Bücher der Reihe Texts in Applied Mathematics

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.

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 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.

The result of lectures given by the authors at New York University, the University of Utah, and Michigan State University, the material is written for students who have had only one term of calculus, but it contains material that can be used in modeling courses in applied mathematics at all levels through early graduate courses.

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 is the third and yet further updated edition of a highly regarded mathematical text. Brenner develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis.

Many books on stability theory of motion have been published in various lan guages, including English. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations.

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

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.

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.

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.

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

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.

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 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.

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.

Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future.There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role.The following topics are covered:* least-squares approximation and regularization methods* interpolation by algebraic and trigonometric polynomials* basic results on best approximations* Euclidean approximation* Chebyshev approximation* asymptotic concepts: error estimates and convergence rates* signal approximation by Fourier and wavelet methods* kernel-based multivariate approximation* approximation methods in computerized tomographyProviding numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.