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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations

First Course In Integral Equations, A (Paperback, Second Edition): Abdul-Majid Wazwaz First Course In Integral Equations, A (Paperback, Second Edition)
Abdul-Majid Wazwaz
R1,269 Discovery Miles 12 690 Ships in 12 - 17 working days

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods.This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.Click here for solutions manual.

Nonlinear Partial Differential Equations for Future Applications - Sendai, Japan, July 10-28 and October 2-6, 2017 (Paperback,... Nonlinear Partial Differential Equations for Future Applications - Sendai, Japan, July 10-28 and October 2-6, 2017 (Paperback, 1st ed. 2021)
Shigeaki Koike, Hideo Kozono, Takayoshi Ogawa, Shigeru Sakaguchi
R4,096 Discovery Miles 40 960 Ships in 10 - 15 working days

This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier-Stokes equations, new estimates for a compressible Gross-Pitaevskii-Navier-Stokes system, singular limits for the Keller-Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.

Density Evolution Under Delayed Dynamics - An Open Problem (Paperback, 1st ed. 2020): Jerome Losson, Michael C. Mackey, Richard... Density Evolution Under Delayed Dynamics - An Open Problem (Paperback, 1st ed. 2020)
Jerome Losson, Michael C. Mackey, Richard Taylor, Marta Tyran-Kaminska
R2,831 Discovery Miles 28 310 Ships in 10 - 15 working days

This monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations. Though the authors have no definitive solution to the problem, they offer this contribution in an attempt to define the problem as they see it, and to sketch out several obvious attempts that have been suggested to solve the problem and which seem to have failed. They hope that by being available to the general mathematical community, they will inspire others to consider-and hopefully solve-the problem. Serious attempts have been made by all of the authors over the years and they have made reference to these where appropriate.

The Kurzweil-Henstock Integral and Its Differential - A Unified Theory of Integration on R and Rn (Hardcover): Solomon Leader The Kurzweil-Henstock Integral and Its Differential - A Unified Theory of Integration on R and Rn (Hardcover)
Solomon Leader
R7,350 Discovery Miles 73 500 Ships in 12 - 17 working days

This up-to-the-minute reference/text provides a comprehensive review o f the Kurzweil{Henstock integration process on the real line and in hi gher dimensionsypresenting a unified theory of integration that highli ghts Riemann{Stieltjes, Stieltjes, and Lebesgue integrals as well as i ntegrals of elementary calculus. Furnishes practical applications of t he definitions and theorems in each section as well as appended sets o f exercises Contains novel concepts in differential analysis for eleg ant formulations of theorems and proofs

Perspectives in Dynamical Systems III: Control and Stability - DSTA, Lodz, Poland December 2-5, 2019 (Hardcover, 1st ed. 2021):... Perspectives in Dynamical Systems III: Control and Stability - DSTA, Lodz, Poland December 2-5, 2019 (Hardcover, 1st ed. 2021)
Jan Awrejcewicz
R4,417 Discovery Miles 44 170 Ships in 12 - 17 working days

This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference "Dynamical Systems: Theory and Applications", held in Lodz, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems. The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

Partial Integral Operators and Integro-Differential Equations - Pure and Applied Mathematics (Hardcover): J urgen Appell,... Partial Integral Operators and Integro-Differential Equations - Pure and Applied Mathematics (Hardcover)
J urgen Appell, Anatolij Kalitvin, Petr Zabrejko
R8,796 Discovery Miles 87 960 Ships in 12 - 17 working days

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.

First Course In Integral Equations, A (Hardcover, Second Edition): Abdul-Majid Wazwaz First Course In Integral Equations, A (Hardcover, Second Edition)
Abdul-Majid Wazwaz
R2,229 Discovery Miles 22 290 Ships in 12 - 17 working days

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods.This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.Click here for solutions manual.

Fractional Differentiation Inequalities (Hardcover, 2009 ed.): george A. Anastassiou Fractional Differentiation Inequalities (Hardcover, 2009 ed.)
george A. Anastassiou
R4,057 R3,232 Discovery Miles 32 320 Save R825 (20%) Ships in 12 - 17 working days

In this book the author presents the Opial, Poincare, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by Canavati, Riemann-Liouville and Caputo. The univariate and multivariate cases are both examined. Each chapter is self-contained. The theory is presented systematically along with the applications. The application to information theory is also examined.

This monograph is suitable for researchers and graduate students in pure mathematics. Applied mathematicians, engineers, and other applied scientists will also find this book useful."

Integral Expansions Related to Mehler-Fock Type Transforms (Hardcover): B.N. Mandal, Nanigopal Mandal Integral Expansions Related to Mehler-Fock Type Transforms (Hardcover)
B.N. Mandal, Nanigopal Mandal
R3,847 Discovery Miles 38 470 Ships in 12 - 17 working days

An important class of integral expansions generated by Sturm-Liouville theory involving spherical harmonics is commonly known as Mehler-Fock integral transforms. In this book, a number of integral expansions of such type have been established rigorously. As applications, integral expansions of some simple function are also obtained.

The Rademacher System in Function Spaces (Paperback, 1st ed. 2020): Sergey V. Astashkin The Rademacher System in Function Spaces (Paperback, 1st ed. 2020)
Sergey V. Astashkin
R4,432 Discovery Miles 44 320 Ships in 10 - 15 working days

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.

Probability and Stochastics (Hardcover, 2011 ed.): Erhan Cinlar Probability and Stochastics (Hardcover, 2011 ed.)
Erhan Cinlar
R1,797 Discovery Miles 17 970 Ships in 12 - 17 working days

This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form.

The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes.

Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises.

The bookis based on the author's lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics.

Erhan Cinlar has received many awards for excellence in teaching, including the President's Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style."

Transmutation Operators and Applications (Paperback, 1st ed. 2020): Vladislav V. Kravchenko, Sergei M. Sitnik Transmutation Operators and Applications (Paperback, 1st ed. 2020)
Vladislav V. Kravchenko, Sergei M. Sitnik
R2,993 Discovery Miles 29 930 Ships in 10 - 15 working days

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.

Interference Calculus - A General Framework for Interference Management and Network Utility Optimization (Hardcover, 2012):... Interference Calculus - A General Framework for Interference Management and Network Utility Optimization (Hardcover, 2012)
Martin Schubert, Holger Boche
R2,892 Discovery Miles 28 920 Ships in 10 - 15 working days

This book develops a mathematical framework for modeling and optimizing interference-coupled multiuser systems. At the core of this framework is the concept of general interference functions, which provides a simple means of characterizing interdependencies between users. The entire analysis builds on the two core axioms scale-invariance and monotonicity.
The proposed network calculus has its roots in power control theory and wireless communications. It adds theoretical tools for analyzing the typical behavior of interference-coupled networks. In this way it complements existing game-theoretic approaches.
The framework should also be viewed in conjunction with optimization theory. There is a fruitful interplay between the theory of interference functions and convex optimization theory. By jointly exploiting the properties of interference functions, it is possible to design algorithms that outperform general-purpose techniques that only exploit convexity.
The title "network calculus" refers to the fact that the theory of interference functions constitutes a generic theoretical framework for the analysis of interference coupled systems. Certain operations within the framework are "closed," that is, combinations of interference functions are interference functions again. Also, certain properties are preserved under such operations. This, provides a methodology for analyzing different multiuser performance measures that can be expressed as interference functions or combinations of interference functions.

Geometry and Analysis of Metric Spaces via Weighted Partitions (Paperback, 1st ed. 2020): Jun Kigami Geometry and Analysis of Metric Spaces via Weighted Partitions (Paperback, 1st ed. 2020)
Jun Kigami
R1,521 Discovery Miles 15 210 Ships in 10 - 15 working days

The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.

Potential Theory on Sierpinski Carpets - With Applications to Uniformization (Paperback, 1st ed. 2020): Dimitrios Ntalampekos Potential Theory on Sierpinski Carpets - With Applications to Uniformization (Paperback, 1st ed. 2020)
Dimitrios Ntalampekos
R1,521 Discovery Miles 15 210 Ships in 10 - 15 working days

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpinski carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpinski carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this theory is utilized to prove a uniformization result for Sierpinski carpets. This book is intended for researchers in the fields of potential theory, quasiconformal geometry, geometric group theory, complex dynamics, geometric function theory and PDEs.

Measure and Integration (Paperback, 1st ed. 2019): Satish Shirali, Harkrishan Lal Vasudeva Measure and Integration (Paperback, 1st ed. 2019)
Satish Shirali, Harkrishan Lal Vasudeva
R1,196 Discovery Miles 11 960 Ships in 10 - 15 working days

This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis. Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon-Nikody m Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems. This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.

A Concise Introduction to Measure Theory (Paperback, 1st ed. 2018): Satish Shirali A Concise Introduction to Measure Theory (Paperback, 1st ed. 2018)
Satish Shirali
R1,521 Discovery Miles 15 210 Ships in 10 - 15 working days

This undergraduate textbook offers a self-contained and concise introduction to measure theory and integration. The author takes an approach to integration based on the notion of distribution. This approach relies on deeper properties of the Riemann integral which may not be covered in standard undergraduate courses. It has certain advantages, notably simplifying the extension to "fuzzy" measures, which is one of the many topics covered in the book. This book will be accessible to undergraduate students who have completed a first course in the foundations of analysis. Containing numerous examples as well as fully solved exercises, it is exceptionally well suited for self-study or as a supplement to lecture courses.

50 Years with Hardy Spaces - A Tribute to Victor Havin (Paperback, Softcover reprint of the original 1st ed. 2018): Anton... 50 Years with Hardy Spaces - A Tribute to Victor Havin (Paperback, Softcover reprint of the original 1st ed. 2018)
Anton Baranov, Sergei Kisliakov, Nikolai Nikolski
R2,931 Discovery Miles 29 310 Ships in 10 - 15 working days

Written in honor of Victor Havin (1933-2015), this volume presents a collection of surveys and original papers on harmonic and complex analysis, function spaces and related topics, authored by internationally recognized experts in the fields. It also features an illustrated scientific biography of Victor Havin, one of the leading analysts of the second half of the 20th century and founder of the Saint Petersburg Analysis Seminar. A complete list of his publications, as well as his public speech "Mathematics as a source of certainty and uncertainty", presented at the Doctor Honoris Causa ceremony at Linkoeping University, are also included.

Solutions Manual to a Modern Theory of Integration (Paperback): Solutions Manual to a Modern Theory of Integration (Paperback)
R815 Discovery Miles 8 150 Ships in 12 - 17 working days

This solutions manual is geared toward instructors for use as a companion volume to the book, A Modern Theory of Integration, (AMS Graduate Studies in Mathematics series, Volume 32).

Modern Problems in Applied Analysis (Paperback, Softcover reprint of the original 1st ed. 2018): Piotr Drygas, Sergei Rogosin Modern Problems in Applied Analysis (Paperback, Softcover reprint of the original 1st ed. 2018)
Piotr Drygas, Sergei Rogosin
R2,603 Discovery Miles 26 030 Ships in 10 - 15 working days

This book features a collection of recent findings in Applied Real and Complex Analysis that were presented at the 3rd International Conference "Boundary Value Problems, Functional Equations and Applications" (BAF-3), held in Rzeszow, Poland on 20-23 April 2016. The contributions presented here develop a technique related to the scope of the workshop and touching on the fields of differential and functional equations, complex and real analysis, with a special emphasis on topics related to boundary value problems. Further, the papers discuss various applications of the technique, mainly in solid mechanics (crack propagation, conductivity of composite materials), biomechanics (viscoelastic behavior of the periodontal ligament, modeling of swarms) and fluid dynamics (Stokes and Brinkman type flows, Hele-Shaw type flows). The book is addressed to all readers who are interested in the development and application of innovative research results that can help solve theoretical and real-world problems.

Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA'21) (Paperback, 1st... Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA'21) (Paperback, 1st ed. 2022)
Andrzej Dzielinski, Dominik Sierociuk, Piotr Ostalczyk
R3,591 Discovery Miles 35 910 Ships in 12 - 17 working days

This book touches upon various aspects of a very interesting, and growing in popularity category of models of dynamical systems. These are the so-called fractional-order systems. Such models are not only relevant for many fields of science and technology, but may also find numerous applications in other disciplines applying the mathematical modelling tools. Thus, the book is intended for a very wide audience of professionals who want to expand their knowledge of systems modelling and its applications. The book includes the selections of papers presented at the International Conference on Fractional Calculus and its Applications organized by the Warsaw University of Technology and was held online on 6-8 September 2021. The International Conference on Fractional Calculus and its Applications (ICFDA) has an almost twenty years history. It started in Bordeaux (France) in 2004, followed by Porto (Portugal) 2006, Istanbul (Turkey) 2008, Badajoz (Spain) 2010, Nanjing (China) 2012, Catania (Italy) 2014, Novi Sad (Serbia) 2016, Amman (Jordan) 2018. Next ICFDA was planned in 2020 in Warsaw (Poland), but COVID-19 pandemic shifted it to 6-8 September 2021. Hence, the organizers were forced to change the form of the conference to the online one. In the volume twenty eight high-quality research papers presented during the ICFDA 2021 eleven Regular Sessions with an additional online Discussion Session are presented. The presented papers are scientifically inspiring, leading to new fruitful ideas. They cover a very broad range of many disciplines. Nowadays, and especially in such a subject as fractional calculus, it is very difficult to assign papers to specific scientific areas. So, many of the papers included have an interdisciplinary character.

Advanced Boundary Element Methods - Treatment of Boundary Value, Transmission and Contact Problems (Paperback, Softcover... Advanced Boundary Element Methods - Treatment of Boundary Value, Transmission and Contact Problems (Paperback, Softcover reprint of the original 1st ed. 2018)
Joachim Gwinner, Ernst Peter Stephan
R2,738 Discovery Miles 27 380 Ships in 10 - 15 working days

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods - efficient computational tools that have become extremely popular in applications. Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research. The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Function Spaces and Inequalities - New Delhi, India, December 2015 (Paperback, Softcover reprint of the original 1st ed. 2017):... Function Spaces and Inequalities - New Delhi, India, December 2015 (Paperback, Softcover reprint of the original 1st ed. 2017)
Pankaj Jain, Hans-Jurgen Schmeisser
R2,888 Discovery Miles 28 880 Ships in 10 - 15 working days

This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev-Besov and Triebel-Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11-15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Complex Analysis and Dynamical Systems - New Trends and Open Problems (Paperback, Softcover reprint of the original 1st ed.... Complex Analysis and Dynamical Systems - New Trends and Open Problems (Paperback, Softcover reprint of the original 1st ed. 2018)
Mark Agranovsky, Anatoly Golberg, Fiana Jacobzon, David Shoikhet, Lawrence Zalcman
R3,636 Discovery Miles 36 360 Ships in 10 - 15 working days

This book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency - the Schramm-Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.

From Classical to Modern Analysis (Paperback, Softcover reprint of the original 1st ed. 2018): Rinaldo B. Schinazi From Classical to Modern Analysis (Paperback, Softcover reprint of the original 1st ed. 2018)
Rinaldo B. Schinazi
R1,521 Discovery Miles 15 210 Ships in 10 - 15 working days

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis. To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuity on metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

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