MA 401-001, FA06, Applied Differential Equations II

TTh 11:45-1:00, HA 366, but some classes will be in computer lab TBA

Professor: S. R. Lubkin
515-1904, lubkin at eos.ncsu.edu, http://www4.ncsu.edu/~lubkin
Office hours: Cox 513B, Tues & Thurs 3 pm

Official listing: Wave, heat and Laplace equations. Solutions by separation of variables and expansion in Fourier Series or other appropriate orthogonal sets. Sturm-Liouville problems. Introduction to methods for solving some classical partial differential equations. Use of power series as a tool in solving ordinary differential equations.
 
Preq: MA 301 or 341. Credit for both MA 401 and 501 will not be given.
 
Goals: Upon successfully compl eting this course, you will be skilled in using the core methods in the mathematical analysis of the fundamental linear PDE's that engineers use. You will be familiar with the properties of the heat/diffusion equation, the wave equation, and the Laplace equation. You will be able to find series solutions to these PDE, by hand and by computer.

Required Text: Nakhle Asmar, Partial Differential Equations with Fourier Series and Boundary Value Problems, 2nd ed. A list of known errors will be maintained (please report them). Note that a Student Solutions Manual is free online at http://www.math.missouri.edu/~nakhle/pdebvp/student-manual.pdf

If the book doesn't resonate with you...? Some people like using Schaum's Outline of Advanced Mathematics for Engineers and Scientists and/or Schaum's Outline of Fourier Analysis with Applications to Boundary Value Problems (less than $20 each) for extra practice problems and fully worked examples. There will be supplementary material posted on the class website on courses.ncsu.edu

Grades final exam 30%, 2 midterms @ 15%, 20% HW and quizzes, 20% team projects.
I cannot promise that your HW and quizzes will be graded with great precision, but I can promise that your HW/quiz grade will be representative of your work. Maple calculations will be required on most of the assignments.

Schedule

Policies

• You are expected to come to class. If you miss class and need to turn in an assignment, it should go to my mailbox in HA 245, and you should drop me an e-mail telling me.
  
• If you have a disability or conflict that I need to know about, let me know as soon as possible (not the week of the first exam). Note that I am not sympathetic about vacation plans.
  
• You are welcome to work on HW with other students, but with some restrictions. Since the point of HW is learning, you should work with others only to the extent that it facilitates your learning and your partner's learning. Giving each other ideas, explaining, and finding each other's errors do help learning. Copying answers does not improve anyone's learning; letting your partner do the work does not help your learning. 
• You are welcome to use Maple or any other computer package to help on the HW. Please say when you are using technological help. For example, "Integrating this term by parts (Maple) yields...."
  
• You may not work with others on the exams. Most quizzes will be a solo effort. Group quizzes will be specifically identified as such. In accordance with the NCSU policy on academic integrity, found in the Code of Student Conduct, it is assumed that in turning in any assignment to the instructor, the student has thereby im plicitly taken the honor pledge: "I have neither given nor received unauthorized aid on this test or assignment."
  

Courtesy

• Except in emergency situations, please make sure cell phones are off.
• Please keep bags out of the traffic pattern.
• Some of you may need to eat or drink during class. I don't mind this, but your fellow students might, so please keep noises, crumbs, and odors under control. Food and drink are not allowed in computer labs.
  
• What I do mind is the newspaper. Do not attempt to read it in class.
  

Homework aesthetics

• Please staple homeworks. Don't fold in half. There is a stapler in HA 245.
  
• Every graph must be labeled. Always label all axes. Arrowheads have a very specific meaning indicating the direction of motion or of a vector or time. Arrows do not belong on axes or curves unless they are intended to indicate time or motion or vectors. 
• If you are asked to make an argument, or "show that..." then you need to use enough words to make that argument. Mathematical symbols without context make no sense. Look at your textbook: it is mostly words with symbols used within the sentences. That is how your homework should be written.
  
• If you do calculations in Maple (for instance) and hand in the Maple session,  the printout should be edited for clarity and conciseness just as you would edit your handwritten notes (only giving me your best work). It is easy to make graphs in Maple, but you should only show those graphs which illustrate your point. Delete graphs which do not contribute to your discussion.

Tips

• You are expected not just to own the book, but to read it.
• A great amount of learning happens when you correct your own HW and find your own errors and misconceptions. That is why you will have solutions. Your engagement with the homework should not stop when you hand it in.
• Check the website frequently.
• You are expected to check email daily. I often send reminders or explanations or assignments by email. You are responsible for making sure the email NCSU has for you is the one you check.
  
• If your Maple outputs are getting too big, you can print them 2-up. First, print to a pdf file. Then open the pdf file and specify that its format should be 2 to a page. Then print the pdf 2-up. Smaller than 2 to a page, I can't read.
• I tend to respond pretty promptly to email. I am hard to find by just stopping at my office.
  

Cool stuff

Applets that show vibrations of various phenomena (heat, wave, etc.)
http://www.falstad.com/mathphysics.html

Various Simulations (heat, wave,etc.)
http://www.kettering.edu/~drussell/demos.html

Vibrations of a Drum Head
http://artsci-ccwin.concordia.ca/facstaff/a-c/bird/c241/java/drums/drums.html