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Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available ...
Fundamentals of Differential Equations: Pearson New International EditionEdition
Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software. Fundamentals of Differential Equations, Eighth Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems, Sixth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).
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90.30 USD

Fundamentals of Differential Equations: Pearson New International EditionEdition

by Arthur David Snider, Edward B Saff, R Kent Nagle
Paperback / softback
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This Festschrift contains six research surveys and thirty-three shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10-14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both ...
Stochastic Partial Differential Equations and Related Fields: In Honor of Michael Roeckner SPDERF, Bielefeld, Germany, October 10 -14, 2016
This Festschrift contains six research surveys and thirty-three shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10-14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Roeckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker-Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
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156.450000 USD

Stochastic Partial Differential Equations and Related Fields: In Honor of Michael Roeckner SPDERF, Bielefeld, Germany, October 10 -14, 2016

Hardback
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This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is ...
The Gradient Discretisation Method
This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray-Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.
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62.990000 USD

The Gradient Discretisation Method

by Raphaele Herbin, Cindy Guichard, Thierry Gallouet, Robert Eymard, Jerome Droniou
Paperback / softback
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The book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.Keeping the reader constantly focused on the ...
Integration For Calculus, Analysis, And Differential Equations: Techniques, Examples, And Exercises
The book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.Keeping the reader constantly focused on the three principal epistemological questions: 'What for?', 'Why?', and 'How?', the book is designated as a supplementary instructional tool and consists ofThe Answers to all the 192 Problems are provided in the Answer Key. The book will benefit undergraduates, advanced undergraduates, and members of the public with an interest in science and technology, helping them to master techniques of integration at the level expected in a calculus course.
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39.900000 USD

Integration For Calculus, Analysis, And Differential Equations: Techniques, Examples, And Exercises

by Marat V. Markin
Paperback / softback
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Since publication of the first edition over a decade ago, Green's Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green's function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect ...
Green's Functions with Applications, Second Edition
Since publication of the first edition over a decade ago, Green's Functions with Applications has provided applied scientists and engineers with a systematic approach to the various methods available for deriving a Green's function. This fully revised Second Edition retains the same purpose, but has been meticulously updated to reflect the current state of the art. The book opens with necessary background information: a new chapter on the historical development of the Green's function, coverage of the Fourier and Laplace transforms, a discussion of the classical special functions of Bessel functions and Legendre polynomials, and a review of the Dirac delta function. The text then presents Green's functions for each class of differential equation (ordinary differential, wave, heat, and Helmholtz equations) according to the number of spatial dimensions and the geometry of the domain. Detailing step-by-step methods for finding and computing Green's functions, each chapter contains a special section devoted to topics where Green's functions particularly are useful. For example, in the case of the wave equation, Green's functions are beneficial in describing diffraction and waves. To aid readers in developing practical skills for finding Green's functions, worked examples, problem sets, and illustrations from acoustics, applied mechanics, antennas, and the stability of fluids and plasmas are featured throughout the text. A new chapter on numerical methods closes the book. Included solutions and hundreds of references to the literature on the construction and use of Green's functions make Green's Functions with Applications, Second Edition a valuable sourcebook for practitioners as well as graduate students in the sciences and engineering.
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102.38 USD

Green's Functions with Applications, Second Edition

by Dean G. Duffy
Paperback
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The book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.Keeping the reader constantly focused on the ...
Integration For Calculus, Analysis, And Differential Equations: Techniques, Examples, And Exercises
The book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.Keeping the reader constantly focused on the three principal epistemological questions: 'What for?', 'Why?', and 'How?', the book is designated as a supplementary instructional tool and consists ofThe Answers to all the 192 Problems are provided in the Answer Key. The book will benefit undergraduates, advanced undergraduates, and members of the public with an interest in science and technology, helping them to master techniques of integration at the level expected in a calculus course.
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60.900000 USD

Integration For Calculus, Analysis, And Differential Equations: Techniques, Examples, And Exercises

by Marat V. Markin
Hardback
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This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. ...
Contributions to Partial Differential Equations and Applications
This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference Contributions to PDE for Applications held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.
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188.990000 USD

Contributions to Partial Differential Equations and Applications

Hardback
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This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the ...
Periodic Homogenization of Elliptic Systems
This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.
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115.490000 USD

Periodic Homogenization of Elliptic Systems

by Zhongwei Shen
Hardback
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This monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book ...
Ordinary Differential Equations for Engineers: Problems with MATLAB Solutions
This monograph presents teaching material in the field of differential equations while addressing applications and topics in electrical and biomedical engineering primarily. The book contains problems with varying levels of difficulty, including Matlab simulations. The target audience comprises advanced undergraduate and graduate students as well as lecturers, but the book may also be beneficial for practicing engineers alike.
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230.990000 USD

Ordinary Differential Equations for Engineers: Problems with MATLAB Solutions

by Ali Umit Keskin
Hardback
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This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including ...
Calculus of Variations
This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether's Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and -convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.
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83.990000 USD

Calculus of Variations

by Filip Rindler
Paperback
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This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. ...
Dynamical Systems on 2- and 3-Manifolds
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.< The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.
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146.990000 USD

Dynamical Systems on 2- and 3-Manifolds

by Olga V Pochinka, Timur V Medvedev, Viacheslav Z Grines
Paperback / softback
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This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16-20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists ...
XII Symposium of Probability and Stochastic Processes: Merida, Mexico, November 16-20, 2015
This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16-20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Benedicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.
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145.950000 USD

XII Symposium of Probability and Stochastic Processes: Merida, Mexico, November 16-20, 2015

Hardback
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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). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of ...
Ordinary Differential Equations: Basics and Beyond
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). While proofs are rigorous, the exposition is reader-friendly, aiming for the informality of face-to-face interactions. A unique feature of this book is the integration of rigorous theory with numerous applications of scientific interest. Besides providing motivation, this synthesis clarifies the theory and enhances scientific literacy. Other features include: (i) a wealth of exercises at various levels, along with commentary that explains why they matter; (ii) figures with consistent color conventions to identify nullclines, periodic orbits, stable and unstable manifolds; and (iii) a dedicated website with software templates, problem solutions, and other resources supporting the text (www.math.duke.edu/ode-book). Given its many applications, the book may be used comfortably in science and engineering courses as well as in mathematics courses. Its level is accessible to upper-level undergraduates but still appropriate for graduate students. The thoughtful presentation, which anticipates many confusions of beginning students, makes the book suitable for a teaching environment that emphasizes self-directed, active learning (including the so-called inverted classroom).
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94.490000 USD

Ordinary Differential Equations: Basics and Beyond

by John W Cain, David G. Schaeffer
Paperback / softback
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This Brief reports on heat transfer from a solid boundary in a saturated porous medium. Experiments reveal overall heat transfer laws when the flow along the wall is driven by buoyancy produced by large temperature differences, and mathematical analysis using advanced volume-averaging techniques produce estimates of how heat is dispersed ...
Buoyancy-Driven Flow in Fluid-Saturated Porous Media near a Bounding Surface
This Brief reports on heat transfer from a solid boundary in a saturated porous medium. Experiments reveal overall heat transfer laws when the flow along the wall is driven by buoyancy produced by large temperature differences, and mathematical analysis using advanced volume-averaging techniques produce estimates of how heat is dispersed in the porous zone. Engineers, hydrologists and geophysicists will find the results valuable for validation of laboratory and field tests, as well as testing their models of dispersion of heat and mass in saturated media.
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73.490000 USD

Buoyancy-Driven Flow in Fluid-Saturated Porous Media near a Bounding Surface

by Francis A. Kulacki, Hitoshi Sakamoto
Paperback
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Now in its second edition, this monograph explores the Monge-Ampere equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques ...
The Monge-Ampere Equation
Now in its second edition, this monograph explores the Monge-Ampere equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Ampere equation and a chapter on interior Hoelder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampere-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics. Both researchers and graduate students working on nonlinear differential equations and their applications will find this to be a useful and concise resource.
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157.490000 USD

The Monge-Ampere Equation

by Cristian E. Gutierrez
Paperback / softback
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In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier-Stokes partial differential equations on (x, y, z, t) 3 x [0, T]. Initially converting the PDE to a system of integral equations, the authors ...
Navier-Stokes Equations on R3 x [0, T]
In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier-Stokes partial differential equations on (x, y, z, t) 3 x [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A 3 x [0, T], and provide an explicit novel algorithm based on Sinc approximation and Picard-like iteration for computing the solution. Additionally, the authors include appendices that provide a custom Mathematica program for computing solutions based on the explicit algorithmic approximation procedure, and which supply explicit illustrations of these computed solutions.
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114.450000 USD

Navier-Stokes Equations on R3 x [0, T]

by Gerd Baumann, Don Tucker, Frank Stenger
Paperback / softback
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The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference Dynamical Systems: Theory and Applications, held in Lodz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical ...
Dynamical Systems: Modelling: Lodz, Poland, December 7-10, 2015
The book is a collection of contributions devoted to analytical, numerical and experimental techniques of dynamical systems, presented at the international conference Dynamical Systems: Theory and Applications, held in Lodz, Poland on December 7-10, 2015. The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
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145.950000 USD

Dynamical Systems: Modelling: Lodz, Poland, December 7-10, 2015

Paperback / softback
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Presenting the latest findings in topics from across the mathematical spectrum, this volume includes results in pure mathematics along with a range of new advances and novel applications to other fields such as probability, statistics, biology, and computer science. All contributions feature authors who attended the Association for Women in ...
Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium
Presenting the latest findings in topics from across the mathematical spectrum, this volume includes results in pure mathematics along with a range of new advances and novel applications to other fields such as probability, statistics, biology, and computer science. All contributions feature authors who attended the Association for Women in Mathematics Research Symposium in 2015: this conference, the third in a series of biennial conferences organized by the Association, attracted over 330 participants and showcased the research of women mathematicians from academia, industry, and government.
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230.990000 USD

Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium

Paperback / softback
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This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. ...
Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models
This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.
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125.990000 USD

Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models

by Zhiyong Ma, Yuming Qin
Paperback / softback
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The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum ...
Spectral Theory and Mathematical Physics
The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.
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188.990000 USD

Spectral Theory and Mathematical Physics

Paperback / softback
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This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with ...
Asymptotics of Elliptic and Parabolic PDEs: and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics
This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.
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135.450000 USD

Asymptotics of Elliptic and Parabolic PDEs: and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics

by Zeev Schuss, David Holcman
Hardback
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The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly ...
Open Problems in Mathematics
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash's legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.
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156.450000 USD

Open Problems in Mathematics

Paperback / softback
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This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to ...
Hyperbolic Conservation Laws in Continuum Physics
This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conservation laws. This new edition places increased emphasis on hyperbolic systems of balance laws with dissipative source, modeling relaxation phenomena. It also presents an account of recent developments on the Euler equations of compressible gas dynamics. Furthermore, the presentation of a number of topics in the previous edition has been revised, expanded and brought up to date, and has been enriched with new applications to elasticity and differential geometry. The bibliography, also expanded and updated, now comprises close to two thousand titles. From the reviews of the 3rd edition: This is the third edition of the famous book by C.M. Dafermos. His masterly written book is, surely, the most complete exposition in the subject. Evgeniy Panov, Zentralblatt MATH A monumental book encompassing all aspects of the mathematical theory of hyperbolic conservation laws, widely recognized as the Bible on the subject. Philippe G. LeFloch, Math. Reviews
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230.990000 USD

Hyperbolic Conservation Laws in Continuum Physics

by Constantine M. Dafermos
Paperback / softback
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Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincare conjecture, the Yau-Tian-Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger-Yau-Zaslow conjecture on mirror symmetry, the relative Yau-Tian-Donaldson ...
Geometry and Topology of Manifolds: 10th China-Japan Conference 2014
Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincare conjecture, the Yau-Tian-Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger-Yau-Zaslow conjecture on mirror symmetry, the relative Yau-Tian-Donaldson conjecture in Kahler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue of an embedded minimal hypersurface of the sphere. For the younger generation to approach such problems and obtain the required techniques, it is of the utmost importance to provide them with up-to-date information from leading specialists.The geometry conference for the friendship of China and Japan has achieved this purpose during the past 10 years. Their talks deal with problems at the highest level, often accompanied with solutions and ideas, which extend across various fields in Riemannian geometry, symplectic and contact geometry, and complex geometry.
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145.950000 USD

Geometry and Topology of Manifolds: 10th China-Japan Conference 2014

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This monograph presents a systematic analysis of bubble system mathematics, using the mechanics of two-phase systems in non-equilibrium as the scope of analysis. The author introduces the thermodynamic foundations of bubble systems, ranging from the fundamental starting points to current research challenges. This book addresses a range of topics, including ...
Bubble Systems
This monograph presents a systematic analysis of bubble system mathematics, using the mechanics of two-phase systems in non-equilibrium as the scope of analysis. The author introduces the thermodynamic foundations of bubble systems, ranging from the fundamental starting points to current research challenges. This book addresses a range of topics, including description methods of multi-phase systems, boundary and initial conditions as well as coupling requirements at the phase boundary. Moreover, it presents a detailed study of the basic problems of bubble dynamics in a liquid mass: growth (dynamically and thermally controlled), collapse, bubble pulsations, bubble rise and breakup. Special emphasis is placed on bubble dynamics in turbulent flows. The analysis results are used to write integral equations governing the rate of vapor generation (condensation) in non-equilibrium flows, thus creating a basis for solving a number of practical problems. This book is the first to present a comprehensive theory of boiling shock with applications to problems of critical discharge and flashing under the fast decompression conditions. Reynolds' analogy was the key to solving a number of problems in subcooled forced-flow boiling, the theoretical results of which led to easy-to-use design formulas. This book is primarily aimed at graduate and post-graduate students specializing in hydrodynamics or heat and mass transfer, as well as research expert focused on two-phase flow. It will also serve as a comprehensive reference book for designers working in the field of power and aerospace technology.
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188.990000 USD

Bubble Systems

by Alexander A. Avdeev
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This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. ...
The Mathematics Behind Biological Invasions
This book investigates the mathematical analysis of biological invasions. Unlike purely qualitative treatments of ecology, it draws on mathematical theory and methods, equipping the reader with sharp tools and rigorous methodology. Subjects include invasion dynamics, species interactions, population spread, long-distance dispersal, stochastic effects, risk analysis, and optimal responses to invaders. While based on the theory of dynamical systems, including partial differential equations and integrodifference equations, the book also draws on information theory, machine learning, Monte Carlo methods, optimal control, statistics, and stochastic processes. Applications to real biological invasions are included throughout. Ultimately, the book imparts a powerful principle: that by bringing ecology and mathematics together, researchers can uncover new understanding of, and effective response strategies to, biological invasions. It is suitable for graduate students and established researchers in mathematical ecology.
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94.490000 USD

The Mathematics Behind Biological Invasions

by Jonathan R Potts, Sergei V. Petrovskii, Mark A. Lewis
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This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive ...
Partial Differential Equations and Geometric Measure Theory: Cetraro, Italy 2014
This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2-7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.
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78.740000 USD

Partial Differential Equations and Geometric Measure Theory: Cetraro, Italy 2014

by Enrico Valdinoci, Ireneo Peral, Alessio Figalli
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This book arose from a conference on Singularities and Computer Algebra which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad ...
Singularities and Computer Algebra: Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday
This book arose from a conference on Singularities and Computer Algebra which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra.Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schoenemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists.The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.
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146.990000 USD

Singularities and Computer Algebra: Festschrift for Gert-Martin Greuel on the Occasion of his 70th Birthday

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This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. ...
Analytic Inequalities and Their Applications in PDEs
This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.
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167.990000 USD

Analytic Inequalities and Their Applications in PDEs

by Yuming Qin
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This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in ...
Inverse Problems in Ordinary Differential Equations and Applications
This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.
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125.990000 USD

Inverse Problems in Ordinary Differential Equations and Applications

by Rafael Ramirez, Jaume Llibre
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