Asymptotics and Borel Summability (eBook, PDF)
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Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. It explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. The author covers ODEs, PDEs, difference equations, and other types of problems. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted b...
Incorporating substantial developments from the last thirty years into one resource, Asymptotics and Borel Summability provides a self-contained introduction to asymptotic analysis with special emphasis on topics not covered in traditional asymptotics books. It explains basic ideas, concepts, and methods of generalized Borel summability, transseries, and exponential asymptotics. The author covers ODEs, PDEs, difference equations, and other types of problems. He provides complete mathematical rigor while supplementing it with heuristic material and examples, so that some proofs may be omitted by applications-oriented readers. He also includes both standard and challenging exercises.
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