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This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis. Contents: Introduction and Overview; Volterra Models of Evolving Dynamical Systems: Volterra Equations of the First Kind with Piecewise Continuous Kernels; Volterra Matrix Equation of the First Kind with Piecewise Continuous Kernels; Volterra Op

Nonlinear integral equations. --- Volterra equations. --- Equations, Volterra --- Integral equations --- Integral equations, Nonlinear --- Nonlinear theories

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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.

Inequalities (Mathematics) --- Differential equations. --- Integral equations.

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This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert–Schmidt theorem, and the solution of Abel integral equations by using an elementary method. In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green’s function of a Sturm–Liouville type ordinary differential equation and its applications to physical problems. The book is divided into two parts: integral equations and integral transforms. Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.

Integral equations. --- Mathematical analysis. --- Integral Equations. --- Integral Transforms and Operational Calculus.

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This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of mathematics and physics. The book covers a range of topics including Volterra and Fredholm integral equations, the second kind of integral equations with symmetric kernels, eigenvalues and eigen functions, the Hilbert–Schmidt theorem, and the solution of Abel integral equations by using an elementary method. In addition, the book covers various integral transforms including Fourier, Laplace, Mellin, Hankel, and Z-transforms. One of the unique features of the book is a general method for the construction of various integral transforms and their inverses, which is based on the properties of delta function representation in terms of Green’s function of a Sturm–Liouville type ordinary differential equation and its applications to physical problems. The book is divided into two parts: integral equations and integral transforms. Each chapter is supplemented with numerous illustrative examples to aid in understanding. The clear and concise presentation of the topics covered makes this book an ideal resource for students, researchers, and professionals interested in the theory and application of linear integral equations and integral transforms.

Integral equations. --- Mathematical analysis. --- Integral Equations. --- Integral Transforms and Operational Calculus.

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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Stochastic integral equations. --- Integral equations --- Stochastic analysis --- Analyse mathématique --- Mathematical analysis --- Stochastic integral equations --- Mathematical analysis. --- Analyse mathématique --- Variables aléatoires --- Equations integrales