About the Book
This publication was made possible through a bequest from my beloved late wife. United together in this present collection are those works by the author which have not previously appeared in book form. The following are excepted: Vorlesungen uber Differential und Integralrechnung (Lectures on Differential and Integral Calculus) Vols 1-3, Birkhauser Verlag, Basel (1965-1968); Aufgabensammlung zur Infinitesimalrechnung (Exercises in Infinitesimal Calculus) Vols 1, 2a, 2b, and 3, Birkhauser Verlag, Basel (1967-1977); two issues from Memorial des Sciences on Conformal Mapping (written together with C. Gattegno), Gauthier-Villars, Paris (1949); Solution of Equations in Euc1idean and Banach Spaces, Academic Press, New York (1973); and Stu- dien uber den Schottkyschen Satz (Studies on Schottky's Theorem), Wepf & Co., Basel (1931). Where corrections have had to be implemented in the text of certain papers, references to these are made at the conc1usion of each paper. In the few instances where this system does not, for technical reasons, seem appropriate, an asterisk in the page margin indicates wherever a correction is necessary and this is then given at the end of the paper.
(There is one exception: the correc- tions to the paper on page 561 are presented on page 722. The works are published in 6 volumes and are arranged under 16 topic headings. Within each heading, the papers are ordered chronologically according to the date of original publication.
Table of Contents:
XIV Conformal Mapping.- 54 Mathematische Miszellen. XV. Zur konformen Abbildung einfach zusammenhangender Gebiete, Jber. Deutsch. Math.-Verein. 38, 168-182(1929).- 60 Uber konforme Abbildungen annahernd kreisformiger Gebiete (Aus einem Brief an L. Bieberbach), Jber. Deutsch. Math.-Verein. 39, 78-81 (1930).- 74 Bemerkung zur vorstehenden Note von Herrn S. Warschawski, Math. Z. 38, 684-686 (1934).- 77 Uber den Habitus der konformen Abbildung am Rande des Abbildungsbereiches, Acta Math. 64, 81-184 (1935).- 81 Sur la conservation des angles dans la transformation conforme d'un domaine au voisinage d'un point frontiere. C.R. Acad. Sc. Paris 202, 727-728 (1936).- 82 Sur la transformation des plis dans la transformation conforme au voisinage d'un point frontiers C.R. Acad. Sc. Paris 202, 1135-1137 (1936).- 83 Zur Randverzerrung bei konformer Abbildung (Dem Gedachtnis von Leon Lichtenstein gewidmet), Prace Mat.-Fiz. 44, 371-471 (1936).- 135 On the Convergence of Theodorsen's and Garrick's Method of Conformal Mapping, in Proc. Sympos. on Conformal Maps, 1949 (Nat. Bur. Standards, Washington, D.C [Appl. Math. Ser. 18], 149-163 (1952).- 136 On a Discontinuous Analogue of Theodorsen's and Garrick's Method, in Proc. Sympos. on Conformal Maps, 1949 (Nat. Bur. Standards Washington, D.C. [Appl. Math. Ser. 18]), 165-174 (1952).- 146 Conformal Mapping of A Special Ellipse on the Unit Circle, in Experiments in the Computation of Conformal Maps (Nat. Bur. Standards, Washington, D.C. [Appl. Math. Ser. 42]), 1-2 (1955).- 147 Theodorsen's and Garrick's Method for Conformal Mapping of the Unit Circle into an Ellipse, in Experiments in the Computation of Conformal Maps (Nat. Bur. Standards, Washington, D.C. [Appl. Math. Ser. 42]), 3-5 (1955).- XV Numerical Analysis.- 85 Konvergenzdiskussion und Fehlerabschatzung fur die Newton'sche Methode bei Gleichungssystemen, Comment. Math. Helv. 9, 79-103 (1936/1937).- 88 Uber eine Modifikation des Newtonschen Naherungsverfahrens, Inst. Math. Tbilissi 2, 241-250 (1937).- 92 Uber die Konvergenz und die Abrundungsfestigkeit des Newtonschen Verfahrens, Rec. Math. Moscou (44) 2, 1073-1095 (1937).- 93 Uber einen Fall der Konvergenz des Newtonschen Naherungsverfahrens, Rec. Math. Moscou (45) 3, 253-258 (1938).- 99 Sur la convergence et l'estimation des erreurs dans quelques procedes de resolution des equations numeriques, in Grave Festschrift (Gosudarstv Izdat. Tehn.-Teor. Lit., Moscow), 213-234 (1940).- 126 La recherche des periodicites cachees. Analyse Harmonique (Centre Nat. Recherche Sc, Paris [Colloq. Internat. C.N.R.S. 15]), 93-95 (1949).- 130 Sur les matrices peu differentes d'une matrice triangulaire, C.R. Acad. Sc. Paris 233, 1559-1560 (1951).- 134 On the Rounding Off of Difference Tables for Linear Interpolation, Math. Tables and Other Aids to Comp. 6, 212-214 (1952).- 138 On Over and Under Relaxation in the Theory of the Cyclic Single Step Iteration, Math. Tables and Other Aids to Comp. 7, 152-159 (1953).- 140 On Nearly Triangular Matrices, J. Research Nat. Bur. Standards 52, 319-345 (1954).- 151 Note on a Logarithm Algorithm, Math. Tables and Other Aids to Comp. 9, 65-68 (1955).- 157 Determinanten mit uberwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen (Paul Finsler zum 60. Geburtstag), Comment. Math. Helv. 30, 175-210 (1956).- 160 Uber Verfahren von Steffensen und Householder zur Konvergenzverbesserung von Iterationen (Mauro Picone zum 70. Geburtstag), Z. angew. Math, und Phys. 7, 218-229 (1956).- 169 Uber naherungsweise Auflosung von Systemen homogener linearer Gleichungen, Z. angew. Math, und Phys. 8, 280-285 (1957).- 173 A Method of Speeding Up Iterations with Super-Linear Convergence, J. Math. Mech. 7, 117-120 (1958).- 179 On Trends and Problems in Numerical Approximation, in On Num. Approx., Univ. Wisconsin Press, Madison, 3-10 (1959).- 180 On Gauss' Speeding Up Device in the Theory of Single Step Iteration, Math. Tables and Other Aids to Comp. 12, 116-132 (1958).- 212 On Approximation of Equations by Algebraic Equations, SIAM J. Num. An. (B) 1, 104-130 (1964).- 218 Zur Entwicklung der numerischen Analysis, Jber. Deutsch. Math.-Verein. 68, 97-111 (1966).- 221 The Round-off Stability of Iterations, Z. angew. Math, und Mech. 47, 77-81 (1967).- 223 Contributions to the Theory of the Method of Steepest Descent Arch. Rational Mech. An. 26, 257-280 (1967).- 225 Une methode generale de resolution automatique d'une equation polynomial, in Programmation en Mathematique Numerique, Actes Colloq. Internat. C.N.R.S. 165, Besancon 1966 (Edition Centre Nat. Recherche Se, Paris), 179-182 (1968).- 230 A Method for Automatique Solution of Algebraic Equations, in: Constructive Aspects of the Fundamental Theorem of Algebra, IBM Symposium, Zurich 1967 (John Wiley & Sons, New York), 209-224 (1969).- 235 La methode de Newton dans les espaces de Banach, C.R. Acad. Sc. Paris 272, 1251-1253 (1971).- 240 Die Newton-Raphsonsche Methode in Banachraumen, in Methode und Verfahren d. math. Physik 5, 23-28 (1971).- 241 Les estimations des erreurs a posteriori dans les procedes iteratifs, C.R. Acad. Sc. Paris 275, 275-278 (1972).- 241a On Error Estimates A Posteriori in Iterative Procedures, Edmonton Symposium, ISNM 21, 267-275 (1972).- 242 A Posteriori Error Estimates in Iterative Procedures (To the memory of George E. Forsythe), SIAM J. Num. An. 10, 290-298 (1973).- 247 Uber Fehlerabschatzungen a priori und a posteriori, Acta Univ. Carol. Prag 1-2, 111-115 (1974).- 252 An Estimate of the Approximation to a Fixed Point of an Operator, Comp. & Maths, with Appls. 1, 427 (1975).- XVI Miscellany.- 63 Ganzzahligkeit in der Mathematik, Tatigkeitsbericht der Math. Fachschaft an der Universitat Heidelberg, 3-10 (1932).- 111 Besprechung von Bavink, Ergebnisse und Probleme der Naturwissenschaften, Experientia 1, 163-165 (1945).- 111a Besprechung von: Studies and Essays (To R. Courant on his 60th birthday), Experientia 6, 28-29 (1950).- 116 Sur la formule de Moivre-Laplace, C.R. Acad. Sc. Paris 223, 1090-1092 (1946).- 117a G.H. Hardy, Nachruf, Experientia 5, 131-135 (1949).- 137 Two Explicit Formulae for the Distribution Function of the Sums of n Uniformly Distributed Independent Variables (To Ernst Jacobsthal for his 70th birthday), Arch. d.M. 3, 451-459 (1952).- 177 Wilhelm Suss. Freiburger Univ.-Reden (N.F.) 28, 1-16 (1958).- 199a Werner Gautschi, 1927-1959.- 244 (With J. Aczel) On the Characterization of Shannon's Entropy by Shannon's Inequality, J. Australian Math. Soc. 16, 368-374 (1973).- 256 Festvortrag Oberwolfach, Jber. Deutsch. Math.-Verein. 77, 167-172 (1975).- 260 (With Raymond M. Redheffer) Inequalities Related to the Normal Law, in General Inequalities 1, Birkhauser Verlag Basel, 125-129 (1978).- 262 On the Remainder Term of the de Moivre-Laplace Formula (To the 70th birthday of Eugene Lukacs), Aequa. Math. 20, 263-277 (1980).- 266 (Mit E. Landau) Bemerkung zu unserer Abhandlung On the Diophantine Equation ay2 + by + c = dxn, Proc. London Math. Soc. (1921).- Vol. 1-6.- Collected Mathematical papers ordered chronologically according to the date of original publication.
