ELEMENTARY PARTIAL DIFFERENTIAL EQUATIONS II


MAP 4342, Section 01, Spring 2016

(Class #05204)

Elementary Partial Differential Equations II 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 cover solution of first-order quasi-linear partial differential equations by the method of characteristics, classification and reduction to normal form of linear second-order equations, Green's functions, the Fourier and Laplace transforms and other topics, and is potentially of interest not only to mathematics majors but also to other science majors
Course page: ON CAMPUS: http://www.math.fsu.edu/~mesterto/PDEII.html (this page)
OFF CAMPUS: http://www.math.fsu.edu.proxy.lib.fsu.edu/~mesterto/PDEII.html (with your FSUID username and password)
Professor:Dr Mesterton-Gibbons, or Dr M-G for short
Office: 202B Love
Office hours: Please click here. Office hours are subject to change during the semester at 24 hours notice, but current times are always posted online. 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)4 2580
Main website: Professor M-G's Home Page    Email:
Class meets: in 201 Love on Mondays, Wednesdays and Fridays at 12:20—1:10 p.m.
Format: The course will be based on my lecture notes with problems (which I will email to you after class, and which you can also download from here)
Text: There is no required text. However, if you already own a text on partial differential equations—e.g., because you used one for MAP 4341—then I recommend keeping it until the semester has ended, because it will be useful as a reference
Credit: 3 semester hours
Prerequisites:
(i)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 (for the most part), 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 William who likes to be called Dubya or a Margaret Jane who likes to be called Dee Dee, write Dubya or Dee Dee, not William or Margaret 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 (20% apiece) and a final exam (20%), for all of which you must use blue or black ink. If you make a mistake when writing in ink, then just cross it out and make a correction—which is far more efficient temporally than erasing pencilling, and may even earn you otherwise unavailable partial credit (if it turns out that you were right before you changed your mind). Note that 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 clearly (implying legibly) demonstrated: Show all necessary steps in your method, with enough comments or diagrams to convince that you thoroughly understand. On the other hand, don't turn in acres and acres of verbiage: although it is generally better to err on the side of saying too much than on the side of saying too little, saying far too much is usually an indication that you don't really know what you are talking about and are trying to hide it with words.
    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 90%, 80% and 70%, respectively. In borderline cases, a smaller number of completely correct solutions will carry more weight than a proportionate number of fragmentary answers; later scores will carry more weight than earlier scores; and a record of active participation in class will carry more weight than a record of passive attendance. 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. 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
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
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. 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 ever 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. 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. 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). 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. (In particular, you are not allowed to use a cell phone or otherwise have private conversations with others during class; and you are not allowed to create disturbances through arriving late or leaving early.)
Final: Thursday, April 28, 3:00—5:00 p.m. in 201 LOV
How to study: It is important that you keep up with the course from the very beginning, always attempting as many as possible (preferably all) of any 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

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.''


Lecture Notes

  1. First-order equations
  2. More on first-order equations
  3. Effects of nonlinearity
  4. Shocks
  5. Classifying 2nd-order linear PDEs
  6. Green's functions for ODEs
  7. Heat-equation Green's functions
  8. Laplace-equation Green's functions
  9. The Fourier transform
  10. Riemann's method
  11. Hyperbolic versus dispersive waves
  12. Water waves
  13. Boundary layers
  14. Matched asymptotic expansions
  15. More on matched asymptotics
  16. The method of multiple scales

Some Oldish PDE I Notes


Assignments and Final

Assignment 1 (now due at 12:20 p.m. on Monday, February 01, 2016)   Remarks
Assignment 2 (due at 12:20 p.m. on Monday, February 22, 2016)   Remarks
Assignment 3 (now due at 12:20 p.m. on Monday, March 28, 2016)   Remarks
Assignment 4 (now due at 12:20 p.m. on Wednesday, April 20, 2016)   Remarks
Final (Thursday, April 28, 2016, 3:00—5:00 p.m.)   Remarks

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