References

 References to the items that are discussed in your text are in 
Press et al. General references are in References.
 The subjects covered are:
 I. Fortran and C fundamentals
  A.read_comma

, Maopen, random, command line input

 B. Fort calls C, static_variables calloc
  C. functions as arguments
 II. The AMOEBA[1] -- for people with more computer time than
 experience Finding the error in an amoeba result Errinfun
 III. Lagrange interpolation[2] 
  A. The "best" set of N unevenly spaced points -- Findfun
  B Filon's method for calculating a Fourier transform.Fourier1 - Filon_transform 
 IV. Integration Partition
  A. Trapezoidal rule CINT1including Romberg extrapolation[3].
  B. Gauss Quadrature[4] -- Orthogonal Polynomials CINT2 Cint3 
 Cint4 Assign
  C. Monte-Carlo Guiding function integration mcarlo.
 Biased Selection MonteCarlo. 
 IV. Fourier Transform methods Fourier1
  A. Convolution Convolution[5]
  B. Solution of a differential equation in transform space. -- 
 Green's function diffFT
  C. The Fast Fourier Transform[6] Fourier2
 IV. Differential equations[7] diffeq1
  A. Euler's method[8] diffeq1 - Euler
  B. Runge-Kutta[9] diffeq1 - RungeKutta
  D. Predictor Corrector[10] diffeq1 - predcorr 
  C. Boundary value problems[11] (finding eigenvalues and 
 eigenfunctions)diffeqns/shoot.htm
 D. Newton's method[12] Newton and Aitkin's extrapolation Aitkins
 E. Relaxation methods Jacobi jacobi2
 V. Optimization 
  A. Gauss-Jordan[13] GaussJ.htm, and  cholesky matrix inversion.
  B. Modified Newton Raphson[14] Robmin -- more experience than computer 
 time
  C. Directions for the use of .nlfit in README

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.

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[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. 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.

[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. 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.

[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] This method appears in many elementary references. Ibid Chapter 9.4 – called Newton-Raphson method. Hildebrand, F.B. Introduction to Numerical Anaysis, Dover (1956,1974) section 10.10-10.11. A very readable explanation is Rice, J.R. Numerical Methods Software and Analysis, IMSL Reference Edition McGraw Hill (1983).

[13] Ibid. pp. 24-29

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