ELEMENTARY PARTIAL DIFFERENTIAL EQUATIONS II


MAP 4342, Section 01, Spring 2009

(Reference #02311 in Directory of Classes)

Elementary Partial Differential Equations II will be taught from the perspective of an applied mathematician, i.e., it will focus on understanding the 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—but obviously, if you are reading a hard copy of it, then you won't be able to activate the links until you go online)
OFF CAMPUS: http://www.math.fsu.edu.proxy.lib.fsu.edu/~mesterto/PDEII.html (with your FSUID username and password)
Professor: Dr M-G
Office:202B Love (in which I hold office hours)
Phone:(850 64)4 2580
Main website: Professor M-G's Home Page    Email:
Class meets: in 102 LOV, Tuesdays and Thursdays 9:30 a.m. - 10:45 a.m.
Official Text: Richard Haberman,  Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 4th edition (Pearson/Prentice Hall, 2004). Selected topics from Chapters 9-14. However, the course will be based on my lecture notes with problems. (I will email them to you as they become ready; you can also download them from here.)
Credit: 3 semester hours.
Prerequisites:
(i)MAP 4341; or Professor M-G's consent and
(ii)self-motivation and industriousness. Professor M-G's philosophy of learning is perhaps best expressed by the following diagram:
 
Communication:It is your responsibility to register for an FSU computer account so that I can send you email, which you are expected to check regularly. If you prefer to read your email elsewhere then you can arrange to have messages forwarded, but you must still obtain an FSU account in the first instance
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. Please take a sheet of paper, fold it in half, write your first name in large letters on one side and stand it up on your desk so that I can see it. (Write whatever you want me to call you—if you're a William who likes to be called Dubya, write Dubya, not William.) Please bring your name plate 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 (25% each). 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 you must clearly demonstrate that you understand it. In borderline cases, a smaller number of completely correct solutions will carry more weight than a proportionate number of fragmentary answers, and later scores will carry more weight than earlier scores. Partial credit is awarded only when part of a solution is completely correct (not when all of a solution is partially correct, whatever that means, if anything). 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 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). 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).
Helpline:If you get stuck between classes then consider using my Homework Helpline. Just send me your 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 questions).
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.

Lecture Notes

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

Some Old PDE I Notes


Assignments

Assignment 1 (due at 9:30 a.m. on Thursday, January 29, 2009)
Assignment 2 (due at 9:30 a.m. on Thursday, February 19, 2009)
Assignment 3 (due at 9:30 a.m. on Thursday, March 19, 2009)
Assignment 4 (due at 9:30 a.m. on Thursday, April 23, 2009)

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