Helps in solving numerical problems in mathematics, computer science, and engineering. This book employs sinc methods by limiting details as to how or why these methods work. It is suitable to approximate various types of operation, from calculus to partial differential and integral equations.
Aims to investigate the behavior of weak solutions to the elliptic transmission problem in a neighborhood of boundary singularities: angular and conic points or edges. This title deals with the eigenvalue problem for the m-Laplace-Beltrami operator. It covers the transmission problem in conic domains with N different media for an equation.
Introduces the fundamental modeling and analytical techniques required to deepen understanding of biological phenomena. This text includes a section on spiral waves, developments in tumor biology, and covers the numerical solutions of different equations and numerical bifurcation analysis.
Introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters. This book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree.
Helping students understand the concepts and applications, this book keeps to a minimum rigorous mathematical treatments and derivations. It describes each domain analysis with a consistent approach of finite element formulation and solution. It also includes simple examples to show students how to solve related problems.
Suitable for professionals and students in engineering, science, and mathematics who work with partial differential equations, this book focuses on boundary value problems and Fourier series. It offers an overview of solving boundary value problems involving partial differential equations by the methods of separation of variables.
Based on the author's taught course at Arizona State University, this text focuses on the elements needed to understand the applications literature involving delay equations. It covers both the constructive and analytical mathematical models in the subject.
Aiming to present meshfree methods, this work provides the fundamentals of numerical analysis that are important to meshfree methods. It introduces typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods detailing the formulation, numerical implementation and programming.
The Finite Element Method (FEM) has become a kind of universal tool for solving various types of engineering problems. This book introduces the basics and foundation of the FEM, and provides the readers with an understanding of the method, including background, development, application and potential or prospects of the method.
Focusing on growth and decay processes, interacting populations, and heating/cooling problems, this book presents mathematical techniques applicable to models involving differential equations that describe rates of change. It uses flow diagrams and word equations to aid in the model building process and to develop the mathematical equations.
Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics and geometry. This book offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs).
Integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. Whenever a new type of problem is introduced, this text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations.
This book discusses the properties of conformal mappings in the complex plane, a subject closely connected to the study of fractals and chaos. Focusing on analytic aspects of this contemporary topic, it includes a detailed study of the famous Mandelbrot set.
Focuses on the theory and practical applications of Differential Equations to engineering and the sciences. This book emphasises on the methods of solution, analysis, and approximation. It features historical footnotes that trace the development of the discipline and identify outstanding individual contributions.
Ordinary differential equations serve as mathematical models for many exciting real world problems. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections.
Presents and discusses the developments in the study of differential equations. This book covers topics that include pseudo almost automorphic solutions for some non-linear differential equations; positive solutions for p-laplacian dynamic delay differential equations on time scales; semi-linear fractional differential equations; and, more.
Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation.
Reviews the basic theory of partial differential equations of the first and second order and discusses their applications in economics and finance. This book starts with well-known applications to consumer and producer theory, and to the theory of option pricing.
Presents a comprehensive stability analysis of several major types of system models. This book demonstrates the applicability of the developed theory by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems and pulse-width-modulated feedback control systems.
Partial differential equations are used to formulate and thus aid the solution of problems involving functions of several variables, such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity. This book presents research in the study of partial differential equations.
With each methodology given its own chapter, this monograph is a thorough exploration of theories that can be used to find explicit formulas for heat kernels for both elliptic and sub-elliptic operators. The authors show just how diverse those methods are.
Helps students to get a hand at complex calculus problems. This book covers such topics as first-order and second-order differential equations, constant coefficients, undetermined coefficients, variation of parameters, initial-value problems, and the Laplace transform.
Unable to find a suitable coursebook for an introductory PDE course, the author wrote one that combines the needed foundation and theory with tangible applications in physics and other disciplines. Since many practical applications are non-linear, numerical solution techniques are required.
Gives an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. This book presents the concept of orthogonal sets of functions and representations of arbitrary functions in series of functions from such sets.
A differential equation involves an unknown function and its derivative. It is an important subject that lies in the heart of understanding calculus or analysis. Differential Equations For Dummies takes readers step-by-step through this intimidating subject.
Deals with the numerical approximation of partial differential equations. This work provides an illustration of numerical methods, carries out their stability and convergence analysis, derives error bounds, and discusses the algorithmic aspects relative to their implementation.
This book develops the important approaches to the existence and regularity of partial differential equations, in particular of elliptic (and parabolic) type, particularly those aspects and methods that are relevant not only for linear, but also for nonlinear equations.
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them.
This book develops the important approaches to the existence and regularity of partial differential equations, in particular of elliptic (and parabolic) type, particularly those aspects and methods that are relevant not only for linear, but also for nonlinear equations.
Offers a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. Suitable for beginning engineering and math students, this title provides pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects.
Presents the application of the method of characteristics for the numerical solution of hyperbolic type partial differential equations. This book focuses on the numerical solution of the Vlasov equation. It also presents examples with possible combination with fractional step methods in the case of several dimensions.
Offers an elementary introduction to partial differential equations (pdes), primarily focusing on linear equations, but also providing some perspective on nonlinear equations. This title includes an introduction to conservation laws, the uniqueness theorem, viscosity solutions, ill-posed problems, and nonlinear equations of first order.
A research monograph that presents a unified theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener - Ito class including the generalized functionals of Hida as special cases, among others.
Builds upon the basic theory of linear Partial Differential Equations (PDE). This title introduces analytical tools that include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. It develops basic differential geometrical concepts, centred about curvature.
Serves as a comprehensive reference on the finite element method for engineers and mathematicians. This set of three books provides coverage of the theory and the application of the universally used FEM. It covers the basis of the method, its application to solid mechanics and to fluid dynamics.
A study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. It focuses on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry.
In a clear, expository style, this book offers seven articles on topics at the frontier of partial differential equations and spectral theory. The authors discuss recent progress and share their views on future developments, hypotheses and unsolved problems.
Consists of seventeen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at the Middle East Technical University in Ankara, Turkey on August 13-18, 2007.
Dynamical Systems Method (DSM) is a powerful general method for solving operator equations. These equations can be linear or nonlinear, well-posed or ill-posed. The book presents a systematic development of the DSM, and theoretical results are illustrated by a number of numerical examples, which are of independent interest.
The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry.
Presents a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. This work focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. It is for researchers, instructors and graduate students.
This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.
This book explores the differential calculus and its plentiful applications in engineering and the physical sciences. The first six chapters offer a refresher of algebra, geometry, coordinate geometry, trigonometry, the concept of function, etc. since these topics are vital to the complete understanding of calculus.
Covers the integration of the theory of linear Partial Differential Equations and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, this text contains chapters on the mathematical theory of the differential equation, finite difference methods, and finite element methods.
Orthogonal Polynomials and Special Functions (OPSF) have a very rich history, going back to 19th century when mathematicians and physicists tried to solve the important deferential equations of mathematical physics. This book presents the research in the field.
Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.
Develops the methodology according to which classes of discontinuous functions are used in order to investigate a correctness of boundary-value and initial boundary-value problems for the cases with elliptic, parabolic, and hyperbolic equations. This monograph shows a continuous dependence of states of solutions to the boundary-value problems.
Provides developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. This book is application oriented and it contains the theory of Fractional Differential Equations. It provides problems and directions for further investigations.
This book offers an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations. It also shows how to apply the abstract results to various models in the real world focusing on various self-organization models.
Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions.
Contains some of the invited lectures presented at the International Conference Analysis, PDEs and Applications, held in Rome in July 2008, and dedicated to Vladimir G Maz'ya on the occasion of his 70th birthday. This title present surveys as well as fresh results in the areas in which Maz'ya gave seminal contributions.
Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on the random factors. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations.
Focuses on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application. This book offers homework problems at the end of each chapter. It is intended as an introductory course for undergraduate students from science and engineering disciplines.
Offers a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. Suitable for beginning engineering and math students, this title provides pedagogical aids, including an abundance of examples, explanations, Remarks boxes, definitions, and group projects.
Contains the proceedings that were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. This book includes many relevant topics in approximation theory, such as abstract approximation, approximation with constraints, and interpolation and smoothing.
An introductory course on differential stochastic equations and Malliavin calculus. It is based on a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities). It deals with the differential stochastic equations and their connection with parabolic problems.
Mixed-integer nonlinear programming (MINLP) is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers are interested in solving large-scale MINLP instances. This book deals with this topic.
This book provides a readable description of a technique, developed years ago but still current, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally).
Presents the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem.
Incorporating an innovative modeling approach, this book emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. It lets users discover how to identify and harness the mathematics they can use in their careers, and apply it effectively outside the classroom.
Enables a student with some basic knowledge of calculus to learn about differential equations and appreciate their applications. This book focuses on first order differential equations, their methods of solution and their use in mathematical models. It teaches the necessary techniques of solving first order differential equations.
Intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, this book provides an introduction to ordinary differential equations written in classical style.
Presents and discusses the developments in the study of evolution equations. This book covers topics that include a qualitative study of a perturbed critical semi-linear wave equation in variable metric; renormalised solution for a non-linear anisotropic degenerate parabolic equation; periodic solutions of impulsive evolution equations; and, more.
Gives an introduction to Landau-Lifshitz equations and Landau-Lifshitz-Maxwell equations, beginning with the work by Yulin Zhou and Boling Guo in the early 1980s. This book is suitable for those who are interested in partial differential equations, geometric analysis and mathematical physics. It may also be used as an advanced textbook.
An ideal companion to the student textbook Nonlinear Ordinary Differential Equations 4th Edition (OUP, 2007) this text contains over 500 problems and solutions in nonlinear differential equations, many of which can be adapted for independent coursework and self-study.
Deals with the development of asymptotic methods of perturbation theory, making use of group-theoretical techniques. This book investigates several assumptions about specific group properties that lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincare - Birkhoff normal form.
Thoroughly updated and expanded 4th edition of the classic text, including numerous worked examples, diagrams and exercises. An ideal resource for students and lecturers in engineering, mathematics and the sciences it is published alongside a separate Problems and Solutions Sourcebook containing over 500 problems and fully-worked solutions.
Presents the existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. This title provides an introduction to classical finite-dimensional dynamical system theory, including the Weinstein-Moser and Fadell-Rabinowitz bifurcation results.
Offers mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. This focuses on topics such as nonlinear oscillations, deterministic chaos, solitons, reaction-diffusion-driven chemical pattern formation, neuron dynamics and autocatalysis.
Bridges between the mathematical and the technical disciplines. This work sets the mathematical model, emphasizing on the physical magnitude playing the part of the unknown function and on the other hand the laws of mechanics that lead to an ordinary differential equation or system.
Ordinary differential equations play an important role in many problems in mathematics, engineering, physics and other applied sciences. This book covers analytical and numerical aspects of the study of ODEs in combination with practical models and emphasizes initial value problems.
Focuses on the development of robust difference schemes for wide classes of boundary value problems. This book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries.
This book covers adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods as well as examples of their application for a number of nontrivial physical problems.
Structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background, this title includes three appendices for review of linear algebra and crucial concepts in statistics.
Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. This book presents a formal theory of the Cheng-Lin envelope method. It is suitable for college students who want to see immediate applications of what they learn in Calculus.
The Navier-Stokes equations are one of the pillars of fluid mechanics. These equations are useful because they describe the physics of many things of academic and economic interest. This book presents contributions on the application of Navier-Stokes in some engineering applications and describes how the Navier-Stokes equations can be scaled.
Deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. This title presents the theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and specially designed integrators.
Offers an introduction to scientific computing for differential equations. This book provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics.
Traditionally, the theory of pseudo-differential operators was introduced in the Euclidean setting with the aim of tackling a number of important problems in analysis and in the theory of partial differential equations. This book presents a monograph that develops a global quantization theory of pseudo-differential operators on compact Lie groups.
This comprehensive review of the theory includes sample problems and a new technique for analyzing the asymptomatic behavior of differential equation solutions. It shows how to solve second-order differential equations, and how to systematically classify them.
The non-local functional is an integral with the integrand depending on the unknown function at different values of the argument. It has applications in physics, engineering and sciences. This book is dedicated to study of variational calculus for non-local functionals and to theory of boundary value problems for functional differential equations.
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/boundary conditions. This title presents the constructive mathematical techniques. It deals with the asymptotic methods which include self-similarity, balancing argument, and matched asymptotic expansions.
Presents research from around the world on the theory and methods of linear or non-linear evolution equations as well as their further applications. This book includes equations dealing with the asymptotic behaviour of solutions to evolution equations.
Presents an introduction to the ideas, phenomena, and methods of partial differential equations. This book discusses topics such as elliptic, hyperbolic, and parabolic equations, the energy method, maximum principle, and the Fourier Transform. It also features many historical and scientific motivations and applications.
An explanation of how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin in statistical mechanics. The author also compares the Witten Laplacian approach with other techniques.
Includes examples, solved problems, and practice exercises to test skills. This book offers: practice problems with explanations that reinforce knowledge; coverage of various developments in the course field; and review of practices and applications.
Covers the dynamical aspects of ordinary differential equations and explores the relations between dynamical systems and certain fields outside pure mathematics. This book includes bifurcation theory throughout and contains numerous explorations for students to embark upon. It features a simplified treatment of linear algebra.
Emphasises on the qualitative and geometric properties of Ordinary Differential Equations (ODEs) and their solutions. This book includes material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation.
This book introduces sparse and redundant representations with a focus on applications in signal and image processing. It details mathematical modeling for signal sources along with how to use the model for tasks such as denoising, restoration and separation.
What is calculus really for? It helps tell us how and why things change with time. This illustrated introduction to dynamics aims to inspire the interest and enthusiasm of students embarking on a course of mathematical study. It explains why the mathematics which students learn is useful, by exploring the central ideas of calculus and dynamics.
Contains seven survey papers about ordinary differential equations. This title consists papers that features focusing on nonlinear equations. It is suitable for mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations.
Explores developments in the theory of planar quasiconformal mappings with a focus on the interactions with partial differential equations and nonlinear analysis. This book presents a modern approach to the classical theory and features applications across a spectrum of mathematics such as dynamical systems and singular integral operators.
Presents research from around the world on the theory and methods of linear and non-linear evolution equations, as well as their further applications. This book includes the asymptotic behaviour of solutions to evolution equations. It also includes other non-linear differential equations and applications to natural sciences.
Provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. This book contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is suitable in situations where fast oscillations occur.
Based on the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London, this volume provides pseudo-differential operators. Topics include the analysis, applications and computations of pseudo-differential operators in mathematics.
Provides a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. This title includes a spectrum of applications in science, engineering, applied mathematics. It presents a combination of numerical and analytical methods.