COMPACT NUMERICAL METHODS FOR COMPUTERS
CONTENTS BASIC RESULTS INTRODUCTION TRANSFORMS OF ELEMENTARY FUNCTIONS ELEMENTARY PROPERTIES OF TRANSFORMS TRANSFORMS OF DERIVATIVES AND INTEGRALS INVERSE TRANSFORMS CONVOLUTION THE LAPLACE TRANSFORMS OF SOME SPECIAL FUNCTIONS DI?ERENCE EQUATIONS AND DELAY DI?ERENTIAL EQUATIONS Z-TRANSFORMS MULTIDIMENSIONAL LAPLACE TRANSFORMS INVERSION FORMULAE AND PRACTICAL RESULTS THE UNIQUENESS PROPERTY THE BROMWICH INVERSION THEOREM THE POST-WIDDER INVERSION FORMULA INITIAL AND FINAL VALUE THEOREMS SERIES AND ASYMPTOTIC EXPANSIONS PARSEVAL’S FORMULAE THE METHOD OF SERIES EXPANSION EXPANSION AS A POWER SERIES AN ALTERNATIVE TREATMENT OF SERIES EXPANSIONS EXPANSION IN TERMS OF ORTHOGONAL POLYNOMIALS LEGENDRE POLYNOMIALS CHEBYSHEV POLYNOMIALS LAGUERRE POLYNOMIALS THE METHOD OF WEEKS MULTI-DIMENSIONAL LAPLACE TRANSFORM INVERSION CONTENTS QUADRATURE METHODS INTERPOLATION AND GAUSSIAN TYPE FORMULAE EVALUATION OF TRIGONOMETRIC INTEGRALS EXTRAPOLATION METHODS THE P-TRANSFORMATION OF LEVIN THE SIDI MW-TRANSFORMATION FOR THE BROMWICH INTEGRAL METHODS USING THE FAST FOURIER TRANSFORM (FFT) HARTLEY TRANSFORMS DAHLQUIST’S “MULTIGRID” EXTENSION OF FFT INVERSION OF TWO-DIMENSIONAL TRANSFORMS RATIONAL APPROXIMATION METHODS THE LAPLACE TRANSFORM IS RATIONAL THE LEAST SQUARES APPROACH TO RATIONAL APPROXIMATION SIDI’S WINDOW FUNCTION THE COHEN-LEVIN WINDOW FUNCTION PAD´E, PAD´E-TYPE AND CONTINUED FRACTION APPROXIMATIONS PRONY’S METHOD AND Z-TRANSFORMS THE METHOD OF GRUNDY THE METHOD OF TALBOT EARLY FORMULATION A MORE GENERAL FORMULATION CHOICE OF PARAMETERS ADDITIONAL PRACTICALITIES SUBSEQUENT DEVELOPMENT OF TALBOT’S METHOD PIESSENS’ METHOD THE MODI?CATION OF MURLI AND RIZZARDI MODI?CATIONS OF EVANS ET AL THE PARALLEL TALBOT ALGORITHM MULTI-PRECISION COMPUTATION METHODS BASED ON THE POST-WIDDER INVERSION FORMULA METHODS AKIN TO POST-WIDDER INVERSION OF TWO-DIMENSIONAL TRANSFORMS THE METHOD OF REGULARIZATION FREDHOLM EQUATIONS OF THE ?RST KIND — THEORETICAL CONSIDERATIONS THE METHOD OF REGULARIZATION APPLICATION TO LAPLACE TRANSFORMS SURVEY RESULTS COST’S SURVEY THE SURVEY BY DAVIES AND MARTIN LATER SURVEYS NARAYANAN AND BESKOS DU?Y D’AMORE, LACCETTI AND MURLI COHEN TEST TRANSFORMS 10 APPLICATIONS 10 2 APPLICATION 2 HEAT CONDUCTION IN A ROD 10 3 APPLICATION 3 LASER ANEMOMETRY 10 4 APPLICATION 4 MISCELLANEOUS QUADRATURES 10 5 APPLICATION 5 ASIAN OPTIONS