Bøger i Texts in Applied Mathematics serien

Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Computer programs in C, Pascal, and Fortran are presented throughout the text to show readers how to apply differential equations towards quantitative problems.

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.

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 prepares graduate students for research in numerical analysis/computational mathematics by giving a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps them to move rapidly into a research program.

This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. It is devoted to the analysis of dynamical systems and combines features of a detailed introductory textbook with that of a reference source.

The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject.

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior.

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.

This corrected third printing retains the authors'main emphasis on ordinary differential equations. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.

For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods.

This introduction to multiscale methods explores both theory and applications. Examples show how to apply multiscale methods to solve a variety of problems. Exercises then enable readers to build their own skills and put them into practice.

Unlike the many other textbooks on the topic of linear algebra, this book includes mathematical and computational chapters along with examples and exercises with Matlab. The authors use both Matlab and SciLab software as well as covering core standard material.

Diffusion and growth phenomena abound in the real worldsurrounding us.

This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.

This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific dis ciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics.

Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.

During the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity.

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.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as weIl as the classical techniques of applied mathematics.

This textbook, ideal for students and lecturers alike, is a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. It includes a thorough treatment of linear systems.

Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology.

Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering.

This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large systems and numerical integrations.

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.

New edition of a well-known classic in the field; Previous edition sold over 6000 copies worldwide; Fully-worked examples; Many carefully selected problems

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.

Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables.