References. Microcomputer, Macmillan. Angell, I. O. and Jones, B. J. (1983b). Advanced Graphics with the Sinclair ZX

Size: px

Start display at page:

Download "References. Microcomputer, Macmillan. Angell, I. O. and Jones, B. J. (1983b). Advanced Graphics with the Sinclair ZX"

Lily Lynch
5 years ago
Views:

1 References Adams, A. G. (1969).'Areas under the normal curve', Algorithm 39, Computer J., 12. American National Standards Institute (1978). American National Standard for Minimal BASIC, ANSI X3.60. Angell, I. O. (1985). Advanced Graphics with the IBM Personal Computer, Macmillan. Angell, I. O. and Jones, B. J. (1983a). Advanced Graphics with the BBC Model B Microcomputer, Macmillan. Angell, I. O. and Jones, B. J. (1983b). Advanced Graphics with the Sinclair ZX Spectrum, Macmillan. Bajpai, A. C. et 01. (1974). Engineering Mathematics, Wiley. Chatfield, C. (1970). Statistics for Technology, Penguin. Conte, S. D. (1965) Elementary Numerical Analysis, McGraw-Hill. Conte, S. D. and De Boor, C. (1972). Elementary Numerical Analysis - An Algorithmic Approach, 2nd edition, McGraw-Hill. Davis, O. L. and Goldsmith, P. L. (1972). Statistical Methods in Research and Production, 4th edition, Oliver and Boyd. Fox, L. and Mayers, D. F. (1968). Computing Methods for Scientists and Engineers, Oxford University Press. Froberg, C. E. (1970). Introduction to Numerical Analysis, 2nd edition, Addison Wesley. Gosling, P. (1982). Practical BASIC programming, Macmillan. Griffiths, P. and Hill, I. D. (editors) (1985a). 'Algorithm AS66 The normal integral' by I. D. Hill, in Applied Statistics Algorithms, Ellis Horwood, p Griffiths, P. and Hill, I. D. (editors) (1985b). 'Algorithm AS 147 A simple series for the incomplete gamma integral', by Chi-Leung Lau, in Applied Statistics Algorithms, Ellis Horwood, p Griffiths, P. and Hill, I. D. (editors) (1985c). 'Algorithm AS63 The incomplete beta integral', by K. L. Majumler and G. P. Bhattacharjee, in Applied Statistics AlgOrithms, Ellis Horwood, p Hamming, R. W. (1962). Numerical Methods for Scientists and Engineers, McGraw Hill. Iyanaya, S. and Kawadu, Y. (editors) (1980). Encyclopedic Dictionary of Mathematics, Mathematical Society of Japan, MIT Press. Kreyszig, E. (1983). Advanced Engineering Mathematics, 5th edition, Wiley. Lee, J. D. and Lee, T. D. (1982). Statistics and Computer Methods in BASIC, Van Nostrand Reinhold. Mason, J. C. (1983). BASIC Numerical Methods, Butterworths. Mason, J. C. (1984). BASIC Matrix Methods, Butterworths. Miller, A. R. (1981). BASIC Programs for Scientists and Engineers, Sybex. 174

2 References 175 Morgan, B. J. T. (1984). Elements of Simulation, Chapman and Hall. Nevison, 1. M. (1978). The Little Book of BASIC Style, Addison-Wesley. Pearson, K. (editor) (1956). Tables of the Incomplete Gamma Function, Cambridge University Press. Pearson, K. (editor) (1968). Tables of the Incomplete Beta Function, 2nd edition, Cambridge University Press. Ralston, A. and Wilf, H. S. (1962). Mathematical Methods for Digital Computers, Wiley. Scheffe, H. (1959). The Analysis of Variance, Wiley. Stephenson, G. (1969). Mathematical Methods for Science Students, 6th edition, Longmans Green. Stroud, K. A. (1982). Engineering Mathematics, 2nd edition, Macmillan. Wonnacott, T. H. and Wonnacott, R. J. (1981). Regression: A Second Course in Statistics, Wiley.

3 Index Accuracy see Error ACS 161 ALGOL language 2 Amstrad 4 Analysis of variance 72-87, 89 ANOV A see Analysis of variance Array variables 5 ATN 4,161 Average see Mean BASIC language 1-2 BBC micro 4 Bernoulli distribution see Binomial distribution Bernoulli numbers 31 Beta function 37-41, 47 Binomial distribution 9-11,20-1 Bisectional method Bugs 7 C computer language 2 Calculus Chebyshev polynomial Chi-squared 64-8 distribution 42-4 Combinations Complex numbers Complex roots 154,158 Contingency table 64-8 Control variables 5-6 Correlation 88 Cubic equati0ns Cumulative distribution functions see Probability Cumulative frequencies 53-7 Curve fitting see Regression and Interpolation Data, integration of discrete DAT A statement 4 DEF FN 6 Density functions see Probability Determinant Differential equations DIM 5 Discriminant 154 Distribution functions see Probability Eigenvalues Eigenvectors ELSE 6 END 5 Enhancements Equations cubic quadratic simultaneous linear solutionof Error, standard see Standard error Errors, rounding, syntax, precision 6-7, see also Bugs Exponential distribution 18-19,29-30 Exponential random numbers 12, F distribution 45-7 F ratio, F test 46, 72, 74, 77-8,83, 85,89 Factorials FN 6 FOR-NEXT 5 FORTRAN language 2 Fourier coefficients, series Frequency data see Cumulative frequencies Functions 4-6 Gamma function 31-6,42,45,47,69 Gauss elimination 119 Gaussian distribution see Normal distribution Global variables 5 GOSUB 3 176

4 GOTO 2 Graphics 4-5 Harmonic coefficients Harmonic index Hewlett-Packard 4 IBM 4 Identity matrix 89 IF-THEN, IF-THEN-ELSE, IF-THEN- GOTO 6 Ill-conditioning 99, 124 Imaginary 154, 158 Integer variables 5 Integration, numerical 7, Interpolation Inverse matrix Jacobi diagonalisation 114 Lagrange interpolation Least squares estimation see Regression LET 6 Line numbers 3, 8 LN 4,6-7 Local variables 5 LOG 4 LPRINT 4 Matched samples see Paired comparisons Matrix addition, multiplication, read, subtraction, transposition, write determinant of eigenvalues, eigenvectors, real symmetric inversion Maximum value 53-7 Mean 50-2, 72, 88 Means, difference between Median 53-7 Minimum value 53-7 Multiple assignment statements 5 Multiple linear regression Multiple regression coefficient 89 Multiple statement lines 2, 5 N(O, 1) see Normal distribution Newton's method Normal distribution Normal equations 87,89, 99 Numerical integration Index 177 Orthogonal matrix transformation 114 Paired comparisons Pascal language 2 Percentiles 53-7 Permutations Pivotal condensation 119 Poisson distribution 12, 22-4 Polar form 167 Polynomial regression Polynomials see Chebyshev polynomial Portability 4 Presentation 2 PRINT 4 Probability see also Random numbers binomial 20-1 exponential normal 25-8 Poisson 22-4 Procedures 1 Quadratic equation R2 103 Random numbers 4, 8 binomial 9-11 exponential normal Poisson uniform or rectangular 6,12,15,18 Range 53-7 Real roots 154,158 Real symmetric matrix 114 Rectangular distribution see Uniform distribution Regression Regression coefficients 87, 89, 98-9 REM 2 Replicates 77, 83 Residual 76,85, 99 Residual analysis 87, 90 RETURN 2 RND 6 Rounding errors 6-7,99,103,119 Runge-Kutta method Shell sort 53 Significant figures 4 Simpson's rule 7, Simulation 7,10-11,13-14,16-19 Simultaneous equations 7, see also Equations Software viii, 6

5 178 Solution of equations Sorting 53-7 Spectrum 4 Speed 1-3,8 Standard deviation 50-2 Standard error 58-63, Standardised residual 90 Statements 4-5 STEP 5 Stirling's approximation 31 STOP 5 String variables 5 Structure 2-3 Student's t distribution 47-9,58-63 Style 3 Subroutine viii, ix, 1,3,8 Summary statistics 51 Syntax 4 Index t distribution 47-9,58-63 t test THEN 6 Time 7, see also Speed Trapezium rule Triangular matrix 119 U(O, 1) see Uniform distribution Uniform distribution 6,12,15,18 Variables, array, control, global, local, integer, string 4-5 Variables, random see Random numbers Variance 50-2, Variance ratio see F ratio

6 Software Diskette A diskette containing all the programs included in this book for use on an IBM PC is available (ISBN ). Details of prices and availability can be obtained from Publisher for Computing Books Macmillan Education Houndmills Basingstoke RG21 2XS

CAM Ph.D. Qualifying Exam in Numerical Analysis CONTENTS

CAM Ph.D. Qualifying Exam in Numerical Analysis CONTENTS Preliminaries Round-off errors and computer arithmetic, algorithms and convergence Solutions of Equations in One Variable Bisection method, fixed-point