CALCULUS OF VARIATIONS


MAP 4216, Section 01, Spring 2017

(Class #10541)

Calculus of Variations will be taught from the perspective of an applied mathematician, i.e., it will focus on understanding concepts and how to apply them (as opposed to rigorous proofs of existence and uniqueness theorems). The course will introduce both the classical theory of the calculus of variations and the more modern developments of optimal control theory, and is potentially of interest not only to mathematics majors but also to students in the life, management, natural and social sciences
Course page: ON CAMPUS: http://www.math.fsu.edu/~mesterto/CalculusOfVariations.html (this page)
OFF CAMPUS: http://www.math.fsu.edu.proxy.lib.fsu.edu/~mesterto/CalculusOfVariations.html (with your FSUID username and password)
Professor: Dr Mesterton-Gibbons, or Dr M-G for short
Office: 202B Love
Office hours: Please check 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 How to study below)
Phone: (850 64) 42580
Main website: Professor M-G's Home Page    Email:
Goal (long version): To introduce both the classical theory and techniques of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician (focusing on analytic or geometric insight and computational skills, as opposed to rigorous proofs of existence and uniqueness theorems)
Goal (short version): To cause you to understand the text
Class meets: in 107 LOV, Mondays, Wednesdays and Fridays 1:25-2:15 p.m.
Text: Mesterton-Gibbons,  A Primer on the Calculus of Variations and Optimal Control Theory (American Mathematical Society, 2009, ISBN 9780821847725)  Known Errata
Credit: 3 semester hours.
Topics: Fundamental problems, weak and strong extrema, necessary and sufficient conditions, optimal control problems, Pontryagin's maximum principle, and applications.
Prerequisites:
(i) MAP 2302 together with MAA 4226 or MAA 4224 or MAP 4341; or Professor M-G's consent and
(ii) self-motivation and industriousness
My philosophy of learning is perhaps best expressed by the green curve in the diagram below:
 
ALTERNATIVE THEORIES OF LEARNING VERSUS PAIN
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)
Grades: Will be based on four written assignments completed in black or blue ink (and worth 25% apiece)
Grading: Quality of presentation is extremely important, and so there will be penalties (commensurate with degree of infraction) for badly presented work. It is not enough merely to produce an answer: the method by which you obtain it must be sound, and you must show all necessary steps in your method, with enough comments and/or diagrams to convince me that you thoroughly understand. Assignments will be due at the beginning of class on the designated day. Late assignments will be viewed as badly presented, and very late assignments will not be graded (i.e., will achieve a score of zero).
    Minimum scores 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 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 (on the left) or 15 points (on the right) should be interpreted as follows:
10 Practically perfect 15
9 Still very good, but lacking—or wrong about—a significant detail 14
8 Still good, but lacking—or wrong about—significant details 11-13
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) 10
6 A grade that will not be given 9
5 Half right in some appropriate sense (e.g., there were two parts, each worth 5 points, and your first part was practically perfect) 8
1-4 Not even half right and showing little understanding, but some degree of positive effort 1-7
0 Zero effort, or submitted in pencil 0
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 of any illness or other emergency (by email—have, e.g., your best friend contact me if you are too incapacitated yourself), 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).
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). Although you may discuss assignments with others in general terms, the solutions you present must be your very own work ("in general terms" means that discussion is oral and nothing is copied down).
    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.)
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 of the homework problems (even though they do not count directly toward your grade). 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 so 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.

ALL SYLLABI ARE REQUIRED TO INCLUDE THE FOLLOWING STATEMENTS

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 http://fda.fsu.edu/Academics/Academic-Honor-Policy.)

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)
sdrc@admin.fsu.edu
http://www.disabilitycenter.fsu.edu.proxy.lib.fsu.edu/

RECOMMENDED LANGUAGE FOR SYLLABI:

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 http://ace.fsu.edu.proxy.lib.fsu.edu/tutoring or contact tutor@fsu.edu. 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.''


Assignments

Assignment 1 (due at 1:25 p.m. on Friday, February 10, 2017)
Assignment 2 (due at revised deadline of 1:25 p.m. on Friday, March 10, 2017)
Assignment 3 (due at revised deadline of 1:25 p.m. on Wednesday, March 29, 2017)
Assignment 4 (due at 1:25 p.m. on Wednesday, April 26, 2017)

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