Separable Boundary-Value Problems in Physics

Praise for the Second Edition «This book is an excellent introduction to the wide field of boundary value problems.»—Journal of Engineering Mathematics «No doubt this textbook will be useful for both students and research workers.»—Mathematical Reviews A new edition of the highly-acclaimed guide to boundary value problems, now featuring modern computational methods and approximation theory Green's Functions and Boundary Value Problems, Third Edition continues the tradition of the two prior editions by providing mathematical techniques for the use of differential and integral equations to tackle important problems in applied mathematics, the physical sciences, and engineering. This new edition presents mathematical concepts and quantitative tools that are essential for effective use of modern computational methods that play a key role in the practical solution of boundary value problems. With a careful blend of theory and applications, the authors successfully bridge the gap between real analysis, functional analysis, nonlinear analysis, nonlinear partial differential equations, integral equations, approximation theory, and numerical analysis to provide a comprehensive foundation for understanding and analyzing core mathematical and computational modeling problems. Thoroughly updated and revised to reflect recent developments, the book includes an extensive new chapter on the modern tools of computational mathematics for boundary value problems. The Third Edition features numerous new topics, including: Nonlinear analysis tools for Banach spaces Finite element and related discretizations Best and near-best approximation in Banach spaces Iterative methods for discretized equations Overview of Sobolev and Besov space linear Methods for nonlinear equations Applications to nonlinear elliptic equations In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book. New and revised exercises found throughout allow readers to develop their own problem-solving skills, and the updated bibliographies in each chapter provide an extensive resource for new and emerging research and applications. With its careful balance of mathematics and meaningful applications, Green's Functions and Boundary Value Problems, Third Edition is an excellent book for courses on applied analysis and boundary value problems in partial differential equations at the graduate level. It is also a valuable reference for mathematicians, physicists, engineers, and scientists who use applied mathematics in their everyday work.

Electromagnetic surface modes are present at all surfaces and interfaces between material of different dielectric properties. These modes have very important effects on numerous physical quantities: adhesion, capillary force, step formation and crystal growth, the Casimir effect etc. They cause surface tension and wetting and they give rise to forces which are important e.g. for the stability of colloids. This book is a useful and elegant approach to the topic, showing how the concept of electromagnetic modes can be developed as a unifying theme for a range of condensed matter physics. The author concentrates in finding out the basic origin of the force and how they are developed from the collective excitations of the solids. Different materials are treated, e.g. metals, semiconductors, plasmas, liquids and gases all with different collective modes. In close relation to the theoretical background, the reader is served with a broad field of applications. The book serves readers who are concerned with applications to real world problems with a deep knowledge on surface modes, and inspires new developments of the field.

This statistics textbook, with particular emphasis on radiation protection and dosimetry, deals with statistical solutions to problems inherent in health physics measurements and decision making. The authors begin with a description of our current understanding of the statistical nature of physical processes at the atomic level, including radioactive decay and interactions of radiation with matter. Examples are taken from problems encountered in health physics, and the material is presented such that health physicists and most other nuclear professionals will more readily understand the application of statistical principles in the familiar context of the examples. Problems are presented at the end of each chapter, with solutions to selected problems provided online. In addition, numerous worked examples are included throughout the text.

Clinical Problems in Oncology: A Practical Guide to Management is an easy-to-use, compact reference with essential, practical information on managing oncological emergencies, as well as the side effects and complications of cancer and its treatment. Because patient responses can vary widely, depending on the type of treatment prescribed, this resource offers medical professionals the specific information they need to improve the evaluation and treatment of cancer patients at the point of care. The compact format includes a wide range of clinical information, from the dose of drugs that would typically be used, through guidance on the practical procedures that are frequently used to treat oncology patients. Some of the book’s highlights include: • Toxicity grading and management, including at-a-glance summaries of the most common toxicities associated with chemotherapy • Prescribing guidelines, including how to write up electrolyte replacement properly • Information on specialised oncology procedures (such as SIR spheres), and how to manage complications • Types of vascular access lines and how to check their position, access them and troubleshoot problems With an expert team of writers who have contributed materials in their areas of expertise, Clinical Problems in Oncology is an ideal reference for oncologists in training, oncologists in non-training positions, oncology registrars and general practitioners.

This book is a comprehensive account of five extended modules covering the key branches of twentieth-century theoretical physics, taught by the author over a period of three decades to students on bachelor and master university degree courses in both physics and theoretical physics. The modules cover nonrelativistic quantum mechanics, thermal and statistical physics, many-body theory, classical field theory (including special relativity and electromagnetism), and, finally, relativistic quantum mechanics and gauge theories of quark and lepton interactions, all presented in a single, self-contained volume. In a number of universities, much of the material covered (for example, on Einstein’s general theory of relativity, on the BCS theory of superconductivity, and on the Standard Model, including the theory underlying the prediction of the Higgs boson) is taught in postgraduate courses to beginning PhD students. A distinctive feature of the book is that full, step-by-step mathematical proofs of all essential results are given, enabling a student who has completed a high-school mathematics course and the first year of a university physics degree course to understand and appreciate the derivations of very many of the most important results of twentieth-century theoretical physics.

A Modern Course in Statistical Physics is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems. The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems. This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological systems and batteries, adsorption processes in biological systems, diamagnetism, the theory of Bose-Einstein condensation, memory effects in Brownian motion, the hydrodynamics of binary mixtures. A set of exercises and problems is to be found at the end of each chapter and, in addition, solutions to a subset of the problems is provided. The appendices cover Exact Differentials, Ergodicity, Number Representation, Scattering Theory, and also a short course on Probability.

This self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schrodinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics, it strikes a balance between mathematical and physical descriptions. Split into two parts, the first introduces readers to the most familiar coherent states, their origin, their construction, and their application and relevance to various selected domains of physics. Part II, mostly based on recent original results, is devoted to the question of quantization of various sets through coherent states, and shows the link to procedures in signal analysis.

This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies. Provides a step-by-step progressive treatment of topics for ease of understanding. Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value. Includes end of chapter problems, case studies and examples with solutions throughout the book. Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files. Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging

A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses the recent emergence of unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis with potentially significant physical consequences. In addition to prompting a discussion on the role of mathematical methods in the contemporary development of quantum physics, the book features: Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area An overview of recent inventions and advances in understanding functional analytic and algebraic methods for non-selfadjoint operators as well as the use of Krein space theory and perturbation theory Rigorous support of the progress in theoretical physics of non-Hermitian systems in addition to mathematically justified applications in various domains of physics such as nuclear and particle physics and condensed matter physics An ideal reference, Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects is useful for researchers, professionals, and academics in applied mathematics and theoretical and/or applied physics who would like to expand their knowledge of classical applications of quantum tools to address problems in their research. Also a useful resource for recent and related trends, the book is appropriate as a graduate-level and/or PhD-level text for courses on quantum mechanics and mathematical models in physics.

The incidence and prevalence of diabetes is increasing globally, and most health professionals are likely to care for people with diabetes. In such cases they may often find that they have to make clinical decisions without expert support, which can be difficult for both patient and carer. Managing Clinical Problems in Diabetes provides this support by exploring common clinical problems in diabetes care, and providing practical solutions based on evidence and the clinical experience of diabetes educators, endocrinologists, general practitioners, and other health professionals who encounter such problems on a daily basis. Each chapter begins with an introductory section presenting an overview of the management of diabetes, including short and long term complications and management targets across the lifespan. The authors then pose commonly encountered diabetes management problems, developing comprehensive responses from a range of relevant health professionals who each provide management suggestions from their area of practice. Managing Clinical Problems in Diabetes is a vital resource for health professionals involved in the provision of care for people with diabetes.