Bøger i Mathematics in Science & Engineering serien

This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity.

Suitable for users with interests ranging from application modeling to numerical analysis and scientific software development, this book treats standard convergence theory as well as other necessary ingredients for successful numerical simulations of physical systems encountered by the various practitioners.

Introduces the method of lower and upper solutions for ordinary differential equations. Divided into two sections, this book presents the fundamental features of the method. It also pays attention to other settings such as partial differential equations or functional differential equations. It features illustrated theorems by examples.

Features a blend of difference equations theory and its applications to economics. This book deals with the theory of linear (and linearized) difference equations, and nonlinear dynamical systems which have been applied to economic analysis. It studies the important concepts and theorems in difference equations theory.

There is an ever increasing need for modelling complex processes reliably. This book discusses a technique for formulating process models in process technology: stochastic process modelling. It demonstrates how stochastic modelling may be implemented by describing example cases. It also shows how a stochastic model may be formulated for a case.

Provides readers with the different types of functional equations that they can find in practice, showing how they can be solved. This book also deals with functional networks and their applications, a generalization of neural networks that allows solving many practical problems.

Most mathematicians, engineers, and scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framework. It includes a collection of examples of Liapunov functions.

Presents the theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This book represents a blend of methods in general computational analysis, and specific, but also generic, techniques for study of systems theory and its particular branches, such as optimal filtering and information compression.

Covers fundamental aspects of generating fractals through L-system. This work provides insight to various researches in this area for generating fractals through L-system approach and estimating dimensions. It includes topics such as: Fractals generated from L-System including hybrid fractals; Dimension calculation for L-system fractals; and more.

Presents a theoretical approach to complex non-equilibrium phenomena, especially Gibbs/Falk thermodynamics and fluid mechanics. This book emphasizes macroscopic phenomena, focusing specifically on gaseous states, and considering the relations to liquid and crystalline states. It offers a unified theory of all branches of macroscopic physics.

Presents error and complexity in error-free, parallel, and probabilistic methods. This book discusses deterministic and probabilistic methods with error and complexity. It points out the scope and limitation of mathematical error-bounds. It is suitable for those in the fields of computational mathematics, and applied mathematics.

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems.Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknownsHelps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristicsEnables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Provides a survey of results in the field of the cell and cell associated objects modeling. This book investigates applications to modeling in the areas of AIDS, cancers and life longevity, and proves fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions.

Presents a unifying look on different equilibrium concepts in economics, including several models from related sciences. This work describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models.

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. This book presents the reader with a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.

Intended for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, this covers the topics necessary for initial study and immediate application of fractional derivatives fractional differential equations. It also includes tables of fractional derivatives.

Intended for graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems, this book presents a general method for solving operator equations, especially non-linear and ill-posed. It also contains a development of a general method, the dynamical systems method, and DSM for solving operator equations.

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book''s strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methodsCombines mathematical rigor with an illuminating exposition full of historical notes and fascinating detailsEnables researchers, lecturers and students to find material under the single "roof"