Roderick S.C. Wong's Books

Lecture Notes On Applied Analysis

By: Roderick S C Wong

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Lecture Notes On Applied Analysis

By: Roderick S C Wong

There are several subjects in analysis that are frequently used in applied mathematics, theoretical physics and engineering sciences, such as complex variable, ordinary differential equations, special functions, asymptotic methods, integral transforms and distribution theory. However, for graduate students or upper-level undergraduate students who are not going to specialize in these areas, there is no need for them to study these subjects in great depth. Instead, it would probably be more beneficial for them to have an introduction to these topics so that when the need arises, they know what approach to take. With this in mind, this set of lecture notes has been written for a one-semester course. Sufficient details have also been included to make it sufficiently adaptable for self-study. There are in total six chapters with each covering only a few topics. Furthermore, the chapters are all self-contained. The prerequisites for the readers of this book are advanced calculus, a first course in ordinary differential equations and elementary complex variable.

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303

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World Scientific Publishing Company

Published Date

ISBN 10

9813107669

ISBN 13

9789813107663

More Explorations in Complex Functions

By: Richard Beals,Roderick S.C. Wong

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More Explorations in Complex Functions

By: Richard Beals,Roderick S.C. Wong

More Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year’s course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2, 4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE. The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange’s theorem, respectively. Chapters 5—7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10–14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann—Hilbert problem and integral equations, and Darboux’s method for computing asymptotics.

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410

Publisher

Springer Nature

Published Date

ISBN 10

3031282884

ISBN 13

9783031282881

Explorations in Complex Functions

By: Richard Beals,Roderick S. C. Wong

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Explorations in Complex Functions

By: Richard Beals,Roderick S. C. Wong

This textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. 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. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into L-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method. Showcasing an array of accessible excursions, Explorations in Complex Functions is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.

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353

Publisher

Springer Nature

Published Date

ISBN 10

3030545334

ISBN 13

9783030545338

Differential Equations & Asymptotic Theory in Mathematical Physics

Wuhan University, Hubei, China, 20-29 October 2003

By: Zhen Hua,Roderick Wong

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Differential Equations & Asymptotic Theory in Mathematical Physics

Wuhan University, Hubei, China, 20-29 October 2003

By: Zhen Hua,Roderick Wong

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: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences.

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390

Publisher

World Scientific

Published Date

ISBN 10

9812702393

ISBN 13

9789812702395

Special Functions and Orthogonal Polynomials

By: Richard Beals,Roderick Wong

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Special Functions and Orthogonal Polynomials

By: Richard Beals,Roderick Wong

The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-first century'.

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Page Count

489

Publisher

Cambridge University Press

Published Date

ISBN 10

1316578054

ISBN 13

9781316578056

Lecture Notes On Applied Analysis

By: Roderick S C Wong

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Lecture Notes On Applied Analysis

By: Roderick S C Wong

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303

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World Scientific Publishing Company

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ISBN 10

9813107669

ISBN 13

9789813107663

Book's by Roderick S.C. Wong

Lecture Notes On Applied Analysis

Lecture Notes On Applied Analysis

More Explorations in Complex Functions

More Explorations in Complex Functions

Explorations in Complex Functions

Explorations in Complex Functions

Differential Equations & Asymptotic Theory in Mathematical Physics

Differential Equations & Asymptotic Theory in Mathematical Physics

Special Functions and Orthogonal Polynomials

Special Functions and Orthogonal Polynomials

Lecture Notes On Applied Analysis

Lecture Notes On Applied Analysis

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