Boas, Harold P.
Overview
Works:  6 works in 34 publications in 2 languages and 1,142 library holdings 

Genres:  Academic theses 
Roles:  Contributor, Other, Translator, Editor 
Classifications:  QA331, 515.8 
Publication Timeline
.
Most widely held works by
Harold P Boas
A primer of real functions by
Ralph P Boas(
Book
)
20 editions published between 1996 and 2012 in English and Italian and held by 912 WorldCat member libraries worldwide
"This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhereoscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for selfstudy or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days"Publisher description
20 editions published between 1996 and 2012 in English and Italian and held by 912 WorldCat member libraries worldwide
"This is a revised, updated, and augmented edition of a classic Carus monograph with a new chapter on integration and its applications. Earlier editions covered sets, metric spaces, continuous functions, and differentiable functions. To that, this edition adds sections on measurable sets and functions and the Lebesgue and Stieltjes integrals. The book retains the informal chatty style of the previous editions. It presents a variety of interesting topics, many of which are not commonly encountered in undergraduate textbooks, such as the existence of continuous everywhereoscillating functions; two functions having equal derivatives, yet not differing by a constant; application of Stieltjes integration to the speed of convergence of infinite series. For readers with a background in calculus, the book is suitable either for selfstudy or for supplemental reading in a course on advanced calculus or real analysis. Students of mathematics will find here the sense of wonder that was associated with the subject in its early days"Publisher description
Invitation to complex analysis by
Ralph P Boas(
Book
)
7 editions published in 2010 in English and held by 215 WorldCat member libraries worldwide
"This book, whose first edition was written by Ralph P. Boas and published by Random House in 1987, reveals both the power of complex analysis as a tool for applications and the intrinsic beauty of the subject as a fundamental part of pure mathematics. This revised edition by the author's son, Harold P. Boas, himself an awardwinning mathematical expositor, is an ideal choice for a first course in complex analysis, as a classroom text, and for independent study. Distilling the subject into a lucid, engaging, rigorous account of the subject, the authors go beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions. Included are accessible discussions of less wellknown but intriguing topics ranging from Landau's notation and overconvergent series to the PhragmenLindelof theorems. Nearly 70 exercises, with detailed solutions, serve as models for students, and supplementary exercises provide even more material for the classroom."Publisher's description
7 editions published in 2010 in English and held by 215 WorldCat member libraries worldwide
"This book, whose first edition was written by Ralph P. Boas and published by Random House in 1987, reveals both the power of complex analysis as a tool for applications and the intrinsic beauty of the subject as a fundamental part of pure mathematics. This revised edition by the author's son, Harold P. Boas, himself an awardwinning mathematical expositor, is an ideal choice for a first course in complex analysis, as a classroom text, and for independent study. Distilling the subject into a lucid, engaging, rigorous account of the subject, the authors go beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions. Included are accessible discussions of less wellknown but intriguing topics ranging from Landau's notation and overconvergent series to the PhragmenLindelof theorems. Nearly 70 exercises, with detailed solutions, serve as models for students, and supplementary exercises provide even more material for the classroom."Publisher's description
The BochnerMartinelli integral and its applications by
A. M Kytmanov(
Book
)
4 editions published in 1995 in English and held by 11 WorldCat member libraries worldwide
The BochnerMartinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n> 1, the BochnerMartinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the BochnerMartinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood Brown) on removability of compact singularities of holomorphic functions in en when n> 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of BochnerMartinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the BochnerMartinelli integral being the sum of a doublelayer potential and the tangential derivative of a singlelayer potential. Therefore the BochnerMartinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the doublelayer potential. Thus, the BochnerMartinelli integral combines properties of the Cauchy integral and the doublelayer potential
4 editions published in 1995 in English and held by 11 WorldCat member libraries worldwide
The BochnerMartinelli integral representation for holomorphic functions or'sev eral complex variables (which has already become classical) appeared in the works of Martinelli and Bochner at the beginning of the 1940's. It was the first essen tially multidimensional representation in which the integration takes place over the whole boundary of the domain. This integral representation has a universal 1 kernel (not depending on the form of the domain), like the Cauchy kernel in e . However, in en when n> 1, the BochnerMartinelli kernel is harmonic, but not holomorphic. For a long time, this circumstance prevented the wide application of the BochnerMartinelli integral in multidimensional complex analysis. Martinelli and Bochner used their representation to prove the theorem of Hartogs (Osgood Brown) on removability of compact singularities of holomorphic functions in en when n> 1. In the 1950's and 1960's, only isolated works appeared that studied the boundary behavior of BochnerMartinelli (type) integrals by analogy with Cauchy (type) integrals. This study was based on the BochnerMartinelli integral being the sum of a doublelayer potential and the tangential derivative of a singlelayer potential. Therefore the BochnerMartinelli integral has a jump that agrees with the integrand, but it behaves like the Cauchy integral under approach to the boundary, that is, somewhat worse than the doublelayer potential. Thus, the BochnerMartinelli integral combines properties of the Cauchy integral and the doublelayer potential
A primer of real functions by
Ralph P Boas(
)
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
This is a revised, updated and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is thus suitable either for selfstudy or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: for example, the existence of continuous everywhereoscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series
1 edition published in 1996 in English and held by 2 WorldCat member libraries worldwide
This is a revised, updated and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is thus suitable either for selfstudy or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: for example, the existence of continuous everywhereoscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series
Topics on potential theory on Lipschitz domains and boundary control problems by Zhonghai Ding(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
The trace theorem of the Sobolev space H s(Sl) on Lipschitz domain ti has not been proved completely before. In chapter II, a proof of trace theorem for the range \ < s <  and s > f is first given. In Chapter III, the regularities of S in L p and the relations between ( ±  / + /C) 1 and ( ±  I + £ * ) 1 are obtained. Furtherm ore, new regularities of 1C and 1C* on sm ooth domains in aft3 are found, which reveal that 5, rC and JC* have the same regularities on smooth boundaries. In C hapter IV, a new approach based on the potential theory and variational m ethod is proposed to study the linear quadratic regulator problems (LQR) governed by the elliptic equation on Lipschitz domains with point observations on boundary. The LQR problems with or without control constraints are completely solved in this work. The regularities of optim al controls and states and the explicit expressions of optimal controls are derived. The singularities in optim al controls are displayed explicitely through decomposition formulas. Finally in C hapter V, a gradienttruncation m ethod and an iterative truncation m ethod have been developed to com pute optimal controls of (LQR) problems. The test problems show th at both m ethods are insensitive to the partition of boundary. It is found th a t the classical Lagrangian m ultiplier method may fail to provide reliable numerical algorithm on our (LQR) problems
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
The trace theorem of the Sobolev space H s(Sl) on Lipschitz domain ti has not been proved completely before. In chapter II, a proof of trace theorem for the range \ < s <  and s > f is first given. In Chapter III, the regularities of S in L p and the relations between ( ±  / + /C) 1 and ( ±  I + £ * ) 1 are obtained. Furtherm ore, new regularities of 1C and 1C* on sm ooth domains in aft3 are found, which reveal that 5, rC and JC* have the same regularities on smooth boundaries. In C hapter IV, a new approach based on the potential theory and variational m ethod is proposed to study the linear quadratic regulator problems (LQR) governed by the elliptic equation on Lipschitz domains with point observations on boundary. The LQR problems with or without control constraints are completely solved in this work. The regularities of optim al controls and states and the explicit expressions of optimal controls are derived. The singularities in optim al controls are displayed explicitely through decomposition formulas. Finally in C hapter V, a gradienttruncation m ethod and an iterative truncation m ethod have been developed to com pute optimal controls of (LQR) problems. The test problems show th at both m ethods are insensitive to the partition of boundary. It is found th a t the classical Lagrangian m ultiplier method may fail to provide reliable numerical algorithm on our (LQR) problems
A primer of real functions by
Ralph P Boas(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
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Harold P. Boas American mathematician
Harold P. Boas Amerikaans wiskundige
Harold P. Boas amerikansk matematikar
Harold P. Boas amerikansk matematiker
Harold P. Boas matematan Lamerikänik
Harold P. Boas matemàtic estatunidenc
Harold P. Boas matematician american
Harold P. Boas matemático estadounidense
Harold P. Boas matematico statunitense
Harold P. Boas mathématicien américain
Harold P. Boas USamerikanischer Mathematiker
Harold P. Boas Usana matematikisto
Harold P. Boas usona matematikisto
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