Bøger i Texts in Applied Mathematics serien

To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy.Volume I is divided into 23 chapters plus two appendices on Banach and Hilbert spaces and on differential calculus.

This text provides an application oriented introduction to the numerical methods for partial differential equations. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows).

Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful.The material, and topics, have been updated to include recent developments in mathematical modeling.

The remainder of Volume III addresses time-dependent problems: parabolic equations (such as the heat equation), evolution equations without coercivity (Stokes flows, Friedrichs' systems), and nonlinear hyperbolic equations (scalar conservation equations, hyperbolic systems).

This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not chaos).

This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved.

To this end, all the system theoretic concepts introduced throughout the text are illustrated by the same types of examples, namely, diffusion equations, wave and beam equations, delay equations and the new class of platoon-type systems.

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology.

Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models.

Data Assimilation

This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems.

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences.

In its expanded new edition, this book covers boundary layers, multiple scales, homogenisation, slender body theory, symbolic computing, discrete equations and more. Includes exercises derived from current research, drawn from a range of application areas.

This book covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications.

In its expanded second edition, this book describes sources of errors in numerical computations, and provides tools for assessing the accuracy of numerical methods and their solutions. Includes MATLAB programs and detailed description of practical issues.

As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control.

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II.

Now in a second, expanded edition, this book bridges the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics and introduces a range of geometric methods including Lie groups and Euclidean geometry.

The new title of this major revision of Numerical Methods for Wave Equations in Geophysical Fluid Dynamics conveys its broader scope. Aimed at those studying geophysical fluids, it also helps find numerical solutions to time-dependent differential equations.

Reflecting fresh mutual interest between mathematics and physics, this updated second edition interweaves rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that are their mathematical models.

Based on the author's taught course at Arizona State University, this text focuses on the elements needed to understand the applications literature involving delay equations. It covers both the constructive and analytical mathematical models in the subject.

This book deals with the construction, analysis and interpretation of mathematical models to help us understand the world. It develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering.

This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations.

Equations in dimensions one and two constitute the majority of the text, and in particular it is demonstrated that the basic notion of stability and bifurcations of vector fields are easily explained for scalar autonomous equations.

This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools.

In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.