References to the items that are discussed in PressRef.htm are footnoted.

                The subjects covered are:

 

                I. Fortran and C fundamentals

                   A.functions as arguments, command line input

                  B. static_variables, calloc Fort calls C

                II.  The AMOEBA[1] -- for people with more computer time than experience

                  Finding the error in an amoeba minimum Errinfun

                III. Lagrange interpolation[2] 

                   A.  Selection of the “best” set of N unevenly spaced points -- Findfun

                   B Filon's method for calculating a Fourier transform.  Fourier1.doc - Filon_transform
                IV.  Integration Partition

                   A.  Trapezoidal rule integration\CINT1.doc including Romberg extrapolation[3].

B.       Gauss Quadrature[4] -- Orthogonal Polynomials CINT2.DOC Cint3.doc Cint4.doc

Multidimensional integration assignment Assign.doc

                   C.   Monte-Carlo (biased selection) Guiding function in mcarlo, details in MonteCarlo

                V. Fourier Transform methods Fourier1

                A. Convolution[5] Convolution

                   B.  Solution of a differential equation in transform space. -- Green's function diffFT

                   C. The Fast Fourier Transform[6] Fourier2

                VI.  Differential equations[7] DIFFEQ1

                   A. Euler’s method[8] DIFFEQ1- Euler

                   B.  Runge-Kutta[9] DIFFEQ1 - RungeKutta

                   D.  Predictor Corrector with mid-point[10] DIFFEQ1 - predcorr

C.       Boundary value problems (finding eigenvalues and eigenfunctions)[11] shoot.doc

D.      Newton's method Newton.doc and Aitkin's extrapolation Aitkins.doc

E.       Relaxation methods Jacobi.doc jacobi2.DOC

                VII. Optimization

                   A. Gauss-Jordan[12] GaussJ.doc, and Cholesky matrix inversion.Cfposdef - cholesky

                   B.  Modified Newton Raphson[13] --Robmin details more experience than computer time

                   C.  ..\nlfit\README.DOC

 

                A few programming and matrix techniques will be needed to get through this list.  A large fraction of physics reduces to the problem of evaluating an integral to find the action as a function of a set of constants and then minimizing the action with respect to these constants.  This course should show you how to tackle this problem.

 


[1] Press (1986 Fortran) p292  -- I do not agree with all of his default settings.

[2] Ibid. p. 80 --- He scoff's at my notion that this is a best method

[3] Ibid. p9 102-103 --- I do not trust his method of estimating errors

[4] Ibid. pp. 121-126  --- Gives codes for generating weights, I suspect that many will prefer to look them up.

[5] Ibid. pp. 407-414  --- Cannot imagine a convolution without the FFT and thus discusses it after the FFT

[6] Ibid. pages 381-386 Give Press's definition of Fourier transforms -- half the world uses the opposite sign       conventions 3/4 do not use                 the 2 p -- I agree with Press.

                386-390 -- brief explanation of the FFT algorithm.         

[7] Ibid. pp. 547 -577

[8] Ibid. p 550

[9] Ibid. pp 550-560

[10] Ibid. pp. 561-562  Press does not like predictor corrector nor understand this simple method.  His statement about only even powers is false.  His discussion of Stiff Sets of equations pp. 572-577 is very relevant.

[11] Ibid. pp. 578-600 Beware of Press, "We always shoot first, and only then relax." P 581

[12] Ibid. pp. 24-29

[13] Ibid. pp. 523-528 I have extended the Marquardt method considerably -- come to class.