Math 664, Seminar in Applied Mathematics

Distance Learning Sections, 701 and 721

Syllabus

664 Course Home Page

The text is "Introduction to Computation and Modeling for Differential Equations" Lennart Edsberg, John Wiley & Sons, 2008

Problems
Applications Read Sections HW due (click date for problem set)
Beam bending, heat conduction/convection, math finance 4.1;4.2.5;9.3.2;6.1;8.1;5.3.9 July 16
Elasticity, fluid flow 5.3.8;5.3.1 July 23
Schrodinger equation, minimal surface 5.3.7;7.1 July 30
Diffusion (3D and axisymmetric 2D) 5.3.4;5.2 Aug 6

Students will actually solve a number of interesting science and engineering application examples using the general purpose partial differential equation package PDE2D . They will learn to write the (ordinary or partial) differential equations, with boundary and initial conditions, for certain applications, including diffusion and heat conduction, convection, math finance, fluid flow, elasticity and quantum mechanics (Schrodinger equation), in one, two and three space dimensions. Since problems will be solved using "black-box" software, students are not primarily learning about numerical methods, though they will learn something, but rather about modeling real-world applications using differential equations.

Some examples showing typical PDE2D user input and graphical output can be viewed at:

example 1 (3D)

example 2 (2D)

example 3 (1D)

Before classes start (or soon after), you should do the following:

  1. Because TAMU has just installed a firewall around the math servers, you need to go to connect.tamu.edu and log on using your NetID, then install VPN on your PC, so you will be able to get to the computer (wiki-itlab.tamu.edu) where PDE2D is installed. If you are unable to install or use VPN successfully, there is an alternative, which I will tell you about, but only through e-mail.
  2. Download the PDE2D GUI and Interactive Driver here and install on your local PC. Unzip the big ZIP file in the TOP level (important) of your C: drive, and a subdirectory C:\PDE2D.ITL will be created with everything in it. Look at the file README.DEMO for further information about installation. (Do NOT purchase PDE2D, just download the free GUI/Interactive Driver "trial version".)
  3. Download putty and psftp here .
  4. If you can't view PostScript files on your PC, you can download GhostView here.
Creating and running a PDE2D program will then involve the following steps:
  1. Enter a Command Prompt Window on your PC, go to any directory where you have write privileges, and work through EITHER a PDE2D GUI session ("pde2d_gui [name]") or an Interactive Driver session ("pde2d [name]") on your PC. After you have finished answering all questions, a Fortran program "name.FOR" should exist in your working directory. You can make corrections and modifications directly to this program using an editor; I use the old DOS editor ("edit name.FOR"), you probably use something more modern.
  2. Using "psftp", upload your program "name.FOR" to wiki-itlab.tamu.edu. Type "psftp wiki-itlab.tamu.edu" from a Command Prompt Window, you will be prompted for your account and password (which you will be given the week before classes start), then "put name.FOR" or "get name.FOR" to move "name.FOR" to or from wiki-itlab.
  3. Using "putty", log on to your account on wiki-itlab.tamu.edu. Type "putty wiki-itlab.tamu.edu" from a Command Prompt Window, you will again be prompted for your account and password. Change the name of your program from "name.FOR" to "name.f" and execute it using the command "runpde2d name". The machine wiki-itlab.tamu.edu is running Unix (Linux); if you are not familiar with Unix, a short introduction can be found here. You may want to change your password using "passwd".
  4. Note: You can actually run an Interactive Driver session (but NOT a GUI session) on wiki-itlab ("pde2d name") and create your program there rather than on your PC, if you prefer. Since all programs can be created using the Interactive Driver (the GUI is easier to use, but cannot be used for some problems), you could do everything on wiki-itlab.tamu.edu, if desired.
  5. In the unlikely event that the program runs correctly the first time, simply download (using "psftp") the Postscript plotfile "name.ps" and look at it on your PC, using GhostView. Once you are satisfied with the results, e-mail me your PDE2D program (name.FOR or name.f), and I will run it myself to see the results.
  6. If compilation errors are detected in your program, or you don't get results you are happy with (nothing ever works the first time), you need to modify the Fortran program "name.f". I normally edit it there using the Unix editor "vi", but unless you are already familiar with this editor (or another Unix editor installed on wiki-itlab), you probably don't want to learn "vi", just download your program "name.f" back to your PC and modify it there, then upload it back and try again.
  7. It is anticipated that you will have some (hopefully, minor) problems with these procedures the first time, write me if you can't resolve them quickly, don't spend hours trying to resolve them on your own. Note that you have two weeks before the first assignment is due, that should give you enough time to work out bugs in these procedures.
Note that you do not need to be a Fortran programmer to use PDE2D, but you do need to know how to write basic Fortran expressions. The third GUI page has nearly all the information about Fortran you need to use PDE2D; basically Fortran expressions are similar to MATLAB expressions, with a few small differences, for example, variables are NOT case-sensitive, and a to the b power is a**b, not a^b as in MATLAB.

Appendix A (documentation for PDE2D)

Review of Multivariate Calculus (for problem 7c)

Video

PDE2D Video

Optional Videos

The following MATH 610 videos are included for the benefit of any students who are interested in learning more about the finite element methods used by PDE2D. The are not essential for this course.

Chapter 5 Video (5.0-5.4)

Chapter 5 Video (5.5-5.11)