By Ovidiu Costin
Incorporating large advancements from the final thirty years into one source, Asymptotics and Borel Summability offers a self-contained advent to asymptotic research with particular emphasis on themes no longer coated in conventional asymptotics books. the writer explains easy principles, thoughts, and strategies of generalized Borel summability, transseries, and exponential asymptotics. He presents whole mathematical rigor whereas supplementing it with heuristic fabric and examples, in order that a few proofs will be passed over by means of applications-oriented readers.
To supply a feeling of ways new tools are utilized in a scientific approach, the booklet analyzes intimately basic nonlinear traditional differential equations (ODEs) close to a favourite abnormal singular aspect. It permits readers to grasp uncomplicated ideas, delivering a company starting place for extra learn at extra complicated degrees. The ebook additionally examines distinction equations, partial differential equations (PDEs), and different kinds of problems.
Chronicling the growth made in contemporary a long time, this publication indicates how Borel summability can get well specified options from formal expansions, research singular habit, and greatly increase accuracy in asymptotic approximations.
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Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) by Ovidiu Costin