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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

BooksJournals

    • Dynamical Systems Method for Solving Nonlinear Operator Equations

      • 1st Edition
      • Volume 208
      • September 25, 2006
      • Alexander G. Ramm
      • English
      • Hardback
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      • Paperback
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      • eBook
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      Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author.

    • Handbook of Differential Equations: Evolutionary Equations

      • 1st Edition
      • Volume 3
      • October 24, 2006
      • C.M. Dafermos + 1 more
      • English
      • Hardback
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      • eBook
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      The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.Articles will highlight the present as well as expected future directions of development of the field with particular emphasis on applications. The article by Ambrosio and Savaré discussesthe most recent development in the theory of gradient flow of probability measures. After an introduction reviewing the properties of the Wasserstein space and corresponding subdifferential calculus, applications are given to evolutionarypartial differential equations. The contribution of Herrero provides a description of some mathematical approaches developed to account for quantitative as well as qualitative aspects of chemotaxis. Particular attention is paid to the limits of cell'scapability to measure external cues on the one hand, and to provide an overall description of aggregation models for the slim mold Dictyostelium discoideum on the other.The chapter written by Masmoudi deals with a rather different topic - examples of singular limits in hydrodynamics. This is nowadays a well-studied issue given the amount of new results based on the development of the existence theory for rather general systems of equations in hydrodynamics. The paper by DeLellis addreses the most recent results for the transport equations with regard to possible applications in the theory of hyperbolic systems of conservation laws. Emphasis is put on the development of the theory in the case when the governing field is only a BV function.The chapter by Rein represents a comprehensive survey of results on the Poisson-Vlasov system in astrophysics. The question of global stability of steady states is addressed in detail. The contribution of Soner is devoted to different representations of non-linear parabolic equations in terms of Markov processes. After a brief introduction on the linear theory, a class ofnon-linear equations is investigated, with applications to stochastic control and differential games.The chapter written by Zuazua presents some of the recent progresses done on the problem of controllabilty of partial differential equations. The applications include the linear wave and heat equations,parabolic equations with coefficients of low regularity, and some fluid-structure interaction models.

    • Submodular Functions and Optimization

      • 2nd Edition
      • Volume 58
      • July 26, 2005
      • Satoru Fujishige
      • English
      • Hardback
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      • Paperback
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      • eBook
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      It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.

    • Applications of Functional Analysis and Operator Theory

      • 2nd Edition
      • Volume 200
      • February 8, 2005
      • V. Hutson + 2 more
      • English
      • Paperback
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      • Hardback
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      • eBook
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      Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

    • Handbook of Differential Equations:Stationary Partial Differential Equations

      • 1st Edition
      • Volume 2
      • August 19, 2005
      • Michel Chipot + 1 more
      • English
      • Hardback
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      • eBook
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      A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.

    • Infinite Dimensional Linear Control Systems

      • 1st Edition
      • Volume 201
      • July 12, 2005
      • English
      • Hardback
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      • eBook
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      For more than forty years, the equation y’(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date).The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals.The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y’(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research.Key features:· Applications to optimal diffusion processes.· Applications to optimal heat propagation processes.· Modelling of optimal processes governed by partial differential equations.· Complete bibliography.· Includes the latest research on the subject.· Does not assume anything from the reader except basic functional analysis.· Accessible to researchers and advanced graduate students alike

    • Theories of Generalised Functions

      • 1st Edition
      • January 1, 2005
      • R F Hoskins + 1 more
      • English
      • Paperback
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      • eBook
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      Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions... The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins.

    • Fundamental Data Compression

      • 1st Edition
      • November 3, 2005
      • Ida Mengyi Pu
      • English
      • Paperback
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      • eBook
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      Fundamental Data Compression provides all the information students need to be able to use this essential technology in their future careers. A huge, active research field, and a part of many people's everyday lives, compression technology is an essential part of today's Computer Science and Electronic Engineering courses. With the help of this book, students can gain a thorough understanding of the underlying theory and algorithms, as well as specific techniques used in a range of scenarios, including the application of compression techniques to text, still images, video and audio. Practical exercises, projects and exam questions reinforce learning, along with suggestions for further reading.

    • Student Solutions Manual to Boundary Value Problems

      • 5th Edition
      • November 16, 2005
      • David L. Powers
      • English
      • Paperback
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      • eBook
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      This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.

    • The Geometrical Tolerancing Desk Reference

      • 1st Edition
      • July 20, 2005
      • Paul Green
      • English
      • Paperback
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      • eBook
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      Geometrical tolerancing is the standard technique that designers and engineers use to specify and control the form, location and orientation of the features of components and manufactured parts. This innovative book has been created to simplify and codify the use and understanding of geometrical tolerancing. It is a complete, self contained reference for daily use. An indispensable guide for anyone who creates or needs to understand technical drawings.

Related subjects

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