MATH  231 - Calculus of Several Variables

Penn State University - University Park campus

Spring 2008 Syllabus


COURSE DESCRIPTION:   Analytic geometry in space; partial differentiation and applications. (from the Penn State Blue Book)

PREREQUISITES: MATH 141 or MATH 141H. Students who have passed MATH 230 or MATH 230H may not schedule this course. 

TEXTBOOK:  Calculus, Fifth Edition, by James Stewart, published by Thomson (Brooks/Cole).

COURSE COVERAGE: We will cover Chapters 13, 14, and 15 from the text. This includes vectors and how to multiply them, defining lines and surfaces with equations, curvilinear coordinates, calculus of vector functions, and partial derivatives.

CALCULATORS: A graphics calculator is useful as a study and learning tool when used appropriately. However, calculus is a collection of ideas which are not mastered through calculator skills only. Note that no calculators are allowed on the  midterm and final examinations.

HOMEWORK AND QUIZZES: The section instructor will provide his/her policy as a supplement to this syllabus.

MIDTERM EXAMINATION: One 75-minute evening examination will be given during the semester. NO books, notes, or calculators may be used on the examination. Students must bring their University ID card to the exam. The examination will be given from 6:30 to 7:45 PM on the following date:

Midterm Examination: Wednesday, March 5, 2008

Information on the location will be announced at a future date, and may also be found on the bulletin board outside 104 McAllister Building.

IMPORTANT WARNING: Before leaving the examination room, students must make sure that they have "bubbled" their correct student ID number and the test version in their scantron sheets. There will be 5 points penalty if the scantron sheet is not correctly coded and students will receive NO SCORE until the error is corrected.

CONFLICT EXAMINATIONS: For the midterm examination, there is a conflict exam from 5:05 to 6:20 PM on the same night as the regular examination. If students have a conflict with the regular examination time, such as another exam, they may sign up in room 104 McAllister to take the conflict examination. Students who have a valid reason for taking the conflict examination need to sign up by 48 hours before the examination date. The room for the conflict examination is on the top of the sign up sheet. Students who have not signed up for the conflict examination will not be allowed to take it. Students must bring their University ID to the conflict examination. The ID will be checked by the proctor. Although the conflict examination will end at 6:20 PM, no student will be permitted to leave the examination room before 6:25 PM. Any student who leaves before 6:25 PM will receive a grade of zero on the examination and will not be allowed to retake it.

MAKEUP EXAMINATIONS: Students who have a valid documented reason, such as a class conflict or illness during both the conflict and regular examination times are permitted to schedule a makeup examination with no penalty. Students who do not have a valid reason for missing the examination, such as forgetting the date, time, or room of an examination, are also permitted to schedule a makeup, but 30 points will be deducted from their score. The makeup examination is given from 6:30 to 7:45 PM in the evening, usually the week after the regular midterm. The exact date will be announced later.

In order to take a makeup examination, students must sign up at 104 McAllister at least one working day before the makeup examination date and pickup a permission slip form at 104 McAllister. They must get the signature from their instructor in the permission slip and bring it to the makeup examination room. The room for the makeup examination is on the top of the sign up sheet. Students who have taken either the regularly scheduled examination or conflict examination are not permitted to take the makeup examination. Students who have not signed up for the makeup will not be allowed to take it. Students must bring their University ID to the makeup examination. The ID will be checked by the proctor. If a student misses both the regularly scheduled examination and the scheduled makeup, it may be possible to take a makeup examination by appointment with his/her instructor only if there is an unavoidable medical emergency. With a valid, verifiable reason, these makeup examinations will be given by the instructor. All such makeup examinations must be scheduled through the instructor with the approval of the course coordinator, and must be completed no later than one week after the scheduled examination.

FINAL EXAMINATION: The final examination in this course will be comprehensive, and will be given during the week of May 5 - 9, 2008. The date and time of the final examination will be announced by the University Registrar midway through the semester. The final examination may be scheduled on any day during this period.  Do not make plans to leave the university before the end of this week. There are two types of conflict examinations, direct and overload. Direct conflicts are two examinations scheduled at the same time. Students with a direct conflict should file for a conflict examination in Shields Building with the University Registrar. Overload examinations are three or more examinations scheduled within a fifteen hour period, from the beginning of the first examination to the beginning of the third examination. Students may elect to take the three or more examinations on the same day if they wish or request a conflict final examination through the University Registrar. Students must file for direct and overload conflict final examinations at the Registrar's Office between February 18th and March 2nd. Conflict final examination can not be scheduled through mathematics department and there will be no sign up sheet at 104 McAllister for final conflict examination.

LATE-DROP: Students may add/drop a course without academic penalty within the first ten calendar days of the semester. A student may late drop a course within the first twelve weeks of the semester but accrues late drop credits equal to the number of credits in the dropped course. A baccalaureate student is limited to 16 late drop credits. The Late Drop deadline for Spring Semester 2008 is Friday, April 11th.






January 15, 17

13.1, 13.2


January 22, 24

13.3, 13.4


January 29, 31



February 5, 7



February 12, 14

13.6; 14.1


February 19, 21

14.2, 14.3


February 26, 28

14.3, 14.4


March 4, 6

Midterm Review; 13.7


March 10 - 14



March 18, 20

15.1, 15.2


March 25, 27

15.3, 15.4


April 1, 3



April 8, 10



April 15, 17



April 22, 24



April 29, May 1

Review for final

COURSE GRADES: The grade for the course is based on a total of 400 points distributed as shown below and the A, B, C, D and F grade levels also are shown below. The plus and minus grades will be determined within the appropriate ranges.

Midterm Examination


Graded homework and quizzes


Final Examination




A ≥ 360, B ≥ 320, C ≥ 280, D ≥ 250

The course grade will be based EXCLUSIVELY on the midterm examination, homework and/or quizzes, and final examination. There is no "extra-credit" work.

DEFERRED GRADES: Students who are unable to complete the course because of illness or emergency may be granted a deferred grade which will allow the student to complete the course within the first six weeks of the following semester. If the student is scheduled for Math 231, then the student must complete the course within 2 weeks of the following semester. Note that deferred grades are limited to those students who can verify and document a valid reason for not being able to take the final examination. For more information see DF grade.

Tutors and The Math Center ~

If you need extra help, a list of (paid) tutors is maintained in the Mathematics Department Undergraduate Office in room 104 McAllister Building. It is available on-line at It is also available through the Undergraduate Studies in Mathematics homepage at This website is a good source for general information about the Undergraduate Mathematics Program at Penn State, as well as information on evening exam schedules, office hours for instructors, sample exams, etc.

There is also free mathematics tutoring available at the Math Center located in 220 Boucke Bldg.  More information is available in this PDF document.

ACADEMIC INTEGRITY: Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University's Code of Conduct states that all students should act with personal integrity, respect other students' dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.

Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others.

"Academic dishonesty includes, but is no limited to, cheating, plagiarizing, . . ., facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person or work previously used without informing the instructor, or tampering with academic work of other students. . . . A student charged with academic dishonesty will be given oral or written notice of the charge by the instructor. If students believe that they have been falsely accused, they should seek redress through informal discussions with the instructor, the department head, dean or campus executive officer. If the instructor believes that the infraction is sufficiently serious to warrant the referral of the case to Judicial Affairs, or if the instructor will award a final grade of F in the course because of the infraction, the student and instructor will be afforded formal due process procedures." From Policies and Rules, Student Guide to the University Policy 49-20.

Based on the University's Faculty Senate Policy 49-20, a range of academic sanctions may be taken against a student who engages in academic dishonesty.  Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures.

QUESTIONS, PROBLEMS, OR COMMENTS: If you have questions or concerns about the course, please consult your instructor first. If further guidance is needed, you may contact the course coordinator whose address is given below.

COURSE COORDINATOR: Dr. Andrew Belmonte, Office: 322 McAllister. Phone: 814-865-2491
E-mail: belmonte At math dot psu d0t edu