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An Introduction to the Theory of Piezoelectricity
This volume is intended to provide researchers and graduate students with the basic aspects of the continuum modeling of electroelastic interactions in solids. A concise treatment of linear, nonlinear, static and dynamic theories and problems is presented. The emphasis on formulation and understanding of problems useful in device applications rather than solution techniques of mathematical problems. The mathematics used in this book is minimal.
An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile.
An Introduction to Structural Optimization
This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered.
An Introduction to Sequential Dynamical Systems
This text is the first to provide a comprehensive introduction to SDS. Driven by numerous examples and thought-provoking problems, the presentation offers good foundational material on finite discrete dynamical systems which leads systematically to an introduction of SDS. Techniques from combinatorics, algebra and graph theory are used to study a broad range of topics, including reversibility, the structure of fixed points and periodic orbits, equivalence, morphisms and reduction. Unlike other books that concentrate on determining the structure of various networks, this book investigates the dynamics over these networks by focusing on how the underlying graph structure influences the properties of the associated dynamical system.
An Introduction to Scientific Computing : Twelve Computational Projects Solved with MATLAB
This book provides twelve computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts.
An introduction to relativistic processes and the standard model of electroweak interactions
The first part of the volume is devoted to the description of scattering processes in the context of relativistic quantum field theory. The use of the semi-classical approximation allows us to illustrate the relevant computation techniques in a reasonably small amount of space. Our approach to relativistic processes is original in many respects. The second part contains a detailed description of the construction of the standard model of electroweak interactions, with special attention to the mechanism of particle mass generation. The extension of the standard model to include neutrino masses is also described. We have included a number of detailed computations of cross sections and decay rates of pedagogical and phenomenological relevance.
An Introduction to Queueing Theory : Modeling and Analysis in Applications
This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, the work provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students in mathematics, statistics, and applied disciplines such as computer science, operations research, and engineering.
An Introduction to Programming and Numerical Methods in MATLAB
The book covers numerical methods for solving a wide range of problems, from integration to the numerical solution of differential equations or the stimulation of random processes. Examples of programmes that solve problems directly, as well as those that use MATLAB’s high-level commands are given. Each chapter includes extensive examples and tasks, at varying levels of complexity. For practice, the early chapters include programmes that require debugging by the reader, while full solutions are given for all the tasks. The book also includes: A glossary of MATLAB commands / Aappendices of mathematical techniques used in numerical methods / Designed as a text for a first course in programming and algorithm design, as well as in numerical methods courses, the book will be of benefit to a wide range of students from mathematics and engineering, to commerce."
An Introduction to Ordinary Differential Equations
This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines.
An Introduction to Number Theory
An Introduction to Number Theory provides an introduction to the main streams of number theory. Starting with the unique factorization property of the integers, the theme of factorization is revisited several times throughout the book to illustrate how the ideas handed down from Euclid continue to reverberate through the subject. In particular, the book shows how the Fundamental Theorem of Arithmetic, handed down from antiquity, informs much of the teaching of modern number theory. The result is that number theory will be understood, not as a collection of tricks and isolated results, but as a coherent and interconnected theory. A number of different approaches to number theory are presented, and the different streams in the book are brought together in a chapter that describes the class number formula for quadratic fields and the famous conjectures of Birch and Swinnerton-Dyer. The final chapter introduces some of the main ideas behind modern computational number theory and its applications in cryptography.
An Introduction to Meshfree Methods and Their Programming
This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. Typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods are then introduced systematically detailing the formulation, numerical implementation and programming. Many well-tested computer source codes developed by the authors are attached with useful descriptions. The application of the codes can be readily performed using the examples with input and output files given in table form. These codes consist of most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of meshfree methods. Readers can easily practice with the codes provided to effective learn and comprehend the basics of meshfree methods.
An Introduction to Mathematics of Emerging Biomedical Imaging
Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so.
An Introduction to Mathematical Cryptography
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required.
An Introduction to Infinite-Dimensional Analysis
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension.Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
An Introduction to Fluid Mechanics and Transport Phenomena
This book presents the foundations of fluid mechanics and transport phenomena in a concise way. It is suitable as an introduction to the subject as it contains many examples, proposed problems and a chapter for self-evaluation. The solutions to all problems are displayed in the corresponding appendix.
An Introduction to Ethics in Robotics and AI
This book provides an introduction into the ethics of robots and artificial intelligence. The book was written with university students, policy makers, and professionals in mind but should be accessible for most adults. The book is meant to provide balanced and, at times, conflicting viewpoints as to the benefits and deficits of AI through the lens of ethics. As discussed in the chapters that follow, ethical questions are often not cut and dry. Nations, communities, and individuals may have unique and important perspectives on these topics that should be heard and considered. While the voices that compose this book are our own, we have attempted to represent the views of the broader AI, robotics, and ethics communities.
An Introduction to Echo Analysis : Scattering Theory and Wave Propagation
The use of various types of wave energy is an increasingly promising, non-destructive means of detecting objects and of diagnosing the properties of quite complicated materials. An analysis of this technique requires an understanding of how waves evolve in the medium of interest and how they are scattered by inhomogeneities in the medium. These scattering phenomena can be thought of as arising from some perturbation of a given, known system and they are analysed by developing a scattering theory. This monograph provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems.
An introduction to differential geometry with applications to elasticity
Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory.
An Introduction to continuous-time stochastic processes : Theory, models, and applications to finance, biology, and medicine
This book is introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics covered include: * Interacting particles and agent-based models: from polymers to ants * Population dynamics: from birth and death processes to epidemics * Financial market models: the non-arbitrage principle * Contingent claim valuation models: the risk-neutral valuation theory * Risk analysis in insurance
An Introduction To Chemoinformatics
This, the first text written specifically for this field, aims to provide an introduction to the major techniques of chemoinformatics. The first part of the book deals with the representation of 2D and 3D molecular structures, the calculation of molecular descriptors and the construction of mathematical models. The second part describes other important topics including molecular similarity and diversity, the analysis of large data sets, virtual screening, and library design. Simple illustrative examples are used throughout to illustrate key concepts, supplemented with case studies from the literature.
