By Ovidiu Costin
Incorporating giant advancements from the final thirty years into one source, Asymptotics and Borel Summability presents a self-contained creation to asymptotic research with certain emphasis on themes now not coated in conventional asymptotics books. the writer explains easy principles, strategies, and strategies of generalized Borel summability, transseries, and exponential asymptotics. He offers whole mathematical rigor whereas supplementing it with heuristic fabric and examples, in order that a few proofs should be passed over via applications-oriented readers.
To provide a feeling of ways new equipment are utilized in a scientific means, the ebook analyzes intimately normal nonlinear traditional differential equations (ODEs) close to a favourite abnormal singular element. It permits readers to grasp uncomplicated strategies, offering an organization beginning for additional examine at extra complex degrees. The publication additionally examines distinction equations, partial differential equations (PDEs), and different sorts of problems.
Chronicling the growth made in fresh many years, this ebook indicates how Borel summability can get well targeted recommendations from formal expansions, learn singular habit, and drastically increase accuracy in asymptotic approximations.
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Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) by Ovidiu Costin