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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
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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
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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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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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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 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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68.24 USD

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

by Enrico Valdinoci, Ireneo Peral, Alessio Figalli
Paperback
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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 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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Hyperbolic Conservation Laws in Continuum Physics
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230.990000 USD

Hyperbolic Conservation Laws in Continuum Physics

by Constantine M. Dafermos
Paperback
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Geometry and Topology of Manifolds: 10th China-Japan Conference 2014
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145.950000 USD

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

Paperback
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The Mathematics Behind Biological Invasions
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94.490000 USD

The Mathematics Behind Biological Invasions

by Jonathan R Potts, Sergei V. Petrovskii, Mark A. Lewis
Paperback
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Bubble Systems
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188.990000 USD

Bubble Systems

by Alexander A. Avdeev
Paperback
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Geometric Notebook
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7.340000 USD

Geometric Notebook

by Wild Pages Press
Paperback
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Nonlinear Elliptic Partial Differential Equations: An Introduction
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51.18 USD

Nonlinear Elliptic Partial Differential Equations: An Introduction

by Herve Le Dret
Paperback
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The Parameterization Method for Invariant Manifolds: From Rigorous Results to Effective Computations
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125.990000 USD

The Parameterization Method for Invariant Manifolds: From Rigorous Results to Effective Computations

by Jordi-Lluis Figueras, Marta Canadell, Alex Haro
Paperback
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Dynamic Performance Management
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157.490000 USD

Dynamic Performance Management

by Carmine Bianchi
Paperback
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Boundary and Interior Layers, Computational and Asymptotic Methods - Bail 2014
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145.950000 USD

Boundary and Interior Layers, Computational and Asymptotic Methods - Bail 2014

Paperback
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Retarded Potentials and Time Domain Boundary Integral Equations: A Road Map
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89.240000 USD

Retarded Potentials and Time Domain Boundary Integral Equations: A Road Map

by Francisco-Javier Sayas
Paperback
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Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control
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146.990000 USD

Nonautonomous Linear Hamiltonian Systems: Oscillation, Spectral Theory and Control

by Sylvia Novo, Rafael Obaya, Russell Johnson
Paperback
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Nonlinear Differential Equations
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23.88 USD

Nonlinear Differential Equations

by Raimond A Struble
Paperback
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This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and ...
Functional Analysis and Applications
This self-contained textbook discusses all major topics in functional analysis. Combining classical materials with new methods, it supplies numerous relevant solved examples and problems and discusses the applications of functional analysis in diverse fields. The book is unique in its scope, and a variety of applications of functional analysis and operator-theoretic methods are devoted to each area of application. Each chapter includes a set of problems, some of which are routine and elementary, and some of which are more advanced. The book is primarily intended as a textbook for graduate and advanced undergraduate students in applied mathematics and engineering. It offers several attractive features making it ideally suited for courses on functional analysis intended to provide a basic introduction to the subject and the impact of functional analysis on applied and computational mathematics, nonlinear functional analysis and optimization. It introduces emerging topics like wavelets, Gabor system, inverse problems and application to signal and image processing.
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120.29 USD

Functional Analysis and Applications

by Abul Hasan Siddiqi
Hardback
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This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica(R) computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, ...
Dynamical Systems with Applications Using Mathematica(R): 2017
This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica(R) computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.
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94.490000 USD

Dynamical Systems with Applications Using Mathematica(R): 2017

by Stephen Lynch
Hardback
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Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.
Optimization and Differentiation
Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.
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196.22 USD

Optimization and Differentiation

by Simon Serovajsky
Hardback
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The Finite Element Method in Engineering, Sixth Edition provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique-an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how ...
The Finite Element Method in Engineering
The Finite Element Method in Engineering, Sixth Edition provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique-an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how to set up finite element solutions in civil, mechanical and aerospace engineering applications. The new edition features updated real-world examples from MATLAB, Ansys and Abaqus, and a new chapter on additional FEM topics including extended FEM (X-FEM). Professional engineers will benefit from the introduction to the many useful applications of finite element analysis.
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119.43 USD

The Finite Element Method in Engineering

by Singiresu S. Rao
Paperback
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Presenting some recent results on the construction and the moments of Levy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Levy-type processes to existence and uniqueness theorems for Levy-driven ...
Levy Matters VI: Levy-Type Processes: Moments, Construction and Heat Kernel Estimates
Presenting some recent results on the construction and the moments of Levy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Levy-type processes to existence and uniqueness theorems for Levy-driven stochastic differential equations with Hoelder continuous coefficients. Moreover, necessary and sufficient conditions for the existence of moments of Levy-type processes are studied and some estimates on moments are derived. Levy-type processes behave locally like Levy processes but, in contrast to Levy processes, they are not homogeneous in space. Typical examples are processes with varying index of stability and solutions of Levy-driven stochastic differential equations. This is the sixth volume in a subseries of the Lecture Notes in Mathematics called Levy Matters. Each volume describes a number of important topics in the theory or applications of Levy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian world.
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62.990000 USD

Levy Matters VI: Levy-Type Processes: Moments, Construction and Heat Kernel Estimates

by Franziska Kuhn
Paperback
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This book aims to face particles in flows from many different, but essentially interconnected sides and points of view. Thus the selection of authors and topics represented in the chapters, ranges from deep mathematical analysis of the associated models, through the techniques of their numerical solution, towards real applications and ...
Particles in Flows
This book aims to face particles in flows from many different, but essentially interconnected sides and points of view. Thus the selection of authors and topics represented in the chapters, ranges from deep mathematical analysis of the associated models, through the techniques of their numerical solution, towards real applications and physical implications. The scope and structure of the book as well as the selection of authors was motivated by the very successful summer course and workshop Particles in Flows'' that was held in Prague in the August of 2014. This meeting revealed the need for a book dealing with this specific and challenging multidisciplinary subject, i.e. particles in industrial, environmental and biomedical flows and the combination of fluid mechanics, solid body mechanics with various aspects of specific applications.
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167.990000 USD

Particles in Flows

Hardback
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This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses ...
Modeling Life: The Mathematics of Biological Systems
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler's method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
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85.30 USD

Modeling Life: The Mathematics of Biological Systems

by Alan Garfinkel
Hardback
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This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to ...
Lie Groups, Differential Equations, and Geometry: Advances and Surveys
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
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146.990000 USD

Lie Groups, Differential Equations, and Geometry: Advances and Surveys

Hardback
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This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size ...
Attractors Under Discretisation: 2017
This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes - results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
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73.490000 USD

Attractors Under Discretisation: 2017

by Xiaoying Han
Paperback
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This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion ...
Equations Involving Malliavin Calculus Operators: Applications and Numerical Approximation
This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed. The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters. In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introduced in terms of chaos expansions. The main properties of the operators, which are known in the literature for the square integrable processes, are proven using the chaos expansion approach and extended for generalized and test stochastic processes. Chapter 3, Equations involving Malliavin Calculus operators, is devoted to the study of several types of stochastic differential equations that involve the operators of Malliavin calculus, introduced in the previous chapter. Fractional versions of these operators are also discussed. Finally, in Chapter 4, Applications and Numerical Approximations are discussed. Specifically, we consider the stochastic linear quadratic optimal control problem with different forms of noise disturbances, operator differential algebraic equations arising in fluid dynamics, stationary equations and fractional versions of the equations studied - applications never covered in the extant literature. Moreover, numerical validations of the method are provided for specific problems.
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73.490000 USD

Equations Involving Malliavin Calculus Operators: Applications and Numerical Approximation

by Hermann Mena, Tijana Levajkovic
Paperback
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