References

1

S. A. Abramov and K. Yu. Kvashenko, On the greatest common divisor of polynomials which depend on a parameter, Proc. ISSAC '93, Kiev, Ukraine, 152--156.

2

John D. Anderson, Introduction to Flight, 3rd Ed., McGraw-Hill, New York, 1989.

3

American National Standards Institute/Institute of Electrical and Electronic Engineers: IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Std 754-1985, New York, 1985.

4

Uri M. Ascher, Robert M. M. Mattheij, and Robert D. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, 1988.

5

I. N. Baker and P. J. Rippon, ``A Note on Complex Iteration", Amer. Math. Monthly, 92 (1985), 501--504.

6

E. J. Barbeau, Polynomials, Springer-Verlag Problem Books in Mathematics, 1989.

7

A. Barry, ``A class of exact solutions for Richard's equation'', J. Hydrology 142 1993 pp 29--46.

8

Carl M. Bender and Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978.

9

Wolf-Jürgen Beyn, ``Numerical Methods for Dynamical Systems'', in Advances in Numerical Analysis, Will Light, ed., Oxford Science Publications, 1991, pp. 175--236.

10

Jonathan M. Borwein and Peter B. Borwein, and the AGM: A Study in Analytic Number Theory and Computational Complexity Wiley, New York, 1987.

11

Jonathan M. Borwein, personal communication.

12

Manuel Bronstein, ``Symbolic Integration: Towards Practical Algorithms'', in Computer Algebra and Differential Equations, E. Tournier, ed., Academic Press, pp. 59--86.

13

William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 2nd. ed., Wiley, 1969, pp. 423--429.

14

Manuel Bronstein and Bruno Salvy, Full Partial Fraction Decomposition of Rational Functions Proc. ISSAC '93, Kiev, Ukraine, 157--160.

15

A. Cayley, ``A theorem on trees'', Quarterly Journal of Mathematics, Oxford Series, 23 (1889), 376--378.

16

Michael W. Chamberlain, ``Heart to Bell'', College Mathematics Journal 25, No. 1, January 1994, p. 34.

17

Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers 2nd ed., McGraw-Hill, 1988.

18

Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monagan, and Stephen M. Watt, First Leaves: A Tutorial Introduction to Maple V, Springer-Verlag, 1992.

19

Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monagan, and Stephen M. Watt, The Maple V Language Reference Manual, Springer-Verlag, 1991.

20

Bruce W. Char, Keith O. Geddes, Gaston H. Gonnet, Benton L. Leong, Michael B. Monagan, and Stephen M. Watt, The Maple V Library Reference Manual, Springer-Verlag, 1991.

21

Samuel D. Conte and Carl de Boor, Elementary Numerical Analysis, 3rd ed., McGraw-Hill, 1980.

22

Vincent T. Coppola and Richard H. Rand, Symbolic Computation and Perturbation Methods using Elliptic Functions, Trans. Sixth Army Conf. on Applied Maths. and Computing, 1989, 639--676.

23

Robert M. Corless, ``Continued Fractions and Chaos'', American Mathematical Monthly 99, vol. 3, 1992, pp. 203--215.

24

Robert M. Corless, ``Defect-controlled numerical methods and shadowing for chaotic differential equations'', Physica D 60 1992 pp. 323--334.

25

Robert M. Corless, ``Six, Lies, and Calculators'', American Math. Monthly, 100 4 April 1993, pp. 344 -- 350.

26

Robert M. Corless, Bifurcation in a Flow-Induced Vibration Model, Proc. Workshop on Normal Forms and Homoclinic Chaos, AMS Fields Institute Communications, 1993, W. F. Langford and W. Nagata, eds. (to appear).

27

Robert M. Corless, ``What good are numerical simulations of chaotic dynamical systems?'', to appear.

28

Robert M. Corless, ``Error Backward'', to appear.

29

Robert M. Corless, Symbolic Recipes, vols 1 and 2, Springer-Verlag, 1994.

30

Robert M. Corless and Khaled El-Sawy, ``Solution of banded linear systems in Maple using LU factorization'', to appear in the proceedings of the 1994 Maple Summer Workshop, Troy, New York.

31

Robert M. Corless, Gaston H. Gonnet, D. E. G. Hare, and David J. Jeffrey, Lambert's W Function, Tech. Rep. CS-03-93, Dept. Comp. Sci, University of Waterloo, 1993.

32

Robert M. Corless, Gaston H. Gonnet, D. E. G. Hare, and David J. Jeffrey, ``Lambert's W Function in Maple'', Maple Technical Newsletter 9, Spring 1993, pp. 12--22.

33

Robert M. Corless, Gaston H. Gonnet, D. E. G. Hare, David J. Jeffrey, and Donald E. Knuth, ``The Lambert W Function'', to appear.

34

Robert M. Corless and D. J. Jeffrey, ``Well, it isn't quite that simple'', SIGSAM Bulletin 26, vol. 3, August 1992, pp. 2--6.

35

Robert M. Corless and Michael B. Monagan, ``Simplification and the assume facility'', Maple Technical Newsletter, to appear.

36

Robert M. Corless, D. J. Jeffrey, and M. A. H. Nerenberg, The Row-Echelon Decomposition of a Matrix in preparation.

37

J. H. Davenport, Y. Siret, and E. Tournier, Computer Algebra, Academic Press, 1988.

38

Harold T. Davis, Introduction to Linear and Nonlinear Differential and Integral Equations, Dover, 1962.

39

Diamond and Kloeden

40

N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland, 1961.

41

W. H. Enright, 1989, ``A New Error-Control for Initial Value Solvers'', Appl. Math. Comput. 31 pp. 288-301.

42

L. Euler, ``De Serie Lambertina Plurismique Eius Insignibus Proprietatibus", Leonhardi Euleri Opera Omnia, Ser. 1. Opera Mathematica, Bd 6, 1921 (orig. date 1779).

43

Temple H. Fay, ``The Butterfly Curve'', Amer. Math. Monthly 96, No. 5, May 1989, pp. 442--443.

44

Walter Gander and Jirí Hrebícek, Solving Problems in Scientific Computing Using Maple and MATLAB, Springer-Verlag, 1993.

45

Gavelek and Erber

46

Keith O. Geddes, Stephen R. Czapor, and George Labahn, Algorithms for Computer Algebra, Kluwer, 1992.

47

G. Golub and C. van Loan, Matrix Computations, Johns Hopkins, 1983.

48

G. H. Gonnet and D. Gruntz, ``Limit Computation in Computer Algebra'', Technical Report 187, Department for Computer Science, ETH Zürich, 1992.

49

D. F. Griffiths, 1987, ``The dynamics of some linear multistep methods with step-size control'', in Numerical Analysis 1987, D. F. Griffiths and G. A. Watson, eds., Longman Scientific and Technical. pp. 115--134.

50

D. F. Griffiths and J. M. Sanz-Serna, 1986, ``On the scope of the Method of Modified Equations'', SIAM J. Sci. Stat. Comput. 7 No 3 pp 994--1008.

51

D. Gruntz, ``A New Algorithm for Computing Asymptotic Series'', Proc. ISSAC '93, Kiev, Ukraine, pp. 239--244.

52

D. Gruntz, personal communication.

53

Xavier Gourdon and Bruno Salvy, ``Computing one million digits of '', Maple Technical Newsletter 10, Fall 1993, pp. 66--71.

54

E. Hairer, S. P. Norsett, and G. Wanner, Solving Ordinary Differential Equations I, Springer series in computational mathematics 8, Springer-Verlag, Berlin, 1987.

55

G. H. Hardy, A Course of Pure Mathematics 10th. ed. Cambridge University Press, 1952.

56

André Heck, Introduction to Maple, Springer-Verlag, 1993.

57

Russell Jay Hendel, Differentiation via Partial Fractions: A Case against CAS, The College Mathematics Journal 22 5 November 1991, pp. 415--417.

58

Peter Henrici, Applied and Computational Complex Analysis vol I, Wiley-Interscience, 1977.

59

Peter Henrici, Applied and Computational Complex Analysis vol II, Wiley-Interscience, 1977.

60

N. J. Higham, Gaussian Elimination ****

61

J. H. Hubbard and B. H. West, Differential Equations: a Dynamical Systems Approach, Part I, Springer-Verlag, 1991.

62

T. E. Hull, W. H. Enright, B. M. Fellen, and A. E. Sedgwick, ``Comparing numerical methods for ordinary differential equations", SIAM J. Numer. Anal., 9, 1972, pp. 603--637.

63

D. J. Jeffrey, ``The Importance of Being Continuous'', to appear in Math. Magazine.

64

Donald E. Knuth and Boris Pittel, ``A Recurrence Related to Trees'', Proc. Amer. Math. Soc., 105, no. 2, Feb. 1989, pp. 335--349.

65

William M. Kahan, ``Handheld calculator evaluates integrals'', Hewlett-Packard Journal, August 1980, pp. 23--32.

66

William M. Kahan ``Branch cuts for complex elementary functions'', In The state of the art in numerical analysis, M. J. D. Powell and A. Iserles, Eds, Oxford University Press.

67

David Kahaner, Cleve Moler, and Steven Nash, Numerical Methods and Software, Prentice-Hall, ????.

68

R. A. Knoebel, ``Exponentials reiterated'', Amer. Math. Monthly, 88 (1981), 235--252.

69

Cornelius Lanczos Applied Analysis, Dover, 1988.

70

Derek F. Lawden, Elliptic Functions and Applications, Springer-Verlag AMS 80 1989.

71

Norman Levinson and Raymond M. Redheffer, Complex Variables, Holden-Day, 1970. pp. 298--306.

72

T. Y. Li, ``The Cheater's Homotopy'', SIAM Review ****

73

J. L. McCauley, Chaos, Dynamics, and Fractals, Cambridge Nonlinear Science Series 2, 1993.

74

John McCleary, ``How Not to Prove Fermat's Last Theorem'', American Mathematical Monthly 96, No. 5, May 1989, pp. 410--420.

75

M. B. Monagan, Programming in Maple, available by anonymous ftp to the Maple Share Library.

76

Michael B. Monagan and Walter M. Neuenschwander, ``GRADIENT: Algorithmic differentiation in Maple'', Proc. ISSAC '93, Kiev, Ukraine, pp. 68--76.

77

Alexander Morgan, Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems, Prentice-Hall, 1987.

78

J. Morris, ``'', Phil. Mag. 7 37, 1946, p 106.

79

Joel Moses, *** introductory article on Risch integration.

80

Morris Newman, Integral Matrices, Academic Press, New York and London, 1972, p. 15.

81

Ivan Niven, Maxima and Minima without Calculus, Dolciani Mathematical Expositions No. 6, Mathematical Association of America, 1981.

82

Ben Noble and James W. Daniel, Applied Linear Algebra, Prentice-Hall, 1988.

83

Robert E. O'Malley, Jr., Singular Perturbation Methods for Ordinary Differential Equations, Springer-Verlag Applied Mathematical Sciences, 89, 1991.

84

Steven A. Orszag, ``Accurate solution of the Orr-Sommerfeld stability equation'', J. Fluid Mech. 50, 4, 1971, pp. 689--703.

85

J. M. Ortega, Letters to the Editor, American Mathematical Monthly 92 1985 p. 526.

86

E. L. Ortiz, ``The Tau method'', SIAM J. Numer. Anal. 6 1969 pp. 480--492.

87

T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, 1989.

88

G. Pólya and R. C. Read, Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds, Springer-Verlag, 1987.

89

William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, Numerical Recipes, Cambridge University Press, 2nd ed., 1992.

90

Darren Redfern, The Maple Handbook, Springer-Verlag, 1993.

91

E. L. Reiss, ``A new asymptotic method for jump phenomena", SIAM J. Appl. Math, 39 (1980), 440--455.

92

Robert H. Risch, ``The Problem of Integration in Finite Terms'', Trans. AMS 139 1969, pp. 167--189.

93

Robert H. Risch, ``Symbolic Integration of Elementary Functions'', *** where did this appear??? ****.

94

Theodore J. Rivlin, Chebyshev Polynomials, 2nd. ed., Wiley-Interscience, 1990.

95

Gian-Carlo Rota, Finite Operator Calculus, Academic Press, 1975.

96

Bruno Salvy, ``Efficient Programming in Maple: A Case Study'', SIGSAM Bulletin 27, vol. 2, April 1993 pp. 1--12.

97

William Y. Sit, ``An algorithm for solving parametric linear systems'', J. Symb. Comp. 13 1992 pp. 353--394.

98

Helen Skala, ``Contour Maps---A Visual Experience'', The College Mathematics Journal 22, No. 3, May 1991, pp. 241--244.

99

Ralph G. Stanton, Numerical Methods for Science and Engineering,Prentice-Hall, 1961.

100

A. H. Stroud and Don Secrest, Gaussian Quadrature Formulas, Prentice-Hall, 1966.

101

E. C. Titchmarsh, Theory of Functions, 2nd ed., Oxford 1939.

102

Charles Van Loan, Computational Frameworks for the Fast Fourier Transform, SIAM, 1993.

103

Ernst Joachim Weniger, Nonlinear Sequence Transformations for the acceleration of convergence and the summation of divergent series, Computer Physics Reports 10, No. 5, North-Holland, December 1989.

104

J. H. Wilkinson, ``The Perfidious Polynomial'', in M.A.A. Studies in Numerical Analysis, Gene Golub, ed. 1984, pp. 1--28.

105

E. M. Wright, ``The Linear Difference-Differential Equation with Constant Coefficients'', Proc. Royal Soc. Edinburgh, LXII A, 1947, pp. 387--393.

106

LAPACK User's Guide. Orr-sommerfeld by tau-method.

107

Mathematical Handbook