow the advice of the National Weather Service for that area taking the necessary precautions to ensure personal safety. Whenever the National Weather Service and the Emergency Management Agency issue a warning, people in the path of the storm (tornado or severe thunderstorm) should take immediate life saving actions.

When West Alabama is under a severe weather advisory, conditions can change rapidly. It is imperative to get to where you can receive information from the National Weather Service and to follow the instructions provided. Personal safety should dictate the actions that faculty, staff and students take.

The Office of University Relations will disseminate the latest information regarding conditions on campus in the following ways:

  • Weather advisory posted on the UA homepage
  • Weather advisory sent out through UA Alerts to faculty, staff and students
  • Weather advisory broadcast over WVUA at 90.7 FM
  • Weather advisory broadcast over Alabama Public Radio (WUAL) at 91.5 FM
  • Weather advisory broadcast over WVUA-TV/WUOA-TV, and on the website at WVUA-TV Home Team Weather provides a free service you can subscribe to which allows you to receive weather warnings for Tuscaloosa via e-mail or cell phone. Check for more details and to sign up for weather alerts.

In the case of a tornado warning (tornado has been sighted or detected by radar; sirens activated), all university activities are automatically suspended, including all classes and laboratories. If you are in a building, please move immediately to the lowest level and toward the center of the building away from windows (interior classrooms, offices, or corridors) and remain there until the tornado warning has expired. Classes in session when the tornado warning is issued can resume immediately after the warning has expired at the discretion of the instructor. Classes that have not yet begun will resume 30 minutes after the tornado warning has expired provided at least half of the class period remains.

Policy on Academic Misconduct

All students in attendance at The University of Alabama are expected to be honorable and to observe standards of conduct appropriate to a community of scholars. The University of Alabama expects from its students a higher standard of conduct than the minimum required to avoid discipline. At the beginning of each semester and on examinations and projects, the professor, department, or division may require that each student sign the following Academic Honor Pledge: “I promise or affirm that I will not at any time be involved with cheating, plagiarism, fabrication, or misrepresentation while enrolled as a student at The University of Alabama. I have read the Academic Honor Code, which explains disciplinary procedure resulting from the aforementioned. I understand that violation of this code will result in penalties as severe as indefinite suspension from the University.”

See the Code of Student Conduct for more information.

Emergency Contact Information

UA's primary communication tool for sending out information is through its web site at  In the event of an emergency, students should consult this site for further directions. Additional course information will be posted using Blackboard Learn.

Disability Statement

If you are registered with the Office of Disability Services, please make an appointment with me as soon as possible to discuss any course accommodations that may be necessary.

If you have a disability, but have not contacted the Office of Disability Services, please call (205) 348-4285 (Voice) or (205) 348-3081 (TTY) or visit 1000 Houser Hall to register for services. Students who may need course adaptations because of a disability are welcome to make an appointment to see me during office hours. Students with disabilities must be registered with the Office of Disability Services, 1000 Houser Hall, before receiving academic adjustments.

UAct: Ethical Community Statement

The University of Alabama is committed to an ethical, inclusive community defined by respect and civility.  The UAct website ( provides a list of reporting channels that can be used to report incidences of illegal discrimination, harassment, sexual assault, sexual violence, retaliation, threat assessment  or fraud.

UAct: Ethical Community Statement

The University of Alabama is committed to an ethical, inclusive community defined by respect and civility. The UAct website ( provides extensive information on how to report or obtain assistance with a variety of issues, including issues related to dating violence, domestic violence, stalking, sexual assault, sexual violence or other Title IX violations, illegal discrimination, harassment, child abuse or neglect, hazing, threat assessment, retaliation, and ethical violations or fraud.