Bøger i Advances in Applied Mathematics serien

This book presents the mathematics of quantum computation. The purpose is to introduce the topic of quantum computing to students in computer science, physics and mathematics who have no prior knowledge of this field.

The topics include essential, advanced mathematics to access as a refresher or to add to the mathematical education and address the needs of engineers and scientists who need to expand their working knowledge. These topics are driven by applications and exercises with solutions are offered to confirm understanding.

The book includes contributions by top researchers offering topics associated with equations and their relevance and significance in various scientific areas of study and research. The readers will find several important and useful methods and techniques for solving various types of fractional-order models in engineering and science.

The author approaches an old classic problem - the existence of solutions of Navier-Stokes eqs. The main objective is to model and derive of equation of continuity, Euler equation of fluid motion, energy flux equation, Navier-Stokes eqs from the observer point of view and solve classic problem for this interpretation of fluid motion laws.

This book develops foundational concepts in probability and statistics with primary applications in mechanical and aerospace engineering. It was designed utilizing the latest research in statistics learning and in engagement teaching practices.

The book is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear PDEs. It also presents the direct method of symmetry reductions and its more general version.

The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ODEs, PDEs, stochastic DEs, and systems of such equations.

This book is devoted to the qualitative theory of boundary value problems on time scales. It summarizes the most recent contributions in this area.

This book is devoted to the qualitative theory of boundary value problems on time scales. It summarizes the most recent contributions in this area.

The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics.

Mathematical modeling is both a skill and an art and must be practiced in order to maintain and enhance the ability to use those skills. This book will be of interest to instructors and students offering courses focused on discrete modeling or modeling for decision making.

With an introduction to signal processing, this book outlines the fundamental principles and applications of radar. It covers the basics of radar, includes important mathematical derivations, and discusses research and industry trends along with a range of advanced topics and radar technology issues.

A guide to the use of operations research (OR) techniques in decision-making, design, analysis, and management. It examines methods and practical issues related to the development and use of computer implementations. It offers information on how to select and obtain software and describes its important characteristics.

The author has achieved the breakthrough of generalizing the First-Order Theory presented in his previous books, to the efficient computations of arbitrarily high-order sensitivities for nonlinear systems (HONASAP). This breakthrough has many applications, especially when there is a need to quantify nonlinear behavior.

Containing over 6,000 entries, the newest edition of this popular series continues to provide essential formulas, tables, figures and detailed descriptions. Plus, it features many diagrams, group tables, and integrals not available online.It also incorporates topics such as max plus algebra, financial options, pseudospectra, and proof methods.

Quadratic programming is a mathematical technique that allows for the optimization of a quadratic function in several variables. QP is a subset of Operations Research and is the next higher lever of sophistication than Linear Programming. It is a key mathematical tool in Portfolio Optimization and structural plasticity. This is useful in Civil Engineering as well as Statistics.

This book provides a systematic approach to the various methods available for deriving a Green¿s function. It begins by reviewing the historical development of the Green¿s function, the Fourier and Laplace transforms, the classical special functions of Bessel functions and Legendre polynomials, and the Dirac delta function. It then presents Green¿s functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain, including worked examples, problem sets, and illustrations.

Presents the techniques required to undertake basic modeling of biological systems through the development and analysis of dynamical systems. This title includes different types of applications from population biology and epidemiology. It provides examples of problems with solutions followed by exercises to reinforce the examples.

This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on the integration of interactions rather than the spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.

Introduction to Financial Mathematics motivates students through a discussion of personal finances and portfolio management. The book covers nearly all of the syllabus topics of the Financial Mathematics Actuarial examination to provide students with the foundation they require for future studies and in their careers. It begins by covering standard material on the mathematics of interest and goes on to address probabilistic financial models and the valuation of financial derivatives. Many of the examples in the book involve numerical solution of complicated non-linear equations; others ask students to produce algorithms which beg to be implemented as programs.

This textbook presents a strong and clear relationship between theory and practice. It covers basic topics such as Dantzig¿s simplex algorithm, duality, sensitivity analysis, integer optimization models, and network models as well as more advanced topics including interior point algorithms, the branch-and-bound algorithm, cutting planes, and complexity. Along with case studies, it also discusses more advanced techniques such as column generation, multiobjective optimization, and game theory. It also includes computer code in the form of models in GMPL. The book contains appendices covering mathematical proofs, linear algebra, graph theory, convexity, and a background in nonlinear optimization. All chapters contain extensive examples and exercises. .

This book provides a systematic approach to the various methods available for deriving a Green¿s function. It begins by reviewing the historical development of the Green¿s function, the Fourier and Laplace transforms, the classical special functions of Bessel functions and Legendre polynomials, and the Dirac delta function. It then presents Green¿s functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain, including worked examples, problem sets, and illustrations.

This text fills a niche between a calculus-based probability course and a stochastic processes course typically taken by upper undergraduate students. While Markov processes are touched on in probability courses, this book offers the opportunity to concentrate on the topic when additional study is required. It discusses how Markov processes are applied in a number of fields, including economics, physics, and mathematical biology.

Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology.