Basic Partial Differential Equations

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Basic Partial Differential Equations

David. Bleecker
Basic Partial Differential Equations Book PDF

Author : David. Bleecker
Publisher : CRC Press
Page : 1010 pages
File Size : 43,7 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351086981

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Basic Partial Differential Equations by David. Bleecker Pdf

Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.

Essential Partial Differential Equations

David F. Griffiths,John W. Dold,David J. Silvester
Essential Partial Differential Equations Book PDF

Author : David F. Griffiths,John W. Dold,David J. Silvester
Publisher : Springer
Page : 368 pages
File Size : 50,5 Mb
Release : 2015-09-24
Category : Mathematics
ISBN : 9783319225692

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Essential Partial Differential Equations by David F. Griffiths,John W. Dold,David J. Silvester Pdf

This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.

Basic Linear Partial Differential Equations

François Treves
Basic Linear Partial Differential Equations Book PDF

Author : François Treves
Publisher : Academic Press
Page : 493 pages
File Size : 52,5 Mb
Release : 1975-08-08
Category : Mathematics
ISBN : 9780080880259

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Basic Linear Partial Differential Equations by François Treves Pdf

Basic Linear Partial Differential Equations

Partial Differential Equations

Walter A. Strauss
Partial Differential Equations Book PDF

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 50,5 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

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. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

A Basic Course in Partial Differential Equations

Qing Han
A Basic Course in Partial Differential Equations Book PDF

Author : Qing Han
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 42,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852552

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A Basic Course in Partial Differential Equations by Qing Han Pdf

This is a textbook for an introductory graduate course on partial differential equations. Han focuses on linear equations of first and second order. An important feature of his treatment is that the majority of the techniques are applicable more generally. In particular, Han emphasizes a priori estimates throughout the text, even for those equations that can be solved explicitly. Such estimates are indispensable tools for proving the existence and uniqueness of solutions to PDEs, being especially important for nonlinear equations. The estimates are also crucial to establishing properties of the solutions, such as the continuous dependence on parameters. Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study.

Partial Differential Equations and Boundary-Value Problems with Applications

Mark A. Pinsky
Partial Differential Equations and Boundary Value Problems with Applications Book PDF

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 40,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821868898

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Partial Differential Equations and Boundary-Value Problems with Applications by Mark A. Pinsky Pdf

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Partial Differential Equations I

Michael E. Taylor
Partial Differential Equations I Book PDF

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 43,9 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9781441970558

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Partial Differential Equations I by Michael E. Taylor Pdf

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

Partial Differential Equations

Phoolan Prasad,Renuka Ravindran
Partial Differential Equations Book PDF

Author : Phoolan Prasad,Renuka Ravindran
Publisher : New Age International
Page : 268 pages
File Size : 50,6 Mb
Release : 1985
Category : Differential equations, Partial
ISBN : 0852267223

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Partial Differential Equations by Phoolan Prasad,Renuka Ravindran Pdf

This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side. Emphasis is on proofs, which are not only mathematically rigorous, but also constructive, where the structure and properties of the solution are investigated in detail. The authors feel that it is no longer necessary to follow the tradition of introducing the subject by deriving various partial differential equations of continuum mechanics and theoretical physics. Therefore, the subject has been introduced by mathematical analysis of the simplest, yet one of the most useful (from the point of view of applications), class of partial differential equations, namely the equations of first order, for which existence, uniqueness and stability of the solution of the relevant problem (Cauchy problem) is easy to discuss. Throughout the book, attempt has been made to introduce the important ideas from relatively simple cases, some times by referring to physical processes, and then extending them to more general systems.

Partial Differential Equations

Thomas Hillen,I. E. Leonard,Henry van Roessel
Partial Differential Equations Book PDF

Author : Thomas Hillen,I. E. Leonard,Henry van Roessel
Publisher : John Wiley & Sons
Page : 610 pages
File Size : 50,6 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118438435

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Partial Differential Equations by Thomas Hillen,I. E. Leonard,Henry van Roessel Pdf

Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

An Introduction to Partial Differential Equations

Michael Renardy,Robert C. Rogers
An Introduction to Partial Differential Equations Book PDF

Author : Michael Renardy,Robert C. Rogers
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 46,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216874

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An Introduction to Partial Differential Equations by Michael Renardy,Robert C. Rogers Pdf

Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

Applied Partial Differential Equations:

Peter Markowich
Applied Partial Differential Equations Book PDF

Author : Peter Markowich
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 46,7 Mb
Release : 2007-08-06
Category : Mathematics
ISBN : 9783540346463

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Applied Partial Differential Equations: by Peter Markowich Pdf

This book presents topics of science and engineering which occur in nature or are part of daily life. It describes phenomena which are modelled by partial differential equations, relating to physical variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has chosen topics representing his career-long interests, including the flow of fluids and gases, granular flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is presented in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations.

Methods for Partial Differential Equations

Marcelo R. Ebert,Michael Reissig
Methods for Partial Differential Equations Book PDF

Author : Marcelo R. Ebert,Michael Reissig
Publisher : Birkhäuser
Page : 456 pages
File Size : 55,9 Mb
Release : 2018-02-23
Category : Mathematics
ISBN : 9783319664569

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Methods for Partial Differential Equations by Marcelo R. Ebert,Michael Reissig Pdf

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool for the treatment of non-stationary or evolution models and shows how to define energies for different models. Part 3 demonstrates how phase space analysis and interpolation techniques are used to prove decay estimates for solutions on and away from the conjugate line. It also examines how terms of lower order (mass or dissipation) or additional regularity of the data may influence expected results. Part 4 addresses semilinear models with power type non-linearity of source and absorbing type in order to determine critical exponents: two well-known critical exponents, the Fujita exponent and the Strauss exponent come into play. Depending on concrete models these critical exponents divide the range of admissible powers in classes which make it possible to prove quite different qualitative properties of solutions, for example, the stability of the zero solution or blow-up behavior of local (in time) solutions. The last part features selected research projects and general background material.

Introduction To Partial Differential Equations (With Maple), An: A Concise Course

Zhilin Li,Larry Norris
Introduction To Partial Differential Equations With Maple An A Concise Course Book PDF

Author : Zhilin Li,Larry Norris
Publisher : World Scientific
Page : 218 pages
File Size : 40,9 Mb
Release : 2021-09-23
Category : Mathematics
ISBN : 9789811228643

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Introduction To Partial Differential Equations (With Maple), An: A Concise Course by Zhilin Li,Larry Norris Pdf

The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations.The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions.The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.

Partial Differential Equations in Action

Sandro Salsa,Gianmaria Verzini
Partial Differential Equations in Action Book PDF

Author : Sandro Salsa,Gianmaria Verzini
Publisher : Springer
Page : 431 pages
File Size : 40,5 Mb
Release : 2015-05-30
Category : Mathematics
ISBN : 9783319154169

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Partial Differential Equations in Action by Sandro Salsa,Gianmaria Verzini Pdf

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.

Partial Differential Equations

Joseph Wloka
Partial Differential Equations Book PDF

Author : Joseph Wloka
Publisher : Cambridge University Press
Page : 536 pages
File Size : 55,9 Mb
Release : 1987-05-21
Category : Mathematics
ISBN : 0521277590

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Partial Differential Equations by Joseph Wloka Pdf

A rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.