Computer Methods in Physics

This course is devoted to the classic computer or numerical methods useful in physics.  Watcom IDEs (file.wpj, file.tgt) will normally be used to display codes.  Fortran or C will be acquired along with the course if you do not already know one of these.  The course consists of a series of documents with links to C and Fortran code.  The documents attempt to explain specific numerical methods, while the codes provide templates for putting these into practice.  Security has become an issue leading to mostly pdf files on this website.  Details are in LinksAndRedudantCopies.pdf.

A Rosetta stone relating the topics covered in class to the appropriate sections in Press is BobPress.htm , or in compressed notation prefs.htm.  A more general set of references is in References.htm. LinksAndRedudantCopies.htm contains a few words about viewing the documents.

Topics

1.     hello/Welcome.htm .pdf .zip Command prompt, Watcom IDE, Fortran hello, C hello.

2.     interpolation/Welcome.htm .pdf .zip 

a.     interpolation/Bli.htm. .pdf Best Linear Interpolator  includes FORTRAN and C code for comparison.

b.     interpolation/Lagrange.htm .pdf  Most accurate interpolator when large polynomials are appropriate.

c.     interpolation\splinefitting .pdf  Achieves continuous first derivatives by solving for the second derivatives.  (accurate)

d.     interpolation\Quadratic A local extension to linear interpolation.

e.     interpolation/Locate.htm.doc Needed for unevenly spaced data.

3.     definitions/Welcome.docx   Brief hints at the physics and mathematics underlying computer methods

a.     definitions\Random\Welcome.htm

b.     definitions/gofr/Welcome.htm  two body correlation functions

c.     definitions\PeriodBC\Welcome.htm  periodic boundary conditions.

4.     Derivatives\Welcome.htm .docx  Numerical derivatives and the limits to their accuracy.

5.     integration\Welcome.htm .docx  Finite and infinite integrals

6.     solving\Welcome.htm finding f(x) = 0  involves finding x.

7.     MatrixInverse\Welcome.htm Find xi such that εjajixj = 0 for specified N΄N values of  aij

8.     optimization\Welcome.htm  finding f(x) less than all others.  involves finding f and x.  RobMin

9.     MultiplePrecision\Welcome.htm  Curve fitting requires lots of digits.

10.  fittery\Welcome.htm Curve fitting

11.  Fourier\Welcome.htm Fourier methods (fast)

12.  DiffEqns\Welcome.htm .docx

13.  wavefunction\Welcome.htm .docx

a.     wavefunction\SchrodingerEqn.pdf .docx.

b.     wavefunction\ProbabilityCurrent.htm .docx

c.     wavefunction\1-d\Welcome.htm .docx

14.  Progdet/Welcome.pdf  Programming details  plotting, formats, sorting, passing arrays, and so on.

a.     progdet\Linking.htm .docx How to remove a feature of some operating systems.

b.     Progdet\gplot\Welcome.htm  .doc .pdf  .doc, .htm, and .pdf filesare supposed to be the same.

c.     Progdet\SysRoutines\Welcome.htm  short codes that allow most Fortran compilers to be used for the same code.  Topics include system calls, overflow avoidance, opening files and others.

d.     Progdet\sorting\Welcome.htm  Logarithmic sorts and a direct access sort which allows the data to always remain in disk files.

e.     Progdet\ArrayPass\ArrayPass.htm   Details the use of the fact that A(7) is a pointer to the seventh array element.

15.