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Elsevier

Books in Analysis

  • Foundations of Real Analysis

    Expanding Horizons beyond the click
    • 1st Edition
    • William R. Brian
    • English
    Foundations of Real Analysis: Expanding Horizons beyond the click covers the central topics of analysis, like continuity, differentiation, and integration, with a particular emphasis on set-theoretic and topological aspects of the real line, such as the Baire Category Theorem and the infinite-length Banach-Mazur games. These mathematical spectacles aim to challenge the student’s preconceptions about the real line, while at the same time the main part of the text builds up a more well-founded intuition. The book connects analysis with other adjacent areas of mathematics, including important arguments and ideas from topology, measure theory, abstract algebra, descriptive set theory, and functional analysis.It is richly illustrated and includes a wealth of interesting examples and counterexamples, such as Hilbert’s space-filling curves and Volterra’s non-integrable derivative aims to give students a thorough and rigorous introduction to real analysis, leaning on the more intuitive and imaginative aspects of the subject, while also revealing some of the broader context of modern mathematics in which the subject is situated. This introductory course is designed not only for future analysts, but for anyone wanting to understand analysis and to sharpen their mathematical insight. The text is well suited to a two-semester university course, but can also be used for self-study by the curious reader.

  • Measure and Integration

    Concepts, Examples, and Applications
    • 1st Edition
    • Ahmed Ghatasheh + 2 more
    • English
    Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefully crafted, practical examples. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking, problem-solving, and new areas of research powered by real analysis.

  • Generalized Quantum Calculus with Applications

    • 1st Edition
    • Svetlin G. Georgiev + 1 more
    • English
    Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula.Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

  • Fuzzy Mathematics, Graphs, and Similarity Measures

    Analysis and Application Across Global Challenges
    • 1st Edition
    • John Mordeson + 1 more
    • English
    Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges. Following a full grounding in fuzzy graph indices, connectivity in fuzzy graph structures, lattice isomorphisms, and similarity measures, the book applies these models in analyzing world challenges, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change.Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor’s manual supports teaching across a range of course contexts.

  • Advanced Mathematics for Engineering Students

    The Essential Toolbox
    • 1st Edition
    • Brent J. Lewis + 2 more
    • English
    Advanced Mathematics for Engineering Students: The Essential Toolbox provides a concise treatment for applied mathematics. Derived from two semester advanced mathematics courses at the author’s university, the book delivers the mathematical foundation needed in an engineering program of study. Other treatments typically provide a thorough but somewhat complicated presentation where students do not appreciate the application. This book focuses on the development of tools to solve most types of mathematical problems that arise in engineering – a “toolbox” for the engineer. It provides an important foundation but goes one step further and demonstrates the practical use of new technology for applied analysis with commercial software packages (e.g., algebraic, numerical and statistical).

  • Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

    • 1st Edition
    • Dumitru Motreanu
    • English
    Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.

  • Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

    • 1st Edition
    • Abraham Ungar
    • English
    Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

  • Means in Mathematical Analysis

    Bivariate Means
    • 1st Edition
    • Gheorghe Toader + 1 more
    • English
    Means in Mathematical Analysis addresses developments in global analysis, non-linear analysis, and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations and probability theory. The series comprises highly specialized research monographs written by eminent scientists, handbooks and selected multi-contributor reference works (edited volumes), bringing together an extensive body of information. It deals with the fundamental interplay of nonlinear analysis with other headline domains, particularly geometry and analytic number theory, within the mathematical sciences.

  • Computational Analysis of Structured Media

    • 1st Edition
    • Simon Gluzman + 2 more
    • English
    Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices.

  • Finite Elements for Analysis and Design

    Computational Mathematics and Applications Series
    • 1st Edition
    • J. E. Akin
    • English
    The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.

  • Handbook of Mathematical Formulas and Integrals

    • 1st Edition
    • Alan Jeffrey
    • English
    If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse.

  • Calculus and Its Applications

    • 1st Edition
    • P. Mainardi + 1 more
    • English
    Calculus and its Applications provides information pertinent to the applications of calculus. This book presents the trapping technique in defining geometrical and physical entities that are usually regarded as limits of sums. Organized into 20 chapters, this book begins with an overview of the notion of average speed that seems to appear first as a qualitative concept. This text then presents the concepts of external and internal parameters to increase the appreciation of parametric functions. Other chapters consider separable differential equations with more detail than usual with their suitability in describing physical laws. This book discusses as well the study of variable quantities whose magnitude is determined by the magnitudes of several other variables. The final chapter deals with a homogeneous differential equation and auxiliary equations consisting imaginary roots. This book is a valuable resource for mathematicians and students. Readers whose interests span a variety of fields will also find this book useful.

  • Elementary Calculus

    • 1st Edition
    • P.R. Masani + 2 more
    • Ralph P. Boas
    • English
    Elementary Calculus presents a three semester introductory course on calculus. This book reveals the conceptual development of the calculus, taking into cognizance the technical and applied sides and standards of clarity and rigor that prevail in mathematics. The topics discussed include the basic laws of numbers, classification of real functions, and concept of instantaneous velocity. The limits of functions defined on intervals, derivatives of the trigonometric functions, and standard logarithmic function are also reviewed. This text likewise considers integration by substitution, lengths of plane curves, and simple harmonic motion. This publication is designed for students who have a knowledge of elementary trigonometry, and either have had a one semester course on analytic or coordinate geometry or might take such a course with calculus.

  • Mathematical Analysis Fundamentals

    • 1st Edition
    • Agamirza Bashirov
    • English
    The author’s goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options.

  • A Course in Real Analysis

    • 2nd Edition
    • John N. McDonald + 1 more
    • English
    Approx.668 pages

  • Doing Bayesian Data Analysis

    A Tutorial Introduction with R
    • 1st Edition
    • John Kruschke
    • English
    There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods.

  • Advanced Calculus

    A Transition to Analysis, Student Solutions Manual (e-only)
    • 1st Edition
    • Joseph B. Dence + 1 more
    • English

  • Advanced Calculus

    A Transition to Analysis
    • 1st Edition
    • Thomas P. Dence + 1 more
    • English
    Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis – providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. It covers exponential function, and the development of trigonometric functions from the integral. The text is designed for a one-semester advanced calculus course for advanced undergraduates or graduate students.

  • Stability of Dynamical Systems

    • 1st Edition
    • Volume 5
    • Xiaoxin Liao + 2 more
    • English
    The main purpose of developing stability theory is to examine dynamic responses of a system to disturbances as the time approaches infinity. It has been and still is the object of intense investigations due to its intrinsic interest and its relevance to all practical systems in engineering, finance, natural science and social science. This monograph provides some state-of-the-art expositions of major advances in fundamental stability theories and methods for dynamic systems of ODE and DDE types and in limit cycle, normal form and Hopf bifurcation control of nonlinear dynamic systems.

  • Practical Data Analysis in Chemistry

    • 1st Edition
    • Volume 26
    • Marcel Maeder + 1 more
    • English
    The majority of modern instruments are computerised and provide incredible amounts of data. Methods that take advantage of the flood of data are now available; importantly they do not emulate 'graph paper analyses' on the computer. Modern computational methods are able to give us insights into data, but analysis or data fitting in chemistry requires the quantitative understanding of chemical processes. The results of this analysis allows the modelling and prediction of processes under new conditions, therefore saving on extensive experimentation. Practical Data Analysis in Chemistry exemplifies every aspect of theory applicable to data analysis using a short program in a Matlab or Excel spreadsheet, enabling the reader to study the programs, play with them and observe what happens. Suitable data are generated for each example in short routines, this ensuring a clear understanding of the data structure. Chapter 2 includes a brief introduction to matrix algebra and its implementation in Matlab and Excel while Chapter 3 covers the theory required for the modelling of chemical processes. This is followed by an introduction to linear and non-linear least-squares fitting, each demonstrated with typical applications. Finally Chapter 5 comprises a collection of several methods for model-free data analyses.

  • Measure Theory

    A First Course
    • 1st Edition
    • Carlos S Kubrusly
    • English
    This contemporary first course focuses on concepts and ideas of Measure Theory, highlighting the theoretical side of the subject. Its primary intention is to introduce Measure Theory to a new generation of students, whether in mathematics or in one of the sciences, by offering them on the one hand a text with complete, rigorous and detailed proofs--sketchy proofs have been a perpetual complaint, as demonstrated in the many Amazon reader reviews critical of authors who "omit 'trivial' steps" and "make not-so-obvious 'it is obvious' remarks." On the other hand, Kubrusly offers a unique collection of fully hinted problems. On the other hand, Kubrusly offers a unique collection of fully hinted problems. The author invites the readers to take an active part in the theory construction, thereby offering them a real chance to acquire a firmer grasp on the theory they helped to build. These problems, at the end of each chapter, comprise complements and extensions of the theory, further examples and counterexamples, or auxiliary results. They are an integral part of the main text, which sets them apart from the traditional classroom or homework exercises.JARGON BUSTER:measure theoryMeasure theory investigates the conditions under which integration can take place. It considers various ways in which the "size" of a set can be estimated.This topic is studied in pure mathematics programs but the theory is also foundational for students of statistics and probability, engineering, and financial engineering.

  • Real Analysis with an Introduction to Wavelets and Applications

    • 1st Edition
    • Don Hong + 2 more
    • English
    Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications.

  • Working Analysis

    • 1st Edition
    • Jeffery Cooper
    • English
    Working Analysis is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical computation is developed as an important aspect of mathematical analysis.

  • Infinitesimal Methods of Mathematical Analysis

    • 1st Edition
    • J S Pinto
    • English
    This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.

  • Geometric Computations with Interval and New Robust Methods

    Applications in Computer Graphics, GIS and Computational Geometry
    • 1st Edition
    • H Ratschek + 1 more
    • English
    This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free.

  • Foundations of Complex Analysis in Non Locally Convex Spaces

    Function Theory without Convexity Condition
    • 1st Edition
    • Volume 193
    • A. Bayoumi
    • English
    All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field.Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory.Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem.Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions.The new concept of Quasi-differentiabil... introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one.The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems.bull; The book contains new generalized versions of:i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others.ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author.bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995.bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

  • Handbook of Mathematical Formulas and Integrals

    • 3rd Edition
    • Alan Jeffrey
    • English
    The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. The Third Edition has new chapters covering solutions of elliptic, parabolic and hyperbolic equations and qualitative properties of the heat and Laplace equation.

  • A Primer of Lebesgue Integration

    • 2nd Edition
    • H. S. Bear
    • English
    The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.

  • Computable Calculus

    • 1st Edition
    • Oliver Aberth
    • English
    Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls. The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs.

  • An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93

    • 2nd Edition
    • Robert M. Young
    • English
    An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

  • Introductory Analysis

    A Deeper View of Calculus
    • 1st Edition
    • Richard J. Bagby
    • English
    Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.

  • Introductory Analysis

    The Theory of Calculus
    • 2nd Edition
    • John A. Fridy
    • English
    Introductory Analysis, Second Edition, is intended for the standard course on calculus limit theories that is taken after a problem solving first course in calculus (most often by junior/senior mathematics majors). Topics studied include sequences, function limits, derivatives, integrals, series, metric spaces, and calculus in n-dimensional Euclidean space

  • Handbook of Analysis

    CD-ROM Version
    • 1st Edition
    • Eric Schechter
    • English
    This version of Handbook of Analysis provides convenient access to reference material on the foundations of mathematical analysis. It is appropriate for advanced undergraduates and beginning graduate students in mathematics, as well as practitioners. The CD-ROM is a unified presentation of the foundation of virtually all of mathematics, with the exception of geometry.

  • A Course in Real Analysis

    • 1st Edition
    • John N. McDonald + 1 more
    • English
    A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently by progressing from the concrete to the abstract. McDonald and Weiss have also created real application chapters on probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of material to cover.

  • Problems in Real Analysis

    • 2nd Edition
    • Charalambos D. Aliprantis + 1 more
    • English
    A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods. Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.

  • Principles of Real Analysis

    • 3rd Edition
    • Charalambos D. Aliprantis
    • Owen Burkinshaw
    • English
    With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

  • Partial Differential Equations & Boundary Value Problems with Maple V

    • 1st Edition
    • George A. Articolo
    • English
    George Articulo covers all the material found in traditional partial differentiation equations and boundary value courses in this textbook. Its unique approach allows students to learn the mathematics first, then use Maple graphics capabilities to visualize both static and animated behavior of the solution. The book provides many example problems using commands that render two- or three-dimensional animated graphics. The author focuses on the natural union between partial differential equations and a powerful computational language such as Maple.

  • Inequalities for Differential and Integral Equations

    • 1st Edition
    • Volume 197
    • English
    Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.

  • Fractal Imaging

    • 1st Edition
    • Wei-Kao Lu
    • English
    Fractal image compression technology, one of the major digital image compression techniques, has been a well kept secret for many years. While there are many books written on other technologies, such as DCT/JPEG andwavelet theory, few books touch the subject of fractal image compression. Fractal Imaging presents the logic, technology, and various uses of fractal imaging by analyzing a complete, usable fractal image representation system. This detailed work will be a must for engineers interested in building fractal imaging systems. It will also be of interest to the general public, showing how mathematics once again plays a central role in our lives, where art and science intersect.

  • Causal Symmetric Spaces

    • 1st Edition
    • Volume 18
    • Gestur Olafsson + 1 more
    • English
    This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces.

  • Introduction to Stochastic Dynamic Programming

    • 1st Edition
    • Sheldon M. Ross
    • English

  • Harmonic Analysis and Special Functions on Symmetric Spaces

    • 1st Edition
    • Volume 16
    • Gerrit Heckman
    • English
    The two parts of this sharply focused book, Hypergeometric and Special Functions and Harmonic Analysis on Semisimple Symmetric Spaces, are derived from lecture notes for the European School of Group Theory, a forum providing high-level courses on recent developments in group theory. The authors provide students and researchers with a thorough and thoughtful overview, elaborating on the topic with clear statements of definitions and theorems and augmenting these withtime-saving examples. An extensive set of notes supplements the text.Heckman and Schlichtkrull extend the ideas of harmonic analysis on semisimple symmetric spaces to embrace the theory of hypergeometric and spherical functions and show that the K-variant Eisenstein integrals for G/H are hypergeometric functions under this theory. They lead readers from the fundamentals of semisimple symmetric spaces of G/H to the frontier, including generalization, to the Riemannian case. This volume will interest harmonic analysts, those working on or applying the theory of symmetric spaces; it will also appeal to those with an interest in special functions.

  • Calculus

    Introductory Theory and Applications in Physical and Life Science
    • 1st Edition
    • R. M. Johnson
    • English
    This lucid and balanced introduction for first year engineers and applied mathematicians conveys the clear understanding of the fundamentals and applications of calculus, as a prelude to studying more advanced functions. Short and fundamental diagnostic exercises at the end of each chapter test comprehension before moving to new material.

  • Recursive Functionals

    • 1st Edition
    • Volume 131
    • L.E. Sanchis
    • English
    This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results. Although aiming basically at a theory of higher order computability, attention is restricted to second order functionals, where the arguments are numerical functions and the values, when defined, are natural numbers. This theory is somewhat special, for to some extent it can be reduced to first order theory, but when properly extended and relativized it requires the full machinery of higher order computations. In the theory of recursive monotonic functionals the author formulates a reasonable notion of computation which provides the right frame for what appears to be a convincing form of the extended Church's thesis. At the same time, the theory provides sufficient room to formulate the classical results that are usually derived in terms of singular functionals. Presented are complete proofs of Gandy's selector theorem, Kleene's theorem on hyperarithmetical predicates, and Grilliot's theorem on effectively discontinuous functionals.

  • An Introduction to Wavelets

    • 1st Edition
    • Volume 1
    • Charles K. Chui
    • English
    An Introduction to Wavelets is the first volume in a new series, WAVELET ANALYSIS AND ITS APPLICATIONS. This is an introductory treatise on wavelet analysis, with an emphasis on spline wavelets and time-frequency analysis. Among the basic topics covered in this book are time-frequency localization, integral wavelet transforms, dyadic wavelets, frames, spline-wavelets, orthonormal wavelet bases, and wavelet packets. In addition, the author presents a unified treatment of nonorthogonal, semiorthogonal, and orthogonal wavelets. This monograph is self-contained, the only prerequisite being a basic knowledge of function theory and real analysis. It is suitable as a textbook for a beginning course on wavelet analysis and is directed toward both mathematicians and engineers who wish to learn about the subject. Specialists may use this volume as a valuable supplementary reading to the vast literature that has already emerged in this field.

  • Principles of Real Analysis

    • 2nd Edition
    • Charalambos D. Aliprantis + 1 more
    • English
    This major textbook on real analysis is now available in a corrected and slightly amended reprint. It covers the basic theory of integration in a clear, well-organized manner using an imaginative and highly practical synthesis of the 'Daniell method' and the measure-theoretic approach. It is the ideal text for senior undergraduate and first-year graduate courses in real analysis, assuming student familiarity with advanced calculus and basic algebraic concepts.

  • Real Reductive Groups I

    • 1st Edition
    • Volume 132
    • Nolan R. Wallach
    • English
    Real Reductive Groups I is an introduction to the representation theory of real reductive groups. It is based on courses that the author has given at Rutgers for the past 15 years. It also had its genesis in an attempt of the author to complete a manuscript of the lectures that he gave at the CBMS regional conference at The University of North Carolina at Chapel Hill in June of 1981. This book comprises 10 chapters and begins with some background material as an introduction. The following chapters then discuss elementary representation theory; real reductive groups; the basic theory of (g, K)-modules; the asymptotic behavior of matrix coefficients; The Langlands Classification; a construction of the fundamental series; cusp forms on G; character theory; and unitary representations and (g, K)-cohomology. This book will be of interest to mathematicians and statisticians.

  • Inverse Spectral Theory

    • 1st Edition
    • Volume 130
    • Jurgen Poschel
    • English

  • Fuzzy Sets and Systems

    Theory and Applications
    • 1st Edition
    • Didier J. Dubois
    • English
    Fuzzy Sets and Systems: Theory and Applications provides a comprehensive research monography that cover all of the important developments in the theory of fuzzy sets and their applications that have taken place during the past several years.