**Best Reference Books on Integral Equations**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Integral Equations Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Integral Equations below.

## 1. Integral Equations

1."Introduction to Integral Equations with Applications" by Abdul J Jerry
“Introduction to Integral Equations with Applications” Book Review: The aim of this book is to examine the theoretical basis and contemporary numerical techniques related to linear integral equations. It is divided into various sections, such as Fredholm integral equations of the first kind, integral equations in higher dimensions, higher quadrature numerical integration rules, Laplace and Fourier transforms, and linear and nonlinear integral equations, each providing separate information. In addition, the book illustrates the use of integral equations to tackle real-world engineering and physics problems. Singular integral equations and their solutions are presented through numerous examples, and end-of-chapter exercises are also provided. Prior knowledge of calculus and differential equations is a prerequisite. The target audience of this book comprises mathematicians, scientists, and engineers.
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2."Integral Equations: A Short Course" by L G Chambers
“Integral Equations: A Short Course” Book Review: The fundamental principles of integral equations are demonstrated in this book by utilizing concepts such as uniform convergence, mean convergence, special functions, and complex integration. It introduces Volterra equations and Fredholm equations of the first and second kind, and then proceeds to the classical theory of Fredholm equations through degenerate kernels to Hilbert-Schmidt operators. The book describes and compares symmetric and Hermitian kernels with matrix algebra. The application of classical integral transformations in solving integral equations is discussed, along with the analysis of Fourier, Laplace, Hilbert, and finite Hilbert transforms. Numerous examples and exercises are included to facilitate comprehension and practice.
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3."Linear Integral Equations" by R P Kanwal
“Linear Integral Equations” Book Review: This book is dedicated to define the theoretical and methodological aspects of linear integral equations. It comprises 11 chapters that delve into specific integral equations with separable kernels and a method of successive approximations. The book also explores the properties of classical Fredholm theory and the applications of linear integral equations to ordinary and partial differential equations. Furthermore, it discusses symmetric kernels, singular integral equations, and the integral transform methods. The subsequent chapters focus on the applications of linear integral equations to mixed boundary value problems, as well as the description of integral equation perturbation methods. The book is suitable for both undergraduate and graduate students pursuing degrees in applied mathematics, theoretical mechanics, and mathematical physics.
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4."Integral Equations and Boundary Value Problems" by M D Raisinghania
“Integral Equations and Boundary Value Problems” Book Review: This book comprises 14 chapters that introduce the basic principles of integral equations and boundary value problems. Beginning with definition and terminology, the book covers integral equation perturbation techniques, the integral transform method, singular integral equations, classical Fredholm theory, and the method of successive approximations. The book presents proofs for theorems and their results, along with several examples. The problems are solved step-by-step, and end-of-chapter exercise sets are included. The book is intended for postgraduate students and students preparing for professional and engineering examinations, such as CSIR, NET/JRF, SLET, and GATE.
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5."Integral Equations (Dover Books on Mathematics)" by F G Tricomi
“Integral Equations” Book Review: This book provides a classical perspective on integral equations by offering a detailed explanation of Volterra equations, Fredholm equations, symmetric kernels, orthogonal systems of functions, types of singular or nonlinear integral equations, and more. An analytical framework is employed to scrutinize the mathematical aspects of the applications of integral equations. A set of exercises is included for practice. The book assumes fundamental knowledge of differential and integral calculus as well as the basics of the theory of functions. It is intended for physicists, engineers, and students at the graduate or advanced undergraduate level.
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6."Integral Equations and Application" by C Corduneanu
“Integral Equations and Applications” Book Review: This book serves as an introduction to integral equations and describes the methods for applying the theory. The book addresses the role of Volterra equations as a unifying tool in the study of functional equations. It analyzes the relationship between abstract Volterra equations and other types of functional-differential equations. This book is particularly useful for researchers and graduate students studying this subject.
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7."Differential Equations and Integral Transforms : for BSc and BTech Students of All Indian Universities" by Rakesh Kumar / Nagendra Kumar
“Differential Equations and Integral Transforms” Book Review: This book provides an introduction to differential equations and integral transforms from a mathematical perspective, with the aim of solving initial and boundary value problems, as well as other physical problems. The book consists of 12 chapters, which are divided into two sections. The first section focuses on differential equations and explores their solutions, including those of partial differential equations, using various methods such as Laplace transform, series solutions, Charpit’s method, and Monge’s methods. The second section covers integral transforms, including the Laplace transform and its applications, Fourier series, and Fourier transform and their applications. This book is appropriate for undergraduate science and engineering students.
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8."Integral Equations And Boundary Value Problems" by Pundir
“Integral Equations and Boundary Value Problems” Book Review: This book explores the Hilbert-Schmidt theory of symmetric kernels and the solutions of Fredholm integral equations. It also covers the solutions of integral equations of the second kind using successive approximation and substitution methods. Additionally, the book introduces the classical Fredholm theory, singular integral equations, integral transform methods, and boundary value problems. Further chapters delve into Green’s function, Dirac Delta function, modified Green’s function, higher dimensional Green’s function, and perturbation theory.
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9."Applied Integral Equations" by Chakrabarti | |

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10."Integral Equations" by Hochstadt
“Integral Equations” Book Review: This book provides a brief overview of integral equations, incorporating both classical and analytical approaches. The book is organized into seven chapters, starting with an introduction to integral equations, elementary techniques, the theory of compact operators, and their applications to boundary value problems in multiple dimensions. It also covers various transform techniques and the development of the classical Fredholm technique. The book thoroughly analyzes the applications of the Schauder fixed-point theorem to nonlinear equations.
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## 2. Boundary Integral Methods

1."Boundary Integral Methods: Theory and Applications" by Luigi Morino and Renzo Piva
“Boundary Integral Methods: Theory and Applications” Book Review: This book is aimed at researchers, undergraduate and graduate students in engineering, and PhD students in mathematics and mechanics who seek to explore advanced boundary integral methods. Its primary goal is to advance research and development activities in boundary-integral equation methods and boundary element solution algorithms. The book delves into the mathematical foundations and numerical aspects of these methods and provides detailed explanations of their engineering applications. It comprises 50 chapters, which begin with general lectures covering simple layer potentials for elliptical equations of higher order. The book also explores 3D growth using surface integrals and finite elements, 3D sound generated by moving sources, and other approaches with clear proofs. Several chapters feature illustrations to aid students and readers in understanding the concepts better. The book concludes by focusing on boundary element analysis of nonlinear liquid motion in 2D containers.
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2."The Boundary Integral Approach to Static and Dynamic Contact Problems: Equality and Inequality Methods (International Series of Numerical Mathematics)" by H Antes and P D Panagiotopoulos | |

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3."Strongly Elliptic Systems and Boundary Integral Equations" by William McLean
“Strongly Elliptic Systems and Boundary Integral Equations” Book Review: The intended audience for this book comprises undergraduate and graduate engineering students specializing in mathematics and mechanics. The book presents mathematical models for a range of critical problems in engineering and the physical sciences. It is the first work to provide a comprehensive account of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. The book includes in-depth coverage of three specific examples: the Laplace equation, the Helmholtz equation, and the equations of linear elasticity. It has been designed to equip readers with the knowledge necessary to engage with current research literature on boundary element methods.
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4."Selected Topics in Boundary Integral Formulations for Solids and Fluids (CISM International Centre for Mechanical Sciences)" by Vladimir Kompiš
“Selected Topics in Boundary Integral Formulations for Solids and Fluids (CISM International Centre for Mechanical Sciences)” Book Review: The target audience for this book is undergraduate and graduate engineering students studying mathematics and mechanics. It presents a variety of special approaches for solving problems using BEM formulations, including singular and non-singular, multi-domain, and meshless techniques. The book also covers hybrid and reciprocity-based FEM methods for linear and non-linear problems in solid and fluid mechanics, as well as acoustic fluid-structure interaction. Numerous applications are included, such as noise radiation from rolling bodies, acoustic radiation in closed and infinite domains, 3D dynamic piezoelectricity, Stefan problems, and coupled problems. Each chapter concludes with a set of problems that allows readers to test and enhance their knowledge.
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5."Boundary Integral Methods: Numerical and Mathematical Aspects: 1 (Computational Engineering)" by M A Goldberg
“Boundary Integral Methods: Numerical and Mathematical Aspects: 1 (Computational Engineering)” Book Review: This book is designed to meet the needs of undergraduate and graduate engineering students specializing in mathematics. It covers a diverse range of research topics, including recent developments that leverage the Laplace transform and the dual reciprocity method (DRM) to solve both linear and non-linear reaction-diffusion equations. The book also presents a novel approach to solving partial differential equations with non-constant coefficients, and offers a detailed explanation of a new ‘direct-mixed’ BEM for solving hypersingular integral equations in acoustics. It explains how to use group theory in BEM algorithms to take advantage of the symmetries present in many boundary integral equations, thereby significantly reducing system sizes. Each chapter of the book is accompanied by proper numerical proofs and corresponding theorems, making it an excellent resource for future reference.
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6."Boundary Integral Methods in Fluid Mechanics" by H Power and L C Wrobel
“Boundary Integral Methods in Fluid Mechanics” Book Review: This book has been developed for undergraduate and graduate engineering students specializing in Mechanics. It consolidates classical and contemporary research on the use of integral equation numerical techniques for addressing fluid dynamic problems. The book adopts the boundary element method (BEM), which is widely recognized as one of the most effective numerical methods for solving boundary value problems. It has been structured into eight main parts. The first part offers an overview of the fundamental principles and equations governing fluid motion. The second part presents formulations and applications of BEM as the foundation for numerically solving inviscid and viscous flow problems. The third part covers potential theory, while the fourth part provides details on numerical solutions of potential flow problems. The fifth part discusses boundary integral equations for low Reynolds number flow. The sixth part offers a comprehensive overview of the completed double layer integral equation method for Stokes flow. The seventh part discusses the low Reynolds number deformation of viscous drops and gas bubbles. Finally, the eighth part explores the Navier-Stokes equations.
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7."Progress in Boundary Element Methods" by BREBBIA
“Progress in Boundary Element Methods” Book Review: This book is designed for undergraduate and graduate engineering students specializing in Mechanics. It emphasizes the solution of non-linear and time-dependent problems and the development of numerical techniques to enhance method efficiency. The book is organized into eight chapters. Recent research presented in the book provides a simple transformation that linearizes the governing equations, enabling the solution of a wide range of non-homogeneous problems without internal cells. Chapter 2 provides a summary of the main integral equations used for solving two- and three-dimensional scalar wave propagation problems, which are best suited for boundary elements and generally give poor results when solved using finite elements. In Chapter 3, the advantages of using boundary integral equations for the problem of fracture mechanics are demonstrated. One of the most notable features of BEM is its potential to describe the problem solely as a function of the boundary unknowns, and Chapter 4 explains how this can be achieved for two- and three-dimensional elastostatic problems. Other chapters discuss fluid-structure interaction, viscoplasticity, and boundary integral equations for thin plates.
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8."Natural Boundary Integral Method and Its Applications (Mathematics and Its Applications)" by De-hao Yu
“Natural Boundary Integral Method and Its Applications (Mathematics and Its Applications)” Book Review: This book is intended for undergraduate and graduate engineering students specializing in Mathematics. It provides an explanation that many boundary value problems of partial differential equations can be transformed into boundary integral equations through natural boundary reduction with integral methods. The book introduces the natural boundary integral method systematically and includes the variational principle following the natural boundary reduction and some useful properties.The book covers domain decomposition methods based on natural boundary reduction.
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9."Advances in Boundary Element Techniques (Springer Series in Computational Mechanics)" by James H Kane and Giulio Maier
“Advances in Boundary Element Techniques (Springer Series in Computational Mechanics)” Book Review: This book is an ideal resource for practitioners, researchers, and graduate students in engineering, mathematics, and the physical sciences who want to broaden their perspective or stay up-to-date in the essential areas of computational simulation. It comprehensively explains all methods and descriptions of boundary element analysis (BEA). The book provides a definitive representation of the significant capabilities and applications that fall under the general category of advanced boundary element analysis, covering mechanical, thermal, fluid, and electromagnetic phenomena.
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10."Linear Difference Equations with Discrete Transform Methods (Mathematics and Its Applications)" by A J Jerri
“Linear Difference Equations with Discrete Transform Methods (Mathematics and Its Applications)” Book Review: This book is primarily intended as a textbook for beginning undergraduate mathematics students who are interested in studying difference equations. It provides a comprehensive coverage of the basic concepts of difference equations and the tools of difference and sum calculus that are necessary for analyzing and solving ordinary linear difference equations. The first chapter of the book presents clear examples from various fields, which are then discussed in detail along with their solutions in Chapters 2-7. The book also introduces the mechanics of discrete transforms for solving ordinary difference equations, and teaches the use of operational calculus, such as Laplace and Fourier transforms, to solve differential equations. The book concludes with an explanation of operational sum calculus. This text is a valuable resource for students, practitioners, and researchers who are interested in this area of study.
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## 3. Integral Equations and Variational Methods

1."Inside Interesting Integrals (Undergraduate Lecture Notes in Physics)" by Paul J Nahin
“Inside Interesting Integrals (Undergraduate Lecture Notes in Physics)” Book Review: The book aims to present the concepts of differential equations and definite integrals in a simple and approachable manner for students who have completed the first year of college or high school AP calculus. The focus of the book is on the methods used to evaluate integrals, rather than solely on obtaining the final answer.
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2."Boundary Integral Equation Methods for Solids and Fluids" by Marc Bonnet
“Boundary Integral Equation Methods for Solids and Fluids” Book Review: The focus of this book is to provide an understanding of the mathematical foundation of the boundary element method, along with its computer implementation. The book covers various problems such as linear, wave propagation, infinite domain, mobile boundaries, and unknown boundaries and their solutions using the finite element method. It includes a variety of applications in fluid mechanics, mechanics of solids, acoustics, and electromagnetism.
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3."Boundary Integral Equations in Elasticity Theory (Solid Mechanics and Its Applications)" by A M Linkov
“Boundary Integral Equations in Elasticity Theory (Solid Mechanics and Its Applications)” Book Review: The book aims to introduce the complex variable boundary integral equations (CV-BIE) as a new powerful tool in computational mechanics. It provides a wide range of examples that demonstrate the potential and benefits of this analysis. The book begins with an overview of the theory of real variable potentials, including the hypersingular potential and equations, and also discusses the significant connections between the real variable BIE and its complex variable counterparts.
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4."Inequalities for Differential and Integral Equations (Mathematics in Science and Technology)" by B G Pachpatte and William F Ames
“Inequalities for Differential and Integral Equations (Mathematics in Science and Technology)” Book Review: This book addresses a range of linear and nonlinear inequalities that have wide-ranging applications in the theory of various classes of differential and integral equations. It features many recently-developed inequalities not yet found in other books, making it a valuable reference for researchers in this field as well as a useful tool for engineers and advanced graduate students seeking to expand their knowledge.
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5."Integral Methods in Science and Engineering: Theoretical and Computational Advances" by Christian Constanda and Andreas Kirsch
“Integral Methods in Science and Engineering: Theoretical and Computational Advances” Book Review: This book presents a compilation of articles highlighting the latest advancements in the development of theoretical integral techniques and their applications in science and engineering. It covers various topics, including singular integral equations, numerical integration, finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. The book is aimed at researchers in applied mathematics, physics, mechanical and electrical engineering, as well as graduate students and professionals who require integration as an essential tool in their work.
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6."Mathematical Methods for Engineers and Scientists 3: Fourier Analysis, Partial Differential Equations and Variational Methods" by Kwong-Tin Tang
“Mathematical Methods for Engineers and Scientists 3: Fourier Analysis, Partial Differential Equations and Variational Methods” Book Review: This book covers various topics such as complex analysis, matrix theory, vector and tensor analysis, and Fourier analysis, along with a comprehensive discussion of integral transforms, ordinary and partial differential equations. The book includes numerous examples with selected problem sets and answers to help students fully understand the concepts. Its aim is to make students comfortable with advanced mathematical tools in junior, senior, and beginning graduate courses.
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7."Mathematical Models for Registration and Applications to Medical Imaging (Mathematics in Industry)" by Otmar Scherzer
“Mathematical Models for Registration and Applications to Medical Imaging (Mathematics in Industry)” Book Review: This book offers an overview of the mathematical and computational techniques utilized in image registration. It provides a summary of the current state-of-the-art approaches in this field, along with practical applications and emerging directions with industrial significance in data processing.
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