الصفحة 3
الصفحة 3
Cours doptique : Simulations et exercices résolus avec Maple, Matlab, Mathematica, Mathcad = Optics course: Simulations and exercises solved with Maple, Matlab, Mathematica, Mathcad
Intended for students at the L and M levels of the university as well as for engineers wishing to study certain subjects in greater depth. It covers all the themes of a traditional optics course, from geometric optics to holography, interference, diffraction, coherence and the use of the Fourier transform for spectroscopy. The presentation is developed from mathematical models deriving from typical situations and fundamental examples which are presented in the form of computer programs ready to be implemented. These programs are also available on the CD accompanying the book, for each of the following scientific programming environments: Matlab, Maple, Mathematica and Mathcad. Thus, the reader will be able to modify the parameters of the examples proposed to adapt them to new situations.
Continuous System Simulation
Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.
Computing the Electrical Activity in the Heart
This book describes mathematical models and numerical techniques for simulating the electrical activity in the heart. The book gives an introduction to the most important models of the field, followed by a detailed description of numerical techniques for the models. Particular focus is on efficient numerical methods for large scale simulations on both scalar and parallel computers.
Computer Algebra Recipes : An Introductory Guide to the Mathematical Models of Science
Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models. Aimed at science and engineering undergraduates at the sophomore/junior level, this introductory guide to the mathematical models of science is filled with examples from a wide variety of disciplines, including biology, economics, medicine, engineering, game theory, mathematics, physics, and chemistry.
Computer Algebra in Scientific Computing ; 10th International Workshop, CASC 2007, Bonn, Germany, September 16-20, 2007, Proceedings
The book covers not only various expanding applications of computer algebra to scientific computing but also the computer algebra systems themselves and the CA algorithms. Topics addressed are studies in polynomial and matrix algebra, quantifier elimination, and Gröbner bases, as well as stability investigation of both differential equations and difference methods for them. Several papers are devoted to the application of computer algebra methods and algorithms to the derivation of new mathematical models in biology and in mathematical physics.
Mathematical Models for Registration and Applications to Medical Imaging
Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume.
Mathematical Modeling of Concrete Mixture Proportioning
It puts together an understanding of the appropriate principles of ensuring performance and sustainability of concrete. Broadly subdivided into three parts, first part contains the fundamental aspects introducing the constituent materials, the concepts of concrete mixture designs and the mathematical formulations of the various parameters involved in these designs. The second part is dedicated to discussing approaches and recommendations of American, British and European bodies related to mathematical modelling. Lastly, it discusses perceptions and prescriptions towards both the performance assessment and insurance of the resulting concrete compositions.
Mathematical Modeling of Complex Biological Systems : A Kinetic Theory Approach
Describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems—comprised of large populations of interacting cells—whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. The authors propose a new biological model for the analysis of competition between cells of an aggressive host and cells of a corresponding immune system.Because the microscopic description of a biological system is far more complex than that of a physical system of inert matter, a higher level of analysis is needed to deal with such complexity. Mathematical models using kinetic theory may represent a way to deal with such complexity, allowing for an understanding of phenomena of nonequilibrium statistical mechanics not described by the traditional macroscopic approach. The proposed models are related to the generalized Boltzmann equation and describe the population dynamics of several interacting elements (kinetic population models).The particular models proposed by the authors are based on a framework related to a system of integro-differential equations, defining the evolution of the distribution function over the microscopic state of each element in a given system. Macroscopic information on the behavior of the system is obtained from suitable moments of the distribution function over the microscopic states of the elements involved.
Mathematical Modeling for the Life Sciences
Proposing a wide range of mathematical models that are currently used in life sciences may be regarded as a challenge, and that is precisely the challenge that this book takes up. Of course this panoramic study does not claim to offer a detailed and exhaustive view of the many interactions between mathematical models and life sciences. This textbook provides a general overview of realistic mathematical models in life sciences, considering both deterministic and stochastic models and covering dynamical systems, game theory, stochastic processes and statistical methods. Each mathematical model is explained and illustrated individually with an appropriate biological example. Finally three appendices on ordinary differential equations, evolution equations, and probability are added to make it possible to read this book independently of other literature.
Mathematical Methods in Robust Control of Linear Stochastic Systems
Linear stochastic systems are successfully used to provide mathematical models for real processes in fields such as aerospace engineering, communications, manufacturing, finance and economy. This monograph presents a useful methodology for the control of such stochastic systems with a focus on robust stabilization in the mean square, linear quadratic control, the disturbance attenuation problem, and robust stabilization with respect to dynamic and parametric uncertainty.
Mathematical Aspects of Classical and Celestial Mechanics
In this book we describe the basic principles, problems, and methods of clssical mechanics. Our main attention is devoted to the mathematical side of the subject. Although the physical background of the models considered here and the applied aspects of the phenomena studied in this book are explored to a considerably lesser extent, we have tried to set forth first and foremost the “working” apparatus of classical mechanics. This apparatus is contained mainly in Chapters 1, 3, 5, 6, and 8. Chapter 1 is devoted to the basic mathematical models of classical - chanics that are usually used for describing the motion of real mechanical systems. Special attention is given to the study of motion with constraints and to the problems of realization of constraints in dynamics. In Chapter 3 we discuss symmetry groups of mechanical systems and the corresponding conservation laws. We also expound various aspects of ord- reduction theory for systems with symmetries, which is often used in appli- tions. Chapter 4 is devoted to variational principles and methods of classical mechanics. They allow one, in particular, to obtain non-trivial results on the existence of periodic trajectories. Special attention is given to the case where the region of possible motion has a non-empty boundary. Applications of the variational methods to the theory of stability of motion are indicated.
Martingales and financial mathematics in discrete time
This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time.
LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay
A fuzzy system is, in a very broad sense, any fuzzy logic-based system where fuzzy logic can be used either asthebasisfor the representation of different forms of system knowledge or the model for the interactions and relationships among the system variables. Fuzzy systems have proven to be an important tool for modeling complex systems for which, due to complexity or imprecision, classical tools are unsuccessful. There have been diverse fields of applications of fuzzy technology from medicine to management, from engineering to behavioral science, from vehicle control to computational linguistics, and so on. Fuzzy modeling is a conjunction to understand the s- tem’s behavior and build useful mathematical models. Different types of fuzzy models have been proposed in the literature, among which the Takagi-Sugeno (T-S) fuzzy model is a rule-based one suitable for the accurate approximation and identi?cation of a wide class of nonlinear systems.
Lewis Fry Richardson : His Intellectual Legacy and Influence in the Social Sciences
A pioneer in meteorology and peace research and remains a towering presence in both fields. This edited volume reviews his work and assesses its influence in the social sciences, notably his work on arms races and their consequences, mathematical models, the size distribution of wars, and geographical features of conflict
Lagrangian Transport in Geophysical Jets and Waves : The Dynamical Systems Approach
This book provides an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical flows. These methods were originally developed in the abstract mathematical setting of dynamical systems theory, through a geometric approach to differential equations. Despite the recent developments in this field and the existence of a substantial body of work on geophysical fluid problems in the dynamical systems and geophysical literature, this is the first introductory text that presents these methods in the context of geophysical fluid flow. The book is organized into seven chapters; the first introduces the geophysical context and the mathematical models of geophysical fluid flow that are explored in subsequent chapters. The second and third cover the simplest case of steady flow, develop basic mathematical concepts and definitions, and touch on some important topics from the classical theory of Hamiltonian systems. The fundamental elements and methods of Lagrangian transport analysis in time-dependent flows that are the main subject of the book are described in the fourth, fifth, and sixth chapters. The seventh chapter gives a brief survey of some of the rapidly evolving research in geophysical fluid dynamics that makes use of this new approach. Related supplementary material, including a glossary and an introduction to numerical methods, is given in the appendices.
Killer Cell Dynamics : Mathematical and Computational Approaches to Immunology
Reviews how mathematics can be used in combination with biological data in order to improve understanding of how the immune system works. This is illustrated largely in the context of viral infections. Mathematical models allow scientists to capture complex biological interactions in a clear mathematical language and to follow them to their precise logical conclusions. This can give rise to counter-intuitive insights which would not be attained by experiments alone, and can be used for the design of further experiments in order to address the mathematical results.
Classification and Modeling with Linguistic Information Granules : Advanced Approaches to Linguistic Data Mining
Many approaches have already been proposed for classification and modeling in the literature. These approaches are usually based on mathematical mod els. Computer systems can easily handle mathematical models even when they are complicated and nonlinear (e.g., neural networks). On the other hand, it is not always easy for human users to intuitively understand mathe matical models even when they are simple and linear. This is because human information processing is based mainly on linguistic knowledge while com puter systems are designed to handle symbolic and numerical information. A large part of our daily communication is based on words. We learn from various media such as books, newspapers, magazines, TV, and the Inter net through words. We also communicate with others through words. While words play a central role in human information processing, linguistic models are not often used in the fields of classification and modeling. If there is no goal other than the maximization of accuracy in classification and modeling, mathematical models may always be preferred to linguistic models. On the other hand, linguistic models may be chosen if emphasis is placed on interpretability.
Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis
This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models.
Cell Surface Receptors : A Short Course on Theory and Methods
Cell Surface Receptors: A Short Course on Theory and Methods, 3rd Edition, links theoretical insights into drug-receptor interactions described in mathematical models with the experimental strategies to characterize the biological receptor of interest.
Bioinformatics
In this textbook present mathematical models in bioinformatics and they describe the biological problems that inspire the computer science tools used to handle the enormous data sets involved. The first part of the book covers the mathematical and computational methods, while the practical applications are presented in the second part. The mathematical presentation is descriptive and avoids unnecessary formalism, and yet remains clear and precise. Emphasis is laid on motivation through biological problems and cross applications. Each of the four chapters in the first part is accompanied by exercises and problems to support an understanding of the techniques presented. Each of the six chapters of the second part is devoted to some specific application domain: sequence alignment, molecular phylogenetics and coalescence theory, genomics, proteomics, RNA, and DNA microarrays. Each chapter concludes with a problems and projects section, to deepen the reader's understanding and to allow for the design of derived methods. Many of the projects involve publicly available software and/or Web-based bioinformatics depositories. Finally, the book closes with a thorough bibliography, reaching from classic research results to very recent findings, providing many pointers for future research.Overall, this volume is ideally suited for a senior undergraduate or graduate course on bioinformatics, with a strong focus on its mathematical and computer science background.
