Book Description

This book covers numerical methods for partial differential equations: discretization methods such as finite difference, finite volume and finite element methods; solution methods for linear and nonlinear systems of equations and grid generation. The book takes account of both the theory and implementation, providing simultaneously both a rigorous and an inductive presentation of the technical details. It contains modern topics such as adaptive methods, multilevel methods and methods for convection-dominated problems.Detailed illustrations and extensive exercises are included.It will provide mathematics students with an introduction to the theory and methods, guiding them in their selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it will provide a general framework for formulation and analysis of methods providing a broader perspective to specific applications. ... Read more

Book Description

A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "arsenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient critera, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear - quadratic multi-player differential games in cases when:
* the player formulate their strategies independently (non co-operative games) and use non-Nash equilibria * the game model recognizes noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty). ... Read more

Book Description

Nonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of theory stability and theory of stabilization of nonlinear systems with random structure in terms of new development of the direct Lyapunov's method. The analysis is focused on dynamic systems with random Markov parameters.

This high-level monograph would be of great interest to all those researching or studying in the fields of applied mathematics, applied engineering and physics - particularly in the areas of stochastic differential equations, dynamical systems, stability and control theory. ... Read more

Book Description

This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance (Monte Carlo, PDE, Stochastic Optimization, Copula, Econometrics). The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages. A companion CD provides ready-to-run codes (VBA, MATLAB). The book originates from class notes and case studies developed within a course on numerical methods in finance held by the authors at Bocconi University.

Book Description

This book presents engineers and scientists with all of the information they need to calculate electric and magnetic fields with a digital computer. It is a cookbook for quick field calculation, mixing mathematics, numerical analysis, and electromagnetic theory to create an easy-to-use, practical guide to static and quasi-static field problems. This new edition covers in detail the most popular, available field-computation software, dealing with the use of each and its advantages and disadvantages relative to different types of problems. The book also deals with the basic principles underlying the operation of each software package. ... Read more

Book Description

This is a book about using MuPAD in teaching undergraduate mathematics and solving undergraduate mathematics problems with MuPAD. The author explains basic principles of MuPAD commands and how to write simple programs or to develop interactive environments for teaching mathematics. The text gives a large number of useful examples from undergraduate mathematics collected by the author during his long teaching experience. A web site with examples, MuPAD graphs, exercises and solutions, etc., supports the book. ... Read more

Book Description

Hardbound. The book aims to provide the reader with a general overview of the mathematical and numerical techniques used for the simulation of matter at the microscopic scale.The emphasis lays upon the numerics, but modelling aspects are also addressed.The contributors come from different scientific communities: physics, theoretical chemistry, mathematical analysis, stochastic analysis, numerical analysis. ... Read more

Book Description

Global optimization concerns the computation and characterization of global optima of nonlinear functions. Such problems are widespread in the mathematical modelling of real systems in a very wide range of applications and the last 30 years have seen the development of many new theoretical, algorithmic and computational contributions which have helped to solve globally multiextreme problems in important practical applications.Most of the existing books on optimization focus on the problem of computing locally optimal solutions. Introduction to Global Optimization, however, is a comprehensive textbook on constrained global optimization that covers the fundamentals of the subject, presenting much new material, including algorithms, applications and complexity results for quadratic programming, concave minimization, DC and Lipschitz problems, and nonlinear network flow. Each chapter contains illustrative examples and ends with carefully selected exercises, designed to help students grasp the material and enhance their knowledge of the methods involved.Audience: Students of mathematical programming, and all scientists, from whatever discipline, who need global optimization methods in such diverse areas as economic modelling, fixed charges, finance, networks and transportation, databases, chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environmental engineering. ... Read more