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

Variational Methods for Numerical Solution of Nonlinear Elliptic Problems (Paperback): Roland Glowinski Variational Methods for Numerical Solution of Nonlinear Elliptic Problems (Paperback)
Roland Glowinski
R2,318 Discovery Miles 23 180 Ships in 12 - 17 working days

Addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems. These methods can be applied to many problems in science and engineering, but this book focuses on their application to problems in continuum mechanics and physics. This book differs from others on the topic by:* Presenting examples of the power and versatility of operator-splitting methods.* Providing a detailed introduction to alternating direction methods of multipliers and their applicability to the solution of nonlinear (possibly non-smooth) problems from science and engineering.* Showing that nonlinear least-squares methods, combined with operator-splitting and conjugate gradient algorithms, provide efficient tools for the solution of highly nonlinear problems.

Delay Differential Equations and Applications to Biology (Paperback, 1st ed. 2021): Fathalla A. Rihan Delay Differential Equations and Applications to Biology (Paperback, 1st ed. 2021)
Fathalla A. Rihan
R3,614 Discovery Miles 36 140 Ships in 10 - 15 working days

This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.

Volterra Integral and Differential Equations, Volume 202 (Hardcover, 2nd edition): Ted A. Burton Volterra Integral and Differential Equations, Volume 202 (Hardcover, 2nd edition)
Ted A. Burton
R5,136 Discovery Miles 51 360 Ships in 12 - 17 working days

Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations.


By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated.


Key Features:


- Smooth transition from ordinary differential equations to integral and functional differential equations.
- Unification of the theories, methods, and applications of ordinary and functional differential equations.
- Large collection of examples of Liapunov functions.
- Description of the history of stability theory leading up to unsolved problems.
- Applications of the resolvent to stability and periodic problems.
1. Smooth transition from ordinary differential equations to integral and functional differential equations.
2. Unification of the theories, methods, and applications of ordinary and functional differential equations.
3. Large collection of examples of Liapunov functions.
4. Description of the history of stability theory leading up to unsolved problems.
5. Applications of the resolvent to stability and periodic problems.

Inverse Scattering Theory and Transmission Eigenvalues (Paperback, 2nd Revised edition): Fioralba Cakoni, David Colton, Houssem... Inverse Scattering Theory and Transmission Eigenvalues (Paperback, 2nd Revised edition)
Fioralba Cakoni, David Colton, Houssem Haddar
R2,144 R1,876 Discovery Miles 18 760 Save R268 (13%) Ships in 12 - 17 working days

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers-a subset of transmission eigenvalues-using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

Iterative Methods for Ill-Posed Problems - An Introduction (Hardcover): Anatoly B. Bakushinsky, Mihail Yu Kokurin, Alexandra... Iterative Methods for Ill-Posed Problems - An Introduction (Hardcover)
Anatoly B. Bakushinsky, Mihail Yu Kokurin, Alexandra Smirnova
R3,520 Discovery Miles 35 200 Ships in 12 - 17 working days

Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Spherical and Plane Integral Operators for PDEs - Construction, Analysis, and Applications (Hardcover): Karl K. Sabelfeld,... Spherical and Plane Integral Operators for PDEs - Construction, Analysis, and Applications (Hardcover)
Karl K. Sabelfeld, Irina A. Shalimova
R5,518 Discovery Miles 55 180 Ships in 12 - 17 working days

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Measure, Integration & Real Analysis (Hardcover, 1st ed. 2020): Sheldon Axler Measure, Integration & Real Analysis (Hardcover, 1st ed. 2020)
Sheldon Axler
R1,291 Discovery Miles 12 910 In Stock

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn-Banach Theorem, Hoelder's Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.

The General Theory of Integration (Hardcover): Ralph Henstock The General Theory of Integration (Hardcover)
Ralph Henstock
R3,718 Discovery Miles 37 180 Ships in 12 - 17 working days

Written by one of the subject's foremost experts, this is the first book on division space integration theory. It is intended to present a unified account of many classes of integrals including the Lebesgue-Bochner, Denjoy-Perron gauge, Denjoy-Hincin, Cesaro-Perron, and Marcinkiewicz-Zygmund integrals. Professor Henstock develops here the general axiomatic theory of Riemann-type integration from first principles in such a way that familiar classes of integrals (such as Lebesgue and Wiener integrals) are subsumed into the general theory in a systematic fashion. In particular, the theory seeks to place Feynman integration on a secure analytical footing. By adopting an axiomatic approach, proofs are, in general, simpler and more transparent than have previously appeared. The author also shows how one proof can prove corresponding results for a wide variety of integrals. As a result, this book will be the central reference work in this subject for many years to come.

Ergodic Theory and Dynamical Systems - Proceedings of the Ergodic Theory Workshops at University of North Carolina at Chapel... Ergodic Theory and Dynamical Systems - Proceedings of the Ergodic Theory Workshops at University of North Carolina at Chapel Hill, 2011-2012 (Hardcover)
Idris Assani
R4,064 Discovery Miles 40 640 Ships in 12 - 17 working days

This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.

Introduction to Integration (Hardcover): H. A. Priestley Introduction to Integration (Hardcover)
H. A. Priestley
R4,202 Discovery Miles 42 020 Ships in 12 - 17 working days

Introduction to integration provides a unified account of integration theory, giving a practical guide to the Lebesgue integral and its uses, with a wealth of illustrative examples and exercises. The book begins with a simplified Lebesgue-style integral (in lieu of the more traditional Riemann integral), intended for a first course in integration. This suffices for elementary applications, and serves as an introduction to the core of the book. The final chapters present selected applications, mostly drawn from Fourier analysis. The emphasis throughout is on integrable functions rather than on measure. The book is designed primarily as an undergraduate or introductory graduate textbook. It is similar in style and level to Priestley's Introduction to complex analysis, for which it provides a companion volume, and is aimed at both pure and applied mathematicians. Prerequisites are the rudiments of integral calculus and a first course in real analysis.

Kurzweil-stieltjes Integral: Theory And Applications (Hardcover): Milan Tvrdy, Giselle Antunes Monteiro, Antonin Slavik Kurzweil-stieltjes Integral: Theory And Applications (Hardcover)
Milan Tvrdy, Giselle Antunes Monteiro, Antonin Slavik
R3,859 Discovery Miles 38 590 Ships in 10 - 15 working days

The book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.

Integral Equations, Boundary Value Problems And Related Problems (Hardcover): Xing Li Integral Equations, Boundary Value Problems And Related Problems (Hardcover)
Xing Li
R3,439 Discovery Miles 34 390 Ships in 12 - 17 working days

In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.

Linear Integral Equations - Theory & Technique (Paperback, 2nd ed. 2013): Ram P. Kanwal Linear Integral Equations - Theory & Technique (Paperback, 2nd ed. 2013)
Ram P. Kanwal
R1,928 Discovery Miles 19 280 Ships in 12 - 17 working days

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. This uncorrected soft cover reprint of the second edition places the emphasis on applications and presents a variety of techniques with extensive examples.Originally published in 1971, Linear Integral Equations is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems also makes the book useful to researchers in many applied fields.

Singular Bilinear Integrals (Hardcover): Brian Raymond Frederick Jefferies Singular Bilinear Integrals (Hardcover)
Brian Raymond Frederick Jefferies
R2,453 Discovery Miles 24 530 Ships in 12 - 17 working days

'This is a deep and beautiful monograph in functional analysis, at the interface with mathematical physics.'Mathematical ReviewsThe integration of vector valued functions with respect to vector valued measures, especially spectral measures, is developed in view of applications in operator theory, scattering theory and semiclassical approximation in quantum physics. New techniques are developed for bilinear integration in cases where the classical approach does not apply.

Equations of Mathematical Diffraction Theory (Paperback): Mezhlum A. Sumbatyan, Antonio Scalia Equations of Mathematical Diffraction Theory (Paperback)
Mezhlum A. Sumbatyan, Antonio Scalia
R1,968 Discovery Miles 19 680 Ships in 12 - 17 working days

Equations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case. Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.

Novel Methods for Solving Linear and Nonlinear Integral Equations (Hardcover): Santanu Saha Ray, Prakash Kumar Sahu Novel Methods for Solving Linear and Nonlinear Integral Equations (Hardcover)
Santanu Saha Ray, Prakash Kumar Sahu
R3,866 Discovery Miles 38 660 Ships in 12 - 17 working days

This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency.

Integral Equations and Their Applications (Hardcover, illustrated edition): M. Rahman Integral Equations and Their Applications (Hardcover, illustrated edition)
M. Rahman
R5,854 Discovery Miles 58 540 Ships in 12 - 17 working days

For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles.Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eight chapters, pedagogically organized. This book is specially designed for those who wish to understand integral equations without having extensive mathematical background.Some knowledge of integral calculus, ordinary differential equations, partial differential equations, Laplace transforms, Fourier transforms, Hilbert transforms, analytic functions of complex variables and contour integrations are expected on the part of the reader.

Recent Trends in Naval Engineering Research (Hardcover, 1st ed. 2021): Anthony A. Ruffa, Bourama Toni Recent Trends in Naval Engineering Research (Hardcover, 1st ed. 2021)
Anthony A. Ruffa, Bourama Toni
R3,340 Discovery Miles 33 400 Ships in 12 - 17 working days

This multidisciplinary volume is the second in the STEAM-H series to feature invited contributions on mathematical applications in naval engineering. Seeking a more holistic approach that transcends current scientific boundaries, leading experts present interdisciplinary instruments and models on a broad range of topics. Each chapter places special emphasis on important methods, research directions, and applications of analysis within the field. Fundamental scientific and mathematical concepts are applied to topics such as microlattice materials in structural dynamics, acoustic transmission in low Mach number liquid flow, differential cavity ventilation on a symmetric airfoil, Kalman smoother, metallic foam metamaterials for vibration damping and isolation, seal whiskers as a bio-inspired model for the reduction of vortex-induced vibrations, multidimensional integral for multivariate weighted generalized Gaussian distributions, minimum uniform search track placement for rectangular regions, antennas in the maritime environment, the destabilizing impact of non-performers in multi-agent groups, inertial navigation accuracy with bias modeling. Carefully peer-reviewed and pedagogically presented for a broad readership, this volume is perfect to graduate and postdoctoral students interested in interdisciplinary research. Researchers in applied mathematics and sciences will find this book an important resource on the latest developments in naval engineering. In keeping with the ideals of the STEAM-H series, this volume will certainly inspire interdisciplinary understanding and collaboration.

Heun's Differential Equations (Hardcover): A. Ronveaux Heun's Differential Equations (Hardcover)
A. Ronveaux
R4,486 Discovery Miles 44 860 Ships in 12 - 17 working days

Heun's equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger's equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).

Henstock-kurzweil Integration On Euclidean Spaces (Hardcover): Tuo Yeong Lee Henstock-kurzweil Integration On Euclidean Spaces (Hardcover)
Tuo Yeong Lee
R3,072 Discovery Miles 30 720 Ships in 10 - 15 working days

The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.

An Introduction to Homogenization (Hardcover, New): Doina Cioranescu, Patrizia Donato An Introduction to Homogenization (Hardcover, New)
Doina Cioranescu, Patrizia Donato
R5,224 R4,473 Discovery Miles 44 730 Save R751 (14%) Ships in 12 - 17 working days

Composite materials are widely used in industry and include such well known examples as superconductors and optical fibers. However, modeling these materials is difficult, since they often has different properties at different points. The mathematical theory of homogenization is designed to handle this problem. The theory uses an idealized homogenous material to model a real composite while taking into account the microscopic structure. This introduction to homogenization theory develops the natural framework of the theory with four chapters on variational methods for partial differential equations. It then discusses the homogenization of several kinds of second-order boundary value problems. It devotes separate chapters to the classical examples of stead and non-steady heat equations, the wave equation, and the linearized system of elasticity. It includes numerous illustrations and examples.

Theory and Numerical Approximations of Fractional Integrals and Derivatives (Paperback): Changpin Li, Min Cai Theory and Numerical Approximations of Fractional Integrals and Derivatives (Paperback)
Changpin Li, Min Cai
R2,594 R2,407 Discovery Miles 24 070 Save R187 (7%) Ships in 12 - 17 working days

Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus and provides a detailed treatment of existing numerical approximations. Theory and Numerical Approximations of Fractional Integrals and Derivatives presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results. The book's core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.

Integral Expansions Related to Mehler-Fock Type Transforms (Paperback): B.N. Mandal, Nanigopal Mandal Integral Expansions Related to Mehler-Fock Type Transforms (Paperback)
B.N. Mandal, Nanigopal Mandal
R1,369 Discovery Miles 13 690 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.

Boundary Integral Equation Methods for Solids & Fluids (Hardcover): M. Bonnet Boundary Integral Equation Methods for Solids & Fluids (Hardcover)
M. Bonnet
R4,838 Discovery Miles 48 380 Ships in 12 - 17 working days

Going far beyond the standard texts, this book extensively covers boundary integral equation (BIE) formulations and the boundary element method (BEM). The first section introduces BIE formulations for potential and elasticity problems, following the modern regularization approach - the fundamental starting point for research in this field. Secondly, a clear description of BIE formulations for wave and elastodynamics problems, in both time and frequency domains is presented. Finally, recent research in the field, related to variational integral formulations, use of geometrical symmetry, shape sensitivity and fracture mechanics is summarised. Within the text a broad range of application areas, industrial as well as research related, are examined. These include:

  • elasticity and small-strain elastoplasticity
  • time-domain and frequency-domain scalar and elastic waves
  • fracture mechanics
Including an extensive bibliography, this text will be of considerable value and interest to graduate students, researchers and lecturers in engineering mechanics, applied maths and physics, as well as industrial practitioners working within these areas.
Integral and Integrodifferential Equations (Hardcover): Ravi P. Agarwal, Donal O'Regan Integral and Integrodifferential Equations (Hardcover)
Ravi P. Agarwal, Donal O'Regan
R6,480 Discovery Miles 64 800 Ships in 12 - 17 working days

This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, will conduce and spur further research in this direction.

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