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Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book presents Volterra integral and functional differential equations in that same framework, allowing the readers to parlay their knowledge of ordinary differential equations into theory.
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Deformations of elastic bodies are encountered in many areas in science, engineering and technology. In the last decades, various numerical approaches using the finite element technique have been developed, but many are not adequate to address the full complexity.This work treats the elasticity of deformed bodies, including the resulting interior stresses and displacements. Other than comparable books, this work also takes into account that some of constitutive relations can be considered in a weak form. To discuss this problem properly, the method of integrodifferential relations is used, and an advanced numerical technique for stress-strain analysis is presented and evaluated using various discretization techniques. The methods presented in this book are of importance for almost all elasticity problems in materials science and mechanical engineering.
Elasticity. --- Plasticity. --- Integro-differential equations. --- Integrodifferential equations --- Differential equations --- Integral equations --- Cohesion --- Deformations (Mechanics) --- Elasticity --- Plastics --- Rheology --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Strains and stresses --- Strength of materials --- Properties --- Integrodifferential Relations. --- Linear Theory. --- Materials Science.
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Volterra integral and differential equations
Volterra equations --- Integro-differential equations --- Integro-differential equations. --- Volterra equations. --- 517.9 --- Equations, Volterra --- Integral equations --- Integrodifferential equations --- Differential equations --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis
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Differential equations --- Integro-differential equations --- Initial value problems --- Perturbation (Mathematics) --- Numerical solutions --- 517.96 --- -Initial value problems --- -Perturbation (Mathematics) --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics --- Problems, Initial value --- Boundary value problems --- Integrodifferential equations --- Integral equations --- Finite differences. Functional and integral equations --- Numerical solutions. --- Perturbation (Mathematics). --- 517.96 Finite differences. Functional and integral equations --- Numerical analysis --- Integro-differential equations - Numerical solutions --- Initial value problems - Numerical solutions
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Moments method (Statistics) --- Integro-differential equations --- Electromagnetism --- Maxwell equations --- Numerical solutions --- Data processing --- -Maxwell equations --- -Moments method (Statistics) --- FDTD --- Maxwellvergelijkingen --- elektrodynamica --- golven --- stabiliteit --- antennes --- finite-difference time-domain method --- elektromagnetisme --- Method of moments (Statistics) --- Mathematical statistics --- Distribution (Probability theory) --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- Integrodifferential equations --- Differential equations --- Integral equations --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Electromagnetism. --- Numerical solutions. --- Data processing. --- Moments method (Statistics). --- Numerical analysis --- Integro-differential equations - Numerical solutions --- Maxwell equations - Data processing --- Maxwell equations - Numerical solutions
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This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike.
Integro-differential equations. --- Integrodifferential equations --- Differential equations --- Integral equations --- Mathematical physics. --- Mathematics. --- Community ecology, Biotic. --- Mathematical models. --- Mathematical Applications in the Physical Sciences. --- Mathematics of Planet Earth. --- Community & Population Ecology. --- Mathematical Modeling and Industrial Mathematics. --- Math --- Science --- Physical mathematics --- Physics --- Models, Mathematical --- Simulation methods --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Ecology --- Population biology --- Mathematics
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This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.
Physics. --- Mathematical Methods in Physics. --- Atoms and Molecules in Strong Fields, Laser Matter Interaction. --- Plasma Physics. --- Classical Continuum Physics. --- Mathematical physics. --- Physique --- Physique mathématique --- Integro-differential equations --- Symmetry (Physics) --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Integrodifferential equations --- Differential equations --- Integral equations --- Conservation laws (Physics) --- Physics --- Integro-differential equations. --- Mechanics. --- Theoretical, Mathematical and Computational Physics. --- Classical Mechanics. --- Classical and Continuum Physics. --- Physical mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Mathematics --- Atoms. --- Plasma (Ionized gases). --- Continuum physics. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Gaseous discharge --- Gaseous plasma --- Magnetoplasma --- Ionized gases --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Chemistry, Physical and theoretical --- Matter --- Stereochemistry --- Constitution
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Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.
Electromagnetism --- Stochastic control theory. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Control theory --- Stochastic processes --- Mathematics. --- AtkinsonЗilcox expansion theorem. --- Beltrami fields. --- Faedo-Galerkin approach. --- Herglotz wave functions. --- Hilbert Uniqueness method. --- Maxwell equations. --- Maxwell operator. --- PDEs. --- applied mathematics. --- auxiliary elliptic problems. --- boundary controllability. --- boundary integral equation. --- boundary value problem. --- chiral material. --- chiral media. --- chirality. --- compact embeddings. --- complex electromagnetic media. --- complex media. --- constitutive relations. --- controllability problem. --- controllability. --- decompositions. --- differential equations. --- dispersive media. --- dyadics. --- eigenvalue problems. --- electric flux density. --- electrical engineering. --- electromagnetic complex media. --- electromagnetic fields. --- electromagnetic media. --- electromagnetic wave scattering. --- electromagnetic waves. --- electromagnetics. --- evolution family approach. --- evolution operators. --- evolution problems. --- exterior problems. --- finite-dimensional space. --- fixed point approach. --- frequency. --- function spaces. --- general scattering theorem. --- generalised integral transforms. --- geometry. --- handedness. --- homogenisation problem. --- homogenisation. --- homogenised media. --- homogenised system. --- infinite Frchet differentiability. --- integrodifferential equations. --- integrodifferential evolution equation. --- interior domain problem. --- magnetic flux density. --- mathematical modelling. --- mathematical theory. --- nonlinear PDEs. --- nonlinear model. --- nonlinear phenomena. --- nonlinear problems. --- nonlinearity. --- operators. --- optical theorem. --- penetrable obstacle. --- perfectly conducting obstacle. --- periodic media. --- physics. --- plane electromagnetic waves. --- reciprocity principle. --- scattering problems. --- scattering process. --- scattering theories. --- scattering theory. --- semigroup approach. --- semigroup arguments. --- semigroup-based approach. --- solvability. --- spaces. --- spectral theory. --- standard differential. --- stochastic integrodifferential equations. --- time domain. --- time-harmonic electromagnetic wave. --- time-harmonic problems. --- time. --- trace operators. --- two-scale expansion. --- variational formulation. --- vector analysis. --- wave motions. --- wave operators. --- well posedness.
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Quantum mechanics. Quantumfield theory --- Electromagnetism. Ferromagnetism --- Information systems --- Electromagnetism --- Maxwell equations --- Moments method (Statistics) --- Integro-differential equations --- Numerical solutions --- Data processing --- EMC --- elektromagnetisme --- 519.63 --- 681.3*G18 --- 537.8 --- -Maxwell equations --- -Moments method (Statistics) --- Method of moments (Statistics) --- Mathematical statistics --- Distribution (Probability theory) --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- Integrodifferential equations --- Differential equations --- Integral equations --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials --- Numerical methods for solution of partial differential equations --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- 537.8 Electromagnetism. Electromagnetic field. Electrodynamics. Maxwell theory --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.63 Numerical methods for solution of partial differential equations --- Numerical analysis --- 681.3 *G18 --- Moments, Méthodes des (statistique) --- Maxwell, Équations de --- Électromagnétisme. --- Data processing. --- Solutions numériques --- Traitement des données. --- Maxwell equations - Numerical solutions --- Maxwell equations - Data processing --- Integro-differential equations - Numerical solutions --- Moments, Méthodes des (statistique) --- Maxwell, Équations de --- Électromagnétisme. --- Solutions numériques --- Traitement des données.
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