Computational references

                  The C Programming Language, Brian W. Kernighan and Dennis M. Ritchie, Prentice Hall (1988) Sets the standard for C.

                  Watfor-77 Users Guide IBM PC with DOS G. Coschi, J.B. Schueler, Watcom Publications Limited, 415 Phillip Street, Waterloo, Ontario, CANADA, N2L 3X2 (519) 886-3700 (1989) One of many manuals

                  Introduction to Computational Physics, Marvin L. De Jong (1991)
Assumes (PC and Basic) appropriate problems for undergraduate physics -- very relevant for simulations --         elementary Monte Carlo, Basic Graphics

Computational Physics, S.E. Koonin (1986) also more recent His codes are in basic. He includes the Numerov algorithm (differential equation method especially suited for Shroedinger equations), Green’s function methods for boundary value problems, and Monte Carlo methods. The method that I most like for solving Poisson’s equation was inspired by this book.

LINPACK User’s Guide, J.J. Dongarra, C.B. Moler, J.R. Bunch, G.W. Stewart, SIAM Philadelphia (1979)I coded the Cholesky decomposition straight from this book. It tells how to handle matrices, band matrices, sparse matrices, and the to us very familiar ill-conditioned matrices.

                  Applied Numerical Methods, Carnahan, Luther, Wilkes (1969)
68 pages on interpolation with good derivations of divided differences and Chebyshev methods (includes economization). In section 8.22 shows explicitly how to construct a set of polynomials orthogonal over a given set of data points. Also contains a very good set of problems.

                  Computational Methods of Linear Algebra, V.N. Faddeeva, translated by Curtis D. Benster, Dover (1959) Examines all sorts of matrix methods including eigenvalues and iterative improvement of solutions. This is where I learned how to increase the accuracy of the first solution to a set of                simultaneous equations.

                  Introduction to Numerical Analysis, F.B. Hildebrand (1956) Also Dover (1974)

Written for desk calculators, contains smoothing techniques – see ..\wsteve\Smoothing derivatives.htm, Gaussian quadrature, iterative techniques for inverting matrices and methods for solving simultaneous equations. One can invert sizable matrices (9 x 9 is my record) by hand with these techniques.

                  The Mathematics of Physics and Chemistry, H. Margenau and G.M. Murphy (1943 and 1956)
Short, compact and to the point. Pages 1-459 simply derive a host of the basics for physics and chemistry. Pages 467-516 present simple and elegant numerical methods. Linear integral equations and group theory round out the book. When other references seem unintelligible, this one explains it simply.

                  Handbook of Mathematical Functions, M. Abramowitz and I. Stegun, editors Dover (1965) Contains tables of mathematical data and short code examples for approximating functions. Generally gives good pade approximates and a complete table of the              Tchebyshev coefficients. Also contains tables of function values

                                    xxxxx xxxxx xxxxx xxxxx

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é (-5)1ù é (-4)1ù max error in linear int 10-5, 10-4

ë 8 û ë 9 û 8, 9 Lagrange terms needed for

full table accuracy

Tables of Functions, Eugene Jahnke, Fritz Emde, Dover (1945)
Sine, cosine and log integrals, Elliptic integrals, Bessel Functions, Mathieu Function, etc. Old and hard to read and by today’s standards limited accuracy, but very useful on occasion.

Fast Fourier Transform and Convolution Algorithms (2nd edition), H. J. Nussbaumer, Springer Verlag (1982)
Contains all sorts of variants on the standard FFT and includes many examples of their use.