Syllabus

Lecture: Monday, Wednesday, Friday, 12:45 to 13:40 in S&E 324.

Instructor: Brett van de Sande,

• Office SE 316,
• E-mail: bvds@pitt.edu,
• web page http://www.geneva.edu/~bvds.

Office hours: By appointment; send me an E-mail if you can not find me.

Textbook: Numerical Recipes in FORTRAN or Numerical Recipes in C by W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Cambridge University Press. Students will also need a box of floppy disks.

Grading: 80% for a series of "mini-projects" done as homework assignments and 20% for the final exam.

Topics:

• Roots of non-linear equations. We will look at a variety of approaches and analyze their effectiveness for a variety of ``test problems.''
• Function minimization.
• Interpolation and extrapolation. We will be rather brief on this subject, using it mainly as a lead-in to numerical integration techniques.
• Numerical integration and differentiation We will spend a lot of time on the important and interesting subject of numerical integration. Differentiation will only be briefly mentioned.
• Systems of linear equations. First we will start with Gauß-Jordan elimination. Then we will study approaches based on matrix factorization. The use of standard libraries BLAS and LAPACK will be emphasized.
• Eigenvalue problems.
• Differential equations. The numerical solution of differential equations can be a difficult subject and our treatment will be very introductory.
• Time permitting, we will finish with a study of more advanced topic. Possibilities include: Monte Carlo integration, or partial differential equations using mesh techniques.

Programming: This course involves a substantial amounts of programming on the part of the student. Students may choose between C (or C++) and FORTRAN. If you are familiar with either of the two languages, feel free to continue using it. Each student must own a reference book (or textbook) for the programming language that they choose. Each student must bring their book to class and show it to the instructor.

There will also be occasions where results will have to be graphed. There are several possibilities for accomplishing this: one would be to use a spreadsheet program such as Microsoft Excel. One could also use MATLAB or Gnuplot; see my Guide to Using Gnuplot.

Also, students will be required to do background reading at several World Wide Web sites as well as download standard subroutines from various Internet sites. Further course information can be found at the MAT 350 web page: http://www.geneva.edu/~bvds/mat350; this page will be updated throughout the term.

Concerning collaboration: I encourage students to discuss with each other how to solve the problems. I also encourage students to look at the example problems in the textbook and elsewhere. However, when you write down your program (or other work) to be handed in, it must be your own work. If the program (or other work) you hand in is copied from another student, a textbook, or elsewhere, that is cheating. If you find yourself in a situation that is questionable, please explain the situation on your homework. For example:

"I got lots of help from John Smith doing problem 3; although I didn't copy, I still don't understand how the subroutine works."

"My dorm burned to the ground yesterday and I lost everything. I then copied Joe Smoke Alarm's homework verbatim; I have no idea what the questions were, let alone the answers."

Homework Assignments

1. Machine Epsilon
2. Root Finding Algorithms
3. Function Minimization
4. Polynomial Interpolation
5. Integration
6. Orthogonal polynomials
7. Some Linear Algebra
8. Linear Equations and Eigenvalue problems.
9. Differential Equations

• You may hand in homework assignments on paper, as E-mail, or on a floppy disk. Any E-mail or floppy disk files should be in plain text format.
• Explain in sentence form what you are doing. Your homeworks should be understandable to someone who does not know how to solve the problem.
• Include any new code that you wrote (source). You should comment your code.
• List any standard subroutines used, including:
  • subroutine name and what it does.
  • what package: BLAS, LAPACK, etc.
  • where from: Netlib, etc. Include the URL (the web address) if it is from an unusual source.
  Don't include any print-outs of standard subroutines in your homeworks.
• Include output of your program. A print-out is not necessary if the results are then graphed. You can output your results to a file.
• Any graphs should be properly labelled and explained.

Mathematical software libraries

• The most useful starting point in your search for subroutines is The Guide to Available Mathematical Software at Oak Ridge.
• Also, you can find lots of software in the Netlib software repository.
• I have an introduction to downloading standard subroutines which uses the first homework as an example.

Information on compilers and computers

• The UNIX computers in the physics lab, SE 227 have FORTRAN and C/C++ available. E-mail me for permission and instructions if you would like to use these machines.
• The UNIX computers in SE 128 have FORTRAN and C/C++ available. However, these computers are old and slow.
• Code Warrior is available in the Geneva computer labs. You will have to learn how to make "projects." C and C++ are available. Even I could learn it in a short time (with a little help).

• Read the list of general instructions I gave you.
• The Fortran compiler is run using the command g77; C is gcc; and C++ is g++.
• If you don't specify an output file name, the executable is put in a file a.out. I like to specify the name for the executable; for example g77 -o macheps macheps.f produces an executable macheps. Executables are run by typing the name of the executable.
• If you use math functions on the UNIX computers, you will have to tell the compiler to link to the math library: gcc myprogram.c -lm The "-lm" at the end of the command tells the compiler to link to this library.
• There will be occasions where different parts of your program will be in different files. For instance, you might have your program in a file junk.cpp and you call a routine in the file macheps.c, then you can compile both using g++ junk.cpp macheps.c.

• The best solution: get LINUX.
• Use a free FORTRAN compiler, G77 for DOS, from Clive Page's Web Site. This is probably the best choice for FORTRAN on Microsoft windows.
• Get both FORTRAN and C compilers, EGCS MING 32 C/C++/GCC/G++ and Fortran 77 (F77/G77) for Win95/WinNT, from Mumit Khan's Web/FTP site.
• Get a C compiler, MingW32 C/C++/GCC/G++ for Win95/WinNT, from Jan-Jaap van der Heijden's Web/FTP site.
• Get a C compiler, Cygnus GNU-Win32 C/C++/GCC/G++, for Win95/WinNT.
• Get GNU Fortran G77 for Win32.

Numerical Recipes is a great book, but it is not perfect. Why you should not use Numerical Recipes?