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Optimization and Approximation
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization.It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area.It also systematically presents affordable approximation methods.Exercises at various levels have been included to support the learning process.
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Statistical Modeling Using Local Gaussian Approximation
Statistical Modeling using Local Gaussian Approximation extends powerful characteristics of the Gaussian distribution, perhaps, the most well-known and most used distribution in statistics, to a large class of non-Gaussian and nonlinear situations through local approximation.This extension enables the reader to follow new methods in assessing dependence and conditional dependence, in estimating probability and spectral density functions, and in discrimination.Chapters in this release cover Parametric, nonparametric, locally parametric, Dependence, Local Gaussian correlation and dependence, Local Gaussian correlation and the copula, Applications in finance, and more. Additional chapters explores Measuring dependence and testing for independence, Time series dependence and spectral analysis, Multivariate density estimation, Conditional density estimation, The local Gaussian partial correlation, Regression and conditional regression quantiles, and a A local Gaussian Fisher discriminant.
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Practical Applied Mathematics : Modelling, Analysis, Approximation
Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world.Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations.Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling.The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow.The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material.Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.
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Sparse Polynomial Approximation of High-Dimensional Functions
Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions.These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data.This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods.These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering.It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations.It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing.It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code.The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
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Wave Phenomena : Mathematical Analysis and Numerical Approximation
This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering.Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena.Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered.The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.
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Approximation Theory and Applications : Piecewise Linear and Generalized Functions
Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics.The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure.However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice.This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields.Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics.Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.
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Quantum Mechanics, Volume 2 : Angular Momentum, Spin, and Approximation Methods
This new edition of the unrivalled textbook introduces concepts such as the quantum theory of scattering by a potential, special and general cases of adding angular momenta, time-independent and time-dependent perturbation theory, and systems of identical particles.The entire book has been revised to take into account new developments in quantum mechanics curricula. The textbook retains its typical style also in the new edition: it explains the fundamental concepts in chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * The quantum mechanics classic in a new edition: written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloë * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly * Comprehensive: in addition to the fundamentals themselves, the book contains more than 170 worked examples plus exercises Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris where he also studied and received his PhD in 1962.In 1973 he became Professor of atomic and molecular physics at the Collège des France.His main research interests were optical pumping, quantum optics and atom-photon interactions.In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D.Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII).He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloë was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Supérieure in Paris.His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center.His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.
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One Night... To Marriage: To Love, Honour and Betray / One Night with Gael / One Night to Wedding Vows
One Night... To Marriage: To Love, Honour and Betray / One Night with Gael / One Night to Wedding Vows
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