Cauchy and the Creation of Complex Function TheoryIn this book, Dr. Smithies analyzes the process through which Cauchy created the basic structure of complex analysis, describing first the eighteenth century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This book is the first to make use of the whole spectrum of available original sources and will be recognized as the authoritative work on the creation of complex function theory. |
Contents
Introduction | 1 |
Cauchys 1814 memoir on definite integrals | 24 |
Miscellaneous contributions 18151825 | 59 |
The 1825 memoir and associated articles | 85 |
The calculus of residues | 113 |
The Lagrange series and the Turin memoirs | 147 |
Summary and conclusions | 186 |
205 | |
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Cauchy and the Creation of Complex Function Theory Frank Smithies,Smithies Frank No preview available - 1997 |
Common terms and phrases
algebraic analytic analytic function appears argument becomes infinite Calcul infinitésimal 1823b Cauchy-Riemann equations Chapter circle closed contour closed curves coefficients complex function theory convergence correction term definite integrals derivatives differential discussion domain double integrals Euler evaluation of definite Exercices d'analyse expansion expression finite and continuous fo(x fo(z formula function f(z geometrical language given gives illustrative examples imaginary substitutions infinite series infinity integral residue integrals round integrand introduced Lagrange series Laplace later Legendre Maclaurin series method modulus notation obtains Oeuvres 1)1 Oeuvres 2)2 paper paths Poisson polar coordinates polynomials power series principal value proof rational function rectangle remarks residue theorem roots Rouché's theorem second Turin memoir Section 2.3 simple pole singularity ẞi supposes takes vanishes writes x₁ y₁ z₁ zeros әм ду
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