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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis

Special Functions and Orthogonal Polynomials (Hardcover, 2 Rev Ed): Richard Beals, Roderick Wong Special Functions and Orthogonal Polynomials (Hardcover, 2 Rev Ed)
Richard Beals, Roderick Wong
R2,115 Discovery Miles 21 150 Ships in 12 - 17 working days

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 Painleve transcendents, which have been termed the 'special functions of the twenty-first century'.

Analysis III - Analytic and Differential Functions, Manifolds and Riemann Surfaces (Paperback, 2015 ed.): Roger Godement Analysis III - Analytic and Differential Functions, Manifolds and Riemann Surfaces (Paperback, 2015 ed.)
Roger Godement; Translated by Urmie Ray
R2,791 Discovery Miles 27 910 Ships in 10 - 15 working days

Volume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques. Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R).

The Krasnosel'skii-Mann Iterative Method - Recent Progress and Applications (Paperback, 1st ed. 2022): Qiao-Li Dong, Yeol... The Krasnosel'skii-Mann Iterative Method - Recent Progress and Applications (Paperback, 1st ed. 2022)
Qiao-Li Dong, Yeol Je Cho, Songnian He, Panos M. Pardalos, Themistocles M. Rassias
R1,568 Discovery Miles 15 680 Ships in 12 - 17 working days

This brief explores the Krasnosel'skii-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.

Numbers and Functions - Steps into Analysis (Paperback, 3rd Revised edition): R. P. Burn Numbers and Functions - Steps into Analysis (Paperback, 3rd Revised edition)
R. P. Burn
R1,456 Discovery Miles 14 560 Ships in 12 - 17 working days

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this third edition of Numbers and Functions, Professor Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of more than 800 problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, of which most are supplied with brief answers, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. Carefully corrected and updated throughout, this new edition also includes extra questions on integration and an introduction to convergence. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.

The Real Numbers and Real Analysis (Paperback, 2011 ed.): Ethan D. Bloch The Real Numbers and Real Analysis (Paperback, 2011 ed.)
Ethan D. Bloch
R1,852 Discovery Miles 18 520 Ships in 10 - 15 working days

This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.

Real Analysis on Intervals (Hardcover, 2014 ed.): A. D. R. Choudary, Constantin P. Niculescu Real Analysis on Intervals (Hardcover, 2014 ed.)
A. D. R. Choudary, Constantin P. Niculescu
R1,623 Discovery Miles 16 230 Ships in 10 - 15 working days

The book targets undergraduate and postgraduate mathematics students and helps them develop a deep understanding of mathematical analysis. Designed as a first course in real analysis, it helps students learn how abstract mathematical analysis solves mathematical problems that relate to the real world. As well as providing a valuable source of inspiration for contemporary research in mathematics, the book helps students read, understand and construct mathematical proofs, develop their problem-solving abilities and comprehend the importance and frontiers of computer facilities and much more. It offers comprehensive material for both seminars and independent study for readers with a basic knowledge of calculus and linear algebra. The first nine chapters followed by the appendix on the Stieltjes integral are recommended for graduate students studying probability and statistics, while the first eight chapters followed by the appendix on dynamical systems will be of use to students of biology and environmental sciences. Chapter 10 and the appendixes are of interest to those pursuing further studies at specialized advanced levels. Exercises at the end of each section, as well as commentaries at the end of each chapter, further aid readers' understanding. The ultimate goal of the book is to raise awareness of the fine architecture of analysis and its relationship with the other fields of mathematics.

Foundations of Differential Calculus (Paperback, Softcover reprint of the original 1st ed. 2000): Euler Foundations of Differential Calculus (Paperback, Softcover reprint of the original 1st ed. 2000)
Euler; Translated by J.D. Blanton
R4,080 Discovery Miles 40 800 Ships in 10 - 15 working days

The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.

Koethe-Bochner Function Spaces (Paperback, Softcover reprint of the original 1st ed. 2004): Pei-Kee Lin Koethe-Bochner Function Spaces (Paperback, Softcover reprint of the original 1st ed. 2004)
Pei-Kee Lin
R2,901 Discovery Miles 29 010 Ships in 10 - 15 working days

This monograph is devoted to the study of Koethe-Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here, giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided, and the theory of Koethe-Bochner spaces is rigorously developed, with a particular focus on open problems. Extensive historical information, references, and questions for further study are included; instructive examples and many exercises are incorporated throughout. Both expansive and precise, this book's unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

A Course in Mathematical Analysis (Hardcover, New): D.J.H. Garling A Course in Mathematical Analysis (Hardcover, New)
D.J.H. Garling
R3,527 Discovery Miles 35 270 Ships in 12 - 17 working days

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume II goes on to consider metric and topological spaces and functions of several variables. Volume III covers complex analysis and the theory of measure and integration.

Classical and Multilinear Harmonic Analysis (Hardcover, New): Camil Muscalu, Wilhelm Schlag Classical and Multilinear Harmonic Analysis (Hardcover, New)
Camil Muscalu, Wilhelm Schlag
R1,864 Discovery Miles 18 640 Ships in 12 - 17 working days

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderon-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

Lectures on Real Analysis (Hardcover, New): Finnur Larusson Lectures on Real Analysis (Hardcover, New)
Finnur Larusson
R3,801 Discovery Miles 38 010 Ships in 12 - 17 working days

This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.

Inequalities Based on Sobolev Representations (Paperback, 2011): george A. Anastassiou Inequalities Based on Sobolev Representations (Paperback, 2011)
george A. Anastassiou
R1,398 Discovery Miles 13 980 Ships in 10 - 15 working days

"Inequalities based on Sobolev Representations" deals exclusively with very general tight integral inequalities of Chebyshev-Gruss, Ostrowski types and of integral means, all of which depend upon the Sobolev integral representations of functions. Applicationsillustrate inequalities that engage in ordinary and weak partial derivatives of the involved functions. This book also derives important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. The results are examined in all directions and through both univariate and multivariate cases. This book is suitable for researchers, graduate students, and seminars in subareas of mathematical analysis, inequalities, partial differential equations and information theory. "

Extensions of Moser-Bangert Theory - Locally Minimal Solutions (Hardcover, 2011 ed.): Paul H. Rabinowitz, Edward W. Stredulinsky Extensions of Moser-Bangert Theory - Locally Minimal Solutions (Hardcover, 2011 ed.)
Paul H. Rabinowitz, Edward W. Stredulinsky
R2,879 Discovery Miles 28 790 Ships in 10 - 15 working days

This self-contained monograph presents extensions of the Moser Bangert approach that include solutions of a family of nonlinear elliptic PDEs on "Rn" and an Allen Cahn PDE model of phase transitions. After recalling the relevant Moser Bangert results, "Extensions of Moser Bangert Theory" pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties.

The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.

Lebesgue and Sobolev Spaces with Variable Exponents (Paperback, Edition.): Lars Diening, Petteri Harjulehto, Peter Hastoe,... Lebesgue and Sobolev Spaces with Variable Exponents (Paperback, Edition.)
Lars Diening, Petteri Harjulehto, Peter Hastoe, Michael Ruzicka
R2,694 Discovery Miles 26 940 Ships in 10 - 15 working days

The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.

Special Functions - A Graduate Text (Hardcover): Richard Beals, Roderick Wong Special Functions - A Graduate Text (Hardcover)
Richard Beals, Roderick Wong
R1,435 Discovery Miles 14 350 Ships in 12 - 17 working days

The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

Classical and Quantum Orthogonal Polynomials in One Variable (Paperback): Mourad E.H. Ismail Classical and Quantum Orthogonal Polynomials in One Variable (Paperback)
Mourad E.H. Ismail
R2,285 Discovery Miles 22 850 Ships in 12 - 17 working days

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback. Its encyclopedic coverage includes classical topics such as Jacobi, Hermite, Laguerre, Hahn, Charlier and Meixner polynomials as well as those discovered over the last 50 years, e.g. Askey-Wilson and Al-Salam-Chihara polynomial systems. Multiple orthogonal polynomials are discussed here for the first time in book form. Many modern applications of the subject are dealt with, including birth and death processes, integrable systems, combinatorics, and physical models. A chapter on open research problems and conjectures is designed to stimulate further research on the subject. Thoroughly updated and corrected since its original printing, this book continues to be valued as an authoritative reference not only by mathematicians, but also a wide range of scientists and engineers. Exercises ranging in difficulty are included to help both the graduate student and the newcomer.

Introduction to Partial Differential Equations - A Computational Approach (Paperback, 1st ed. 2004. 2nd printing 2008): Aslak... Introduction to Partial Differential Equations - A Computational Approach (Paperback, 1st ed. 2004. 2nd printing 2008)
Aslak Tveito, Ragnar Winther
R2,292 Discovery Miles 22 920 Ships in 10 - 15 working days

This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Coverage details such topics as separation of variables, Fourier analysis, maximum principles, and energy estimates. The book introduces numerical methods in parallel to the classical theory and also includes many engaging exercises.

Discourse on Fourier Series (Paperback): Cornelius Lanczos Discourse on Fourier Series (Paperback)
Cornelius Lanczos
R2,009 Discovery Miles 20 090 Ships in 12 - 17 working days

Originally published in 1966, this well-written and still-cited text covers Fourier analysis, a foundation of science and engineering. Many modern textbooks are filled with specialized terms and equations that may be confusing, but this book uses a friendly, conversational tone to clarify the material and engage the reader. The author meticulously develops the topic and uses 161 problems integrated into the text to walk the student down the simplest path to a solution.

Amazing and Aesthetic Aspects of Analysis (Paperback, Softcover reprint of the original 1st ed. 2017): Paul Loya Amazing and Aesthetic Aspects of Analysis (Paperback, Softcover reprint of the original 1st ed. 2017)
Paul Loya
R1,897 Discovery Miles 18 970 Ships in 10 - 15 working days

Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous -N and - definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulae for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.

Sobolev Spaces in Mathematics III - Applications in Mathematical Physics (Hardcover, 2009 ed.): Victor Isakov Sobolev Spaces in Mathematics III - Applications in Mathematical Physics (Hardcover, 2009 ed.)
Victor Isakov
R4,562 Discovery Miles 45 620 Ships in 10 - 15 working days

Victor Isakov This volume contains various results on partial di?erential equations where Sobolev spaces are used. Their selection is motivated by the research int- ests of the editor and the geographicallinks to the places where S. L. Sobolev worked and lived: St. Petersburg, Moscow, and Novosibirsk. Most of the papers are written by leading experts in control theory and inverse pr- lems. Another reason for the selection is a strong link to applied areas. In my opinion, control theory and inverse problems are main areas of di?er- tial equations of importance for some branches of contemporary science and engineering. S. L. Sobolev, as many great mathematicians, was very much motivated by applications. He did not distinguished between pure and - plied mathematics, but, in his own words, between "good mathematics and bad mathematics. " While he possessed a brilliant analytical technique, he most valued innovative ideas, solutions of deep conceptual problems, and not mathematical decorations, perfecting exposition, and "generalizations. " S. L. Sobolev himself never published papers on inverse problems or c- trol theory, but he was very much aware of the state of art and he monitored research on inverse problems. In particular, in his lecture at a Conference on Di?erentialEquationsin1954(found inSobolev'sarchiveandmadeavailable to me by Alexander Bukhgeim), he outlined main inverse problems in g- physics: theinverseseismicproblem, theelectromagneticprospecting, andthe inverse problem of gravimetry.

Period Mappings and Period Domains (Paperback, 2nd Revised edition): James Carlson, Stefan Muller-Stach, Chris Peters Period Mappings and Period Domains (Paperback, 2nd Revised edition)
James Carlson, Stefan Muller-Stach, Chris Peters
R1,597 Discovery Miles 15 970 Ships in 12 - 17 working days

This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kahler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford-Tate groups and their associated domains, the Mumford-Tate varieties and generalizations of Shimura varieties.

Sobolev Spaces in Mathematics II - Applications in Analysis and Partial Differential Equations (Hardcover, 2009 ed.): Vladimir... Sobolev Spaces in Mathematics II - Applications in Analysis and Partial Differential Equations (Hardcover, 2009 ed.)
Vladimir Maz'ya
R4,589 Discovery Miles 45 890 Ships in 10 - 15 working days

Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc.

Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.

Multidimensional Real Analysis II - Integration (Hardcover): J. J. Duistermaat, J. A. C. Kolk Multidimensional Real Analysis II - Integration (Hardcover)
J. J. Duistermaat, J. A. C. Kolk; Translated by J.P.van Braam Houckgeest
R2,859 Discovery Miles 28 590 Ships in 12 - 17 working days

Part two of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of integral analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.

Multidimensional Real Analysis I - Differentiation (Hardcover): J. J. Duistermaat, J. A. C. Kolk Multidimensional Real Analysis I - Differentiation (Hardcover)
J. J. Duistermaat, J. A. C. Kolk; Translated by J.P.van Braam Houckgeest
R2,773 Discovery Miles 27 730 Ships in 12 - 17 working days

Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.

Introductory Real Analysis (Paperback, New edition): A.N. Kolmogorov Introductory Real Analysis (Paperback, New edition)
A.N. Kolmogorov
R723 R626 Discovery Miles 6 260 Save R97 (13%) Ships in 9 - 15 working days

Comprehensive, elementary introduction to real and functional analysis. Self-contained, readily accessible to those with background in advanced calculus. Cover basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, much more. 350 problems.

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