Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.   The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.   The second part of the book presents three special nonlinear inverse problems in detail - the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed.   In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph.   The book is highly illustrated and contains many exercises. This together with the choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students in mathematics and engineering.

Inverse problems (Differential equations). --- Inverse problems (Differential equations) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Appl.Mathematics/Computational Methods of Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- Math --- Science --- Differential equations, partial. --- Differential Equations. --- Mathematical and Computational Engineering.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Partial differential equations --- Differential equations --- Engineering sciences. Technology --- differentiaalvergelijkingen --- ingenieurswetenschappen

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpful in designing graduate courses for mathematically orientated students on electromagnetic wave propagation problems. The students should have some knowledge on vector analysis (curves, surfaces, divergence theorem) and functional analysis (normed spaces, Hilbert spaces, linear and bounded operators, dual space). Written in an accessible manner, topics are first approached with simpler scale Helmholtz Equations before turning to Maxwell Equations. There are examples and exercises throughout the book. It will be useful for graduate students and researchers in applied mathematics and engineers working in the theoretical approach to electromagnetic wave propagation.

Mathematics. --- Partial Differential Equations. --- Functional Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Numerical Analysis. --- Functional analysis. --- Differential equations, partial. --- Numerical analysis. --- Engineering mathematics. --- Mathématiques --- Analyse fonctionnelle --- Analyse numérique --- Mathématiques de l'ingénieur --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Partial differential equations. --- Applied mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Mathematical and Computational Engineering. --- Electromagnetic theory --- Maxwell equations. --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Equations, Maxwell --- Differential equations, Partial --- Light, Electromagnetic theory of --- Electric fields --- Magnetic fields

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Thirteenth International Conference on Integral Methods in Science and Engineering, held July 21–25, 2014, in Karlsruhe, Germany. A broad range of topics is addressed, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Algebra --- Partial differential equations --- Differential equations --- Numerical analysis --- Classical mechanics. Field theory --- Solid state physics --- Applied physical engineering --- differentiaalvergelijkingen --- algebra --- toegepaste mechanica --- mechanica --- numerieke analyse