Boundary Element Methods with Applications to Nonlinear Problems

Featuring current research in economics, finance and management, this book surveys nonlinear estimation techniques and offers new methods and insights into nonlinear time series analysis. Covers Marko

Intended for advanced undergraduate and graduate students, the first four chapters of this book are devoted to the introduction of the finite element concept. The focus then covers two essential areas - heat transfer and fluid mechanics: topics with different finite element formulations. Heat transfer applications begin with the classical one-dimensional thin-rod problem, followed by the two-dimensional heat transfer problem including a variety of boundary conditions. Finally, a complicated-geometry three-dimensional problem, involving a cooled radial turbine rotor, is presented, with the cooling passages treated as 'heat sinks' in the finite element analysis. For fluid mechanics, the concept of 'nodeless' degrees of freedom is introduced, with real-life fluid-flow applications. The time-dependent finite-element analysis topic is addressed through the problem of unsteady stator/rotor flow interaction within a turbomachinery stage. Finally, the concept of 'virtually-deformable finite el

The book gives a comprehensive coverage of most classical nonparametric statistical tests as well as nonparametric techniques in regression and generalized regression, time-to-event analysis, density

Nonlinear Approaches in Engineering Applications 2 focuses on the application of nonlinear approaches to different engineering and science problems. The selection of the topics for this book is based

"A practical, professional guide to MATLAB applications, numerical techniques, and scientific computing MATLAB Numerical Methods with Chemical Engineering Applications shows how to use MATLAB to mode

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtai

This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differentia

Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This b

Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems,

Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems explores how Newton's equation for the motion of one particle in classical mechanics combined with finite difference methods a

Many processes in materials science and engineering, such as the load deformation behaviour of certain structures, exhibit nonlinear characteristics. The computer simulation of such processes therefore requires a deep understanding of both the theoretical aspects of nonlinearity and the associated computational techniques. This book provides a complete set of exercises and solutions in the field of theoretical and computational nonlinear continuum mechanics and is the perfect companion to Nonlinear Continuum Mechanics for Finite Element Analysis, where the authors set out the theoretical foundations of the subject. It employs notation consistent with the theory book and serves as a great resource to students, researchers and those in industry interested in gaining confidence by practising through examples. Instructors of the subject will also find the book indispensable in aiding student learning.

Modern astronomical research is beset with a vast range of statistical challenges, ranging from reducing data from megadatasets to characterizing an amazing variety of variable celestial objects or testing astrophysical theory. Linking astronomy to the world of modern statistics, this volume is a unique resource, introducing astronomers to advanced statistics through ready-to-use code in the public domain R statistical software environment. The book presents fundamental results of probability theory and statistical inference, before exploring several fields of applied statistics, such as data smoothing, regression, multivariate analysis and classification, treatment of nondetections, time series analysis, and spatial point processes. It applies the methods discussed to contemporary astronomical research datasets using the R statistical software, making it invaluable for graduate students and researchers facing complex data analysis tasks. A link to the author's website for this book ca

Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an expli

Statistical Theories and Methods with Applications to Economics and Business highlights recent advances in statistical theory and methods that benefit econometric practice. It deals with exploratory d

"Computer methods continue to be critical in the analysis, simulation, design and optimization of engineering processes and systems. Computational approaches are needed to solve the complex mathematic

This second edition of this book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It i

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference wo

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, creating an exciting interplay between the subjects. This is the first and only book to prove i

Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic f

Employs a Step-by-Step Modular Approach to Structural ModelingConsidering that wavelet transforms have also proved useful in the solution and analysis of engineering mechanics problems, up to now ther

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild condit

This book provides a step-by-step introduction to the least squares resolution of nonlinear inverse problems. For readers interested in projection of non-convex sets, it also presents the geometric th

Introduction to Proteomics is written by seasoned researchers with years of practical experience. In addition to comprehensive discussions of the basic concepts, techniques, and applications of the su

Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems n

Although useful in the theoretical and empirical analysis of nonlinear time series data, recent research has shown that semiparametric methods may be applied to dimensionality problems arising from fu

Spectral methods are well-suited to solve problems modeled by time-dependent partial differential equations: they are fast, efficient and accurate and widely used by mathematicians and practitioners. This class-tested 2007 introduction, the first on the subject, is ideal for graduate courses, or self-study. The authors describe the basic theory of spectral methods, allowing the reader to understand the techniques through numerous examples as well as more rigorous developments. They provide a detailed treatment of methods based on Fourier expansions and orthogonal polynomials (including discussions of stability, boundary conditions, filtering, and the extension from the linear to the nonlinear situation). Computational solution techniques for integration in time are dealt with by Runge-Kutta type methods. Several chapters are devoted to material not previously covered in book form, including stability theory for polynomial methods, techniques for problems with discontinuous solutions, r

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This 2006 book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivated introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivated introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

This book deals with advanced fluid flow methods for design and analysis of engineering systems. Panel methods employing surface distributions of source and vortex singularities based on the solution of boundary integral equations have been extensively used for modelling external and internal aerodynamic flows. Part 1 describes the surface vorticity method and illustrates applications of this technique over a wide range of engineering problems in aerodynamics and turbo-machines, including lifting aerofoils and cascades, mixed-flow and rotating cascades for fans, pumps or turbines, meridional flows in turbo-machines, flow past axisymmetric bodies, ducts and ducted propellers or fans. Part 2 extends surface vorticity modelling to the fairly new CFM field of vortex dynamics or vortex cloud theory, including foundation chapters on convection and viscous diffusion by the random walk technique. Vortex cloud methods are developed, again from first principles, to deal with shear layers, bounda

Bhatti (civil engineering, University of Iowa) presents the finite element method as a fairly straightforward extension of the classical weighted residual and the Rayleigh-Ritz methods for approximate

Applied work in business and economics often require a solid understanding of econometric methods to support decision making. This book provides this, encouraging an active engagement with these metho

Though many 'finite element' books exist, this book provides a unique focus on developing the method for three-dimensional, industrial problems. This is significant as many methods which work well for

Certain constrained combinatorial optimization problems have a natural analogue in the continuous setting of the classical isoperimetric problem. The study of so called combinatorial isoperimetric problems exploits similarities between these two, seemingly disparate, settings. This text focuses on global methods. This means that morphisms, typically arising from symmetry or direct product decomposition, are employed to transform new problems into more restricted and easily solvable settings whilst preserving essential structure. This book is based on Professor Harper's many years' experience in teaching this subject and is ideal for graduate students entering the field. The author has increased the utility of the text for teaching by including worked examples, exercises and material about applications to computer science. Applied systematically, the global point of view can lead to surprising insights and results, and established researchers will find this to be a valuable reference wo

Inverse problems arise in practical situations such as medical imaging, geophysical exploration, and non-destructive evaluation where measurements made on the exterior of a body are used to determine properties of the inaccessible interior. There have been substantial developments in the mathematical theory of inverse problems, and applications have expanded greatly. In this volume, leading experts in the theoretical and applied aspects of inverse problems offer extended surveys on several important topics in modern inverse problems, such as microlocal analysis, reflection seismology, tomography, inverse scattering, and X-ray transforms. Each article covers a particular topic or topics with an emphasis on accessibility and integration with the whole volume. Thus the collection can be at the same time stimulating to researchers and accessible to graduate students.

These lecture notes develop modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum optical system having applications in electronics. Intended for graduate stu

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for al

Financial econometrics is a great success story in economics. Econometrics uses data and statistical inference methods, together with structural and descriptive modeling, to address rigorous economic