MAC 2313, Section 12, Fall 2016

(Class #09496)

Course page: ON CAMPUS: (this page)
OFF CAMPUS: (with your FSUID username and password)
Professor:Dr Mesterton-Gibbons, or Dr M-G for short
Office:202B Love
Office hours: Please click here. Note that office hours are primarily for personal matters that cannot be addressed in class (as opposed to tutorial help, for which see under Course format and How to study below)
Phone:(850 64) 42580
Main website: Professor M-G's Home Page    Email:
Goal:The purpose of this course is to introduce multivariable calculus and some of its applications
Class meets: In 107 LOV, Mondays and Wednesdays 5:15 p.m.—6:05 p.m., Tuesdays and Thursdays 5:15 p.m.—6:30 p.m.
Text:Stewart,  Calculus: Early Transcendentals/Multivariable Calculus: Early Transcendentals), 7th edition (Cengage, 2012, ISBN 978-1-285-15128-1/978-0-538-49787-4), Chapters 12-16
Credit:5 semester hours
Eligibility: Is your responsibility. You must have the prerequisites listed below, and must never have completed with a grade of C- or better a course for which MAC 2313 is a (stated or implied) prerequisite. Moreover, if you have more than eight hours of prior credit in college calculus, then you must reduce your credit for MAC 2313 accordingly
(i)C- or better in MAC 2312 (Calculus with Analytic Geometry II) or appropriate transfer credit (satisfactory completion of at least eight hours of calculus courses equivalent to MAC 2311 and MAC 2312);   and
(ii) self-motivation and industriousness
My philosophy of learning is perhaps best expressed by the green curve in the diagram below:
For further details, please click here.
Communication: I will send email to your FSU email account on a regular basis. It is your responsibility to check it regularly (or arrange to have my messages forwarded, if you prefer to read your email elsewhere)
Your name:
      I don't know who you are, but because everything works so much better when I do, I would like to learn your name as soon as possible. So, please take a sheet of card stock (or even paper), fold it in half, write your name in large letters on one side and stand it up on your desk so that I can see it. (Write what you want me to call you: if you're a John who likes to be called Fred or a Jane who likes to be called Sue, write Fred or Sue, not John or Jane.) Please bring your nameplate to every class until I have finally learnt your name (which will take significantly longer than it used to take when I started out)
Course format: The course will be based on 21 lectures interspersed by interactive problem solving, on which we will spend much of our time. I will send you each lecture as a PDF file as soon as possible after class. I may edit a lecture at any time—in particular, if I discover an error during class—but if so then I will email you a new PDF, and in any event the most up-to-date version will always be posted here. The text will serve primarily as a source of problems (though it will also be handy for its colored diagrams of surfaces and as a reference). After each period I will set homework for the following period, usually by email. Sometimes homework will include reading the next lecture before we actually cover the material in class. I will always assume that you have both read (not necessarily understood) any assigned reading and have at least attempted (not necessarily completed) a significant and representative sample of any homework problems. Questions may be asked at any time—and should be, if there's anything you don't understand. (Perhaps you have a question that you anticipate being answered by one or more of the problems we work together, in which case, it may well be socially minded not to ask your question at the outset. However, if it turns out that you anticipated incorrectly, then be sure to ask your question before the class is over!)
    In particular, you should understand that the purpose of the lectures is to introduce the essential material. Their coverage is not exhaustive: some of the things I expect you to know will be introduced only when the need for them arises in a problem.
    On Tuesdays and Thursdays, we will attempt to end the formal class period after 55-60 minutes so that the last 15-20 minutes can be devoted to individual tutorial help
Test format: You must write your answers in black or blue ink. If you make a mistake, just cross it out and make a correction (a far more efficient process, by the way, than erasing pencilling). Begin each question (but not subsequent parts of the same question) on a fresh sheet of paper, use one side of the paper only, and have your solutions stapled together in order at the end of the examination (without the question sheet, which is yours to keep). Please do not use dog ears; I will bring a stapler to the classroom. Needless to say, your name must appear on Page 1 of your solutions (as opposed to the question sheet, which you are keeping)
Calculator policy: You are allowed to use a Texas Instruments TI30XA Scientific Calculator or a four-function calculator for classroom tests. The use of any other calculator for a classroom test is strictly forbidden
Grades:Will be based on four classroom tests (20% apiece) and a cumulative final examination (20%). Note that it is not enough merely to produce an answer. The method by which you obtain it must be sound, and clearly demonstrated: show all necessary steps in your method, with enough comments and/or diagrams to convince me that you thoroughly understand. Needless to say, clearly implies legibly.
    Precise cut-off points for A, B and C will be determined by the distribution of grades at the end of the semester, but are likely be in the vicinity of (though perhaps lower than) 90%, 80% and 70%, respectively. In borderline cases of A versus B or B versus C, a smaller number of completely correct solutions will carry more weight than a proportionate number of fragmentary answers; later test scores will carry more weight than earlier test scores; and a record of active participation in class will carry more weight than a record of passive attendance (in that order of relative importance among these three factors). Likewise for borderline cases of C versus D—but in addition, for a given points total, a smaller number of minimally satisfactory solutions will carry more weight than a larger number of lower scores. Plus or minus grades may (or may not) be assigned in a manner consistent with standard University practice.
    Please note that partial credit will be awarded only when part of a solution is completely correct—not when all of a solution is partially correct, whatever that means, if anything. Also note that a grade of I will not be given to avoid a grade of F or to give additional study time. Failure to process a course drop will result in a course grade of F
Scores:A score for a question worth 10 points should be interpreted as follows:
10 Practically perfect
9 Still very good, but lacking—or wrong about—a significant detail
8 Still good, but lacking—or wrong about—significant details
7 Minimally satisfactory. You have—just—managed to demonstrate that you basically understand and are at least capable of getting all details correct (although it clearly did not happen this time)
6 A grade that will not be given
5 Half right in some appropriate sense (e.g., there were two parts, each worth 5 points, and your first part was practically perfect)
1-4 Not even half right and showing little understanding, but some degree of positive effort
0 Zero effort, or submitted in pencil
Test solutions: Will always be posted online posted here (along with the test itself). There are two advantages. First, online solutions make grading far more efficient: instead of writing the same corrections on numerous manuscripts, I simply identify the point(s) at which a solution goes awry. Second, the online tests and solutions together form a test bank for use by students in future years (all accessible to you from the top of this page). I caution you, however: never read my solution to a problem until first of all you have seriously attempted the problem yourself. If you have at least made a serious (and I do mean serious) attempt, then—even if you were unable to complete the problem yourself—you will benefit from reading my solution to it; if not, then not (rather, you will merely form a false impression of how well you understand ... as indicated by the above learning-versus-pain diagram)
Attendance policy:You are expected to attend class regularly, and bear the full responsibility for learning anything covered during any class that you miss. On the other hand, it would be extremely anti-social to attend class if you either have, or are coming down with, a contagious disease. So please keep me apprised (by email) of any illness or other emergency, so that I can make any necessary adjustments (and please make friends within the class as soon as possible if you haven't done so already, so that there is someone you can call upon to borrow notes if the need should arise)
Exam policy: No makeup exams. An absence may be excused given sufficient evidence of exceptional or extenuating circumstances (in which case, extra weight will be attached to the other exams). But you must either have discussed the matter with me (well) in advance; or, in the case of illness, have brought me a note from a physician explicitly stating that you were too ill to attend class on the day in question. An unexcused absence will result in a grade of zero
Etiquette: You are firmly bound by Florida State University's Academic Honor Code. Briefly, you have the responsibility to uphold the highest standards of academic integrity in your own work, to refuse to tolerate violations of academic integrity in the University community, and to foster a high sense of integrity and social responsibility on the part of the University community. Even more briefly, you must neither cheat nor enable others to cheat. The penalties for violations can be severe. Please carefully read the section in the FSU Student Handbook on the Honor Code and official procedures for dealing with students who violate it. If you are in any doubt at all as to what constitutes acceptable behavior in this regard, you should ask me for clarification.
    You are also bound by the ordinary rules and customs of polite behavior that prevail in a civilized society. I assume that you know these rules and customs, and I expect you to comply with them. (In particular, you are not allowed to use a cell phone or otherwise have private conversations with others during class.)
Probable test dates:Thursday, September 22
Tuesday, October 18
Thursday, November 10
Tuesday, December 6
Final: Wednesday, December 14, 5:30—7:30 p.m. in 107 LOV
How to study: There is a lot of material to be covered in this course, so it is important that you keep up from the very beginning, always attempting as many as possible (or as necessary) of the homework problems. If you get stuck, then send me a question by email. As soon as I possibly can, which might be as soon as within half an hour, but might also be a day or two later (I have a life, too, you know), I will reply—not to you, but rather to the class alias (after carefully concealing your identity, just in case you are inexplicably bashful about being perceived as smart enough to ask a question).
    Note, however, the following. First, you must identify yourself (i.e., you remain anonymous to the other students in the class, but not to me) in the body of your message (because your username does not identify you to me, and I don't reply to anonymous email). Second, you should be as specific as possible in describing your difficulty: the more precisely you identify how you got stuck, the more helpful my reply is likely to be
Disabilities:If you have a disability requiring academic accommodations, then not only should you register with the Student Disability Resource Center (SDRC), but also you should bring me written confirmation from SDRC during the first week of class. This and other class materials are available in alternative format upon request.


University Attendance Policy:
Excused absences include documented illness, deaths in the family and other documented crises, call to active military duty or jury duty, religious holy days, and official University activities. These absences will be accommodated in a way that does not arbitrarily penalize students who have a valid excuse. Consideration will also be given to students whose dependent children experience serious illness.

Academic Honor Policy:
The Florida State University Academic Honor Policy outlines the University's expectations for the integrity of students' academic work, the procedures for resolving alleged violations of those expectations, and the rights and responsibilities of students and faculty members throughout the process. Students are responsible for reading the Academic Honor Policy and for living up to their pledge to ". . . be honest and truthful and . . . [to] strive for personal and institutional integrity at Florida State University." (Florida State University Academic Honor Policy, found at

Americans With Disabilities Act:
Students with disabilities needing academic accommodation should:
(1) register with and provide documentation to the Student Disability Resource Center; and
(2) bring a letter to the instructor indicating the need for accommodation and what type. This should be done during the first week of class.

This syllabus and other class materials are available in alternative format upon request.

For more information about services available to FSU students with disabilities, contact the:

Student Disability Resource Center
874 Traditions Way
108 Student Services Building
Florida State University
Tallahassee, FL 32306-4167
(850) 644-9566 (voice)
(850) 644-8504 (TDD)


Free Tutoring from FSU

On-campus tutoring and writing assistance is available for many courses at Florida State University. For more information, visit the Academic Center for Excellence (ACE) Tutoring Services' comprehensive list of on-campus tutoring options—see or contact High-quality tutoring is available by appointment and on a walk-in basis. These services are offered by tutors trained to encourage the highest level of individual academic success while upholding personal academic integrity.

Syllabus Change Policy

Except for changes that substantially affect implementation of the evaluation (grading) statement, this syllabus is a guide for the course and is subject to change with advance notice.


  1. Cartesian coordinates in three dimensions
  2. Surfaces as graphs. Contour maps
  3. Vectors
  4. The dot product and cross product
  5. Functions of three variables
  6. Partial derivatives
  7. The tangent plane and directional derivative
  8. The chain rule and the normal to a surface
  9. Local extrema and saddle points
  10. Constrained optimization
  11. Double integrals
  12. Area and volume as multiple integrals
  13. Integrating with respect to natural coordinates
  14. Motion and properties of space curves
  15. Line integrals
  16. Curl: a measure of rotationality
  17. Surface integrals
  18. The flux of a vector through a triangular surface
  19. Shadow area elements
  20. The divergence theorem
  21. Stokes' theorem

Supplementary Materials

  1. The vector and scalar equations of a plane
  2. A sort of potted geometry of three-dimensional space
  3. Level surface area elements for orthogonal coordinates

Solutions to Problems

Nothing here yet!

Solutions to Tests

First Test Solutions
Second Test Solutions
Third Test Solutions
Fourth Test Solutions
Final Solutions

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