Roderick S. C. Wong – författare

Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed.

Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book. Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed.

This volume brings together 30 chapters across five parts, offering a structured, in-depth survey of asymptotic analysis and its applications. Readers will find rigorous treatments of orthogonal polynomials, boundary layer problems, saddle-point integrals, turning point theory, Airy and Bessel expansions, special functions, and modern approaches to difference equations, differential equations, Riemann-Hilbert problems, integrals, and singular perturbation problems. Each chapter blends classical foundations with recent breakthroughs, making the book both a comprehensive reference and a graduate-level textbook with exercises for hands-on learning.Over the past three decades, asymptotic analysis has become indispensable in number theory, combinatorics, probability and statistics, mathematical physics, engineering, and applied sciences, equipping researchers and students with powerful methods for solving complex problems. This book not only surveys the latest advances in asymptotic methods but also demonstrates their practical applications across diverse mathematical models.Designed for advanced undergraduate students, graduate students, researchers, and instructors, the text can be used as a reference guide to modern asymptotic techniques or adapted into course modules, strengthening both theoretical understanding and applied problem-solving.

This volume brings together 30 chapters across five parts, offering a structured, in-depth survey of asymptotic analysis and its applications. Readers will find rigorous treatments of orthogonal polynomials, boundary layer problems, saddle-point integrals, turning point theory, Airy and Bessel expansions, special functions, and modern approaches to difference equations, differential equations, Riemann-Hilbert problems, integrals, and singular perturbation problems. Each chapter blends classical foundations with recent breakthroughs, making the book both a comprehensive reference and a graduate-level textbook with exercises for hands-on learning.Over the past three decades, asymptotic analysis has become indispensable in number theory, combinatorics, probability and statistics, mathematical physics, engineering, and applied sciences, equipping researchers and students with powerful methods for solving complex problems. This book not only surveys the latest advances in asymptotic methods but also demonstrates their practical applications across diverse mathematical models.Designed for advanced undergraduate students, graduate students, researchers, and instructors, the text can be used as a reference guide to modern asymptotic techniques or adapted into course modules, strengthening both theoretical understanding and applied problem-solving.

This is a collection of selected papers written by Frank W J Olver from 1949 to 1999. It contains his most important contributions to the fields of asymptotic analysis and numerical analysis, including the global existence of uniform asymptotic expansions for solution of ordinary differential equations and construction of error bounds. It is a valuable collection for anyone who works in, or uses, asymptotics, and should be on the shelves of all major libraries.

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

Special functions and q-series are currently very active areas of research which overlap with many other areas of mathematics, such as representation theory, classical and quantum groups, affine Lie algebras, number theory, harmonic analysis, and mathematical physics. This book presents the state-of-the-art of the subject and its applications.

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

This invaluable book contains the collected papers of Stephen Smale. These are divided into eight groups: topology; calculus of variations; dynamics; mechanics; economics; biology, electric circuits and mathematical programming; theory of computation; miscellaneous. In addition, each group contains one or two articles by world leaders on its subject which comment on the influence of Smale's work, and another article by Smale with his own retrospective views.

This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences