Introduction To Partial Differential Equations

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Introduction To Partial Differential Equations With Applications

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Author : E. C. Zachmanoglou
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01

Introduction To Partial Differential Equations With Applications written by E. C. Zachmanoglou and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Introduction To Partial Differential Equations

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Author : Peter J. Olver
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-08

Introduction To Partial Differential Equations written by Peter J. Olver and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-08 with Mathematics categories.

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

Partial Differential Equations

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Author : Michael Shearer
language : en
Publisher: Princeton University Press
Release Date : 2015-03-01

Partial Differential Equations written by Michael Shearer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-01 with Mathematics categories.

An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Introduction To Partial Differential Equations With Maple An A Concise Course

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Author : Zhilin Li
language : en
Publisher: World Scientific
Release Date : 2021-09-23

Introduction To Partial Differential Equations With Maple An A Concise Course written by Zhilin Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.

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.

Introduction To Partial Differential Equations With Matlab

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Author : Jeffery M. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Partial Differential Equations With Matlab written by Jeffery M. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value problems with constant coeffi cients in geometrically simple domains. Too often an introductory course focuses exclusively on these core problems and techniques and leaves the student with the impression that there is no more to the subject. Questions of existence, uniqueness, and well-posedness are ignored. In particular there is a lack of connection between the analytical side of the subject and the numerical side. Furthermore nonlinear problems are omitted because they are too hard to deal with analytically. Now, however, the availability of convenient, powerful computational software has made it possible to enlarge the scope of the introductory course. My goal in this text is to give the student a broader picture of the subject. In addition to the basic core subjects, I have included material on nonlinear problems and brief discussions of numerical methods. I feel that it is important for the student to see nonlinear problems and numerical methods at the beginning of the course, and not at the end when we run usually run out of time. Furthermore, numerical methods should be introduced for each equation as it is studied, not lumped together in a final chapter.

Partial Differential Equations An Introduction With Matematica And Maple

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Author : Ioannis P Stavroulakis
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-12-13

Partial Differential Equations An Introduction With Matematica And Maple written by Ioannis P Stavroulakis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-13 with categories.

This textbook is a self-contained introduction to partial differential equations. It is designed for undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations. Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered. The material is illustrated with model examples. Mathematics software products such as Mathematica and Maple in ScientificWorkPlace are used in both graphical and computational aspects.

Introduction To Partial Differential Equations And Hilbert Space Methods

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Author : Karl E. Gustafson
language : en
Publisher: Courier Corporation
Release Date : 1999-01-01

Introduction To Partial Differential Equations And Hilbert Space Methods written by Karl E. Gustafson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.

This volume offers an excellent undergraduate-level introduction to the main topics, methods, and applications of partial differential equations. Chapter 1 presents a full introduction to partial differential equations and Fourier series as related to applied mathematics. Chapter 2 begins with a more comprehensive look at the principal method for solving partial differential equations — the separation of variables — and then more fully develops that approach in the contexts of Hilbert space and numerical methods. Chapter 3 includes an expanded treatment of first-order systems, a short introduction to computational methods, and aspects of topical research on the partial differential equations of fluid dynamics. With over 600 problems and exercises, along with explanations, examples, and a comprehensive section of answers, hints, and solutions, this superb, easy-to-use text is ideal for a one-semester or full-year course. It will also provide the mathematically inclined layperson with a stimulating review of the subject's essentials.

An Introduction To Partial Differential Equations

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Author : Yehuda Pinchover
language : en
Publisher: Cambridge University Press
Release Date : 2005-05-12

An Introduction To Partial Differential Equations written by Yehuda Pinchover and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-12 with Mathematics categories.

A complete introduction to partial differential equations, this is a textbook aimed at students of mathematics, physics and engineering.

An Introduction To Partial Differential Equations

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Author : Daniel J. Arrigo
language : en
Publisher:
Release Date : 2023

An Introduction To Partial Differential Equations written by Daniel J. Arrigo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Differential equations categories.

This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter. In addition, this book: Introduces methods and techniques for solving first and second order PDEs Presents the main four PDEs (the advection equation, the diffusion equation, Laplace's equation, and the wave equation), which are considered to be the cornerstone of Applied Mathematics Contains numerous exercises throughout to facilitate learning and has been class tested over the past 10 years.

Introduction To Partial Differential Equations

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Author : David Borthwick
language : en
Publisher: Springer
Release Date : 2017-01-12

Introduction To Partial Differential Equations written by David Borthwick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-12 with Mathematics categories.

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions: What is the scientific problem we are trying to understand? How do we model that with PDE? What techniques can we use to analyze the PDE? How do those techniques apply to this equation? What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.