Books in Partial differential equations

Mathematical Physics with Partial Differential Equations

1st Edition
December 1, 2011
James Kirkwood
English
eBook
9 7 8 0 1 2 3 8 6 9 9 4 4

Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments. The text presents some of the most important topics and methods of mathematical physics. The premise is to study in detail the three most important partial differential equations in the field – the heat equation, the wave equation, and Laplace’s equation. The most common techniques of solving such equations are developed in this book, including Green’s functions, the Fourier transform, and the Laplace transform, which all have applications in mathematics and physics far beyond solving the above equations. The book’s focus is on both the equations and their methods of solution. Ordinary differential equations and PDEs are solved including Bessel Functions, making the book useful as a graduate level textbook. The book’s rigor supports the vital sophistication for someone wanting to continue further in areas of mathematical physics.

Traveling Wave Analysis of Partial Differential Equations

1st Edition
December 9, 2010
Graham Griffiths + 1 more
English
Hardback
9 7 8 0 1 2 3 8 4 6 5 2 5
eBook
9 7 8 0 1 2 3 8 4 6 5 3 2

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide 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. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

1st Edition
Volume 213
August 6, 2010
Moysey Brio + 2 more
English
Hardback
9 7 8 0 1 2 1 3 3 9 8 1 4
eBook
9 7 8 0 0 8 0 9 1 7 0 4 7

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc.The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them.In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes.

Introductory Differential Equations

3rd Edition
September 9, 2009
Martha L. Abell + 1 more
English
eBook
9 7 8 0 0 8 0 9 5 8 4 5 3

This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a "traditional" curriculum and takes the "traditional" (rather than "dynamical systems") approach. Introductory Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Note that some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries depending on the school, course, or instructor.

Boundary Value Problems

6th Edition
July 24, 2009
David L. Powers
English
Hardback
9 7 8 0 1 2 3 7 4 7 1 9 8
eBook
9 7 8 0 0 8 0 8 8 4 4 1 7

Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods.The book contains nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises.Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems.

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 5
April 29, 2009
C.M. Dafermos + 1 more
English
Hardback
9 7 8 0 4 4 4 5 3 2 2 2 0
eBook
9 7 8 0 0 8 0 9 3 2 5 9 0

Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable

Partial Differential Equations and Boundary Value Problems with Maple

2nd Edition
March 23, 2009
George A. Articolo
English
eBook
9 7 8 0 0 8 0 8 8 5 0 6 3

Partial Differential Equations and Boundary Value Problems with Maple, Second Edition, presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours - an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. This updated edition provides a quick overview of the software w/simple commands needed to get started. It includes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equations. It also incorporates an early introduction to Sturm-Liouville boundary problems and generalized eigenfunction expansions. Numerous example problems and end of each chapter exercises are provided.

Handbook of Differential Equations: Evolutionary Equations

1st Edition
Volume 4
August 19, 2008
C.M. Dafermos + 1 more
English
Hardback
9 7 8 0 4 4 4 5 3 0 3 4 9
eBook
9 7 8 0 0 8 0 9 3 1 9 7 5

The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts.

Handbook of Differential Equations: Stationary Partial Differential Equations

1st Edition
Volume 5
February 4, 2008
Michel Chipot
English
Hardback
9 7 8 0 4 4 4 5 3 2 1 7 6
eBook
9 7 8 0 0 8 0 5 5 7 3 1 1

A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.

Stochastic Differential Equations and Applications

2nd Edition
December 30, 2007
X Mao
English
eBook
9 7 8 0 8 5 7 0 9 9 4 0 2

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.

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Books in Partial differential equations

Mathematical Physics with Partial Differential Equations

Traveling Wave Analysis of Partial Differential Equations

Numerical Time-Dependent Partial Differential Equations for Scientists and Engineers

Introductory Differential Equations

Boundary Value Problems

Handbook of Differential Equations: Evolutionary Equations

Partial Differential Equations and Boundary Value Problems with Maple

Handbook of Differential Equations: Evolutionary Equations

Handbook of Differential Equations: Stationary Partial Differential Equations

Stochastic Differential Equations and Applications