Numerical Solution of Partial Differential Equations: An Introduction

Book Description

This second edition of a highly successful graduate text presents a complete introduction to partial differential equations and numerical analysis. Revised to include new sections on finite volume methods, modified equation analysis, and multigrid and conjugate gradient methods, the second edition brings the reader up-to-date with the latest theoretical and industrial developments. First Edition Hb (1995): 0-521-41855-0 First Edition Pb (1995): 0-521-42922-6

Customer Reviews:

Good Starter.......2001-03-08

This book is a good starter for understanding how to numerically solve (Partial Differential Equations)PDE's. The chapters are arranged in an orderly manner and hints are provided then and there so that you wont need to switch back and forth between them. I myself a researcher in the field of Finite Element Analysis, which extensively involves PDE's for implementing the Finite element model. A thorough knowlegde of PDE's and the nature of their solutions is very important for such fields. This book is definitely the one which describes the nature of PDE's solutions and their interpretation, boundedness and applicability.

Introduction to Pdes and Waves for the Atmosphere and Ocean (Courant Lecture Notes)

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Introduction to Pdes and Waves for the Atmosphere and Ocean (Courant Lecture Notes)
Andrew Majda
Manufacturer: Courant Institute of Mathemetical Sciences
ProductGroup: Book
Binding: Paperback

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Vorticity and Incompressible Flow
Hyperbolic Partial Differential Equations (Courant Lecture Notes)
Calculus of Variations
Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation
An Introduction to Boundary Layer Meteorology (Atmospheric Sciences Library)

ASIN: 0821829548

Book Description

Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such as additional information on geophysical flows, as suggested in the preface.

Book Description

This book presents an upper level text on semilinear evolutionary partial differential equations aimed at the graduate and postgraduate level. Cazenave and Haraux present in a self-contained way, the typical basic properties of solutions to semi-linear evolutionary partial differential equations, with special emphasis on global properties. The main objective of this book is to provide a didactic approach to the subject , and the main readership will be graduate students in mathematical analysis, as well as professional applied mathematicians.

An Introduction to Partial Differential Equations with MATLAB (Chapman & Hall/Crc Applied Mathematics & Nonlinear Science)

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Good and Clear
Very well written with excellent explanations.

An Introduction to Partial Differential Equations with MATLAB (Chapman & Hall/Crc Applied Mathematics & Nonlinear Science)
Matthew P. Coleman
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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Similar Items:

Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics)
Numerical Solution of Partial Differential Equations: Finite Difference Methods (Oxford Applied Mathematics & Computing Science Series)
An Introduction to Programming and Numerical Methods in MATLAB
Introduction to Partial Differential Equations with MATLAB
Applied Partial Differential Equations

ASIN: 1584883731

Book Description

An Introduction to Partial Differential Equations with MATLAB exposes the basic ideas critical to the study of PDEs-- characteristics, integral transforms, Green's functions, and, most importantly, Fourier series and related topics. The author approaches the subject from a motivational perspective, detailing equations only after a need for them has been established. He uses MATLAB software to solve exercises and to generate tables and figures. Included This volume includes are examples of many important PDEs and their applications. The first chapter introduces PDEs and makes analogies to familiar ODE concepts, then strengthens the connection by exploring the method of separation of variables. Chapter 2 examines the "Big Three" PDEs-- the heat, wave, and Laplace equations, and is followed by chapters explaining how these and other PDEs on finite intervals can be solved using the Fourier series, for arbitrary initial and boundary conditions. Chapter 5 investigates characteristics for both first- and second-order linear PDEs, the latter revealing how the Big Three equations are important far beyond their original application to physical problems. The book extends the Fourier method to functions on unbounded domains, gives a brief introduction to distributions, then applies separation of variables to PDEs in higher dimensions, leading to the special funtions, including the orthogonal polynomials. Other topics include Sturm-Liouville problems, adjoint and self-adjoint problems, the application of Green's functions to solving nonhomogeneous PDEs, and an examination of practical numerical methods used by engineers, including the finite difference, finite element, and spectral methods.

Customer Reviews:

Good and Clear.......2005-08-08

I used this book for the first time this past semester. It is well written, although a bit informal for my taste (although the students seemed to like it). There are numerous exercises, although sometimes too many of the plug-and-chug variety, and I wish there were a few more of the highly challenging problems. The order of topics is exactly the way I like it, except that Chapter 5 is a little out of place. However, in a course like this I think it may be impossible to find a natural place for the method of characteristics. Most texts put it first, which doesn't seem right for a course that emphasizes Fourier methods. For our course, I interchanged Chapters 5 and 6. The MATLAB is not heavily integrated. That is a good thing, for a couple of reasons. It means that the mathematics, and not MATLAB, is the main focus, and it allows the text to be used with or without it. We did use MATLAB and it worked well. Overall, this was a good basic introduction to the subject. It steers a course between mathematical rigor on the one hand, and computation, physical intuition and applications on the other, and it does so quite well. I could envision its being used for a higher level course for scientists and engineers, though not for a course with a more theoretical bent.

Very well written with excellent explanations........2004-11-19

First, I have to say that I'm biased because I'm a former student of Prof. Coleman's (Multivariable Calc and ODE's). But I was happy to see that he had written a PDE book and I bought it so that I could relearn PDE's, since the PDE course I had wasn't so great. I haven't been disappointed. I've read most of the first six chapters so far - the book is easy to read and the explanations are clear. There are tons of homework problems and applications. However, I don't have access to MATLAB so I can't really comment on that aspect of the book.

Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

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Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
Alexander Stanoyevitch
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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An Introduction to Partial Differential Equations with MATLAB (Chapman & Hall/Crc Applied Mathematics & Nonlinear Science)

ASIN: 0471697389

Book Description

Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB(r) teaches you how to numerically solve both ordinary and partial differential equations with ease. This innovative resource brings together a skillful treatment of MATLAB and programming alongside current theory and modeling methods. All the tools needed to master MATLAB and then use it to solve differential equations are provided. "Exercises for the Reader" range from routine computations to more advanced conceptual and theoretical questions, while illustrative examples demonstrate MATLAB's powerful ability to solve differential equations. With its thorough coverage of analytic concepts, geometric concepts, programs and algorithms, and applications, Introduction to Numerical Ordinary and Partial Differential Equations Using MATLAB(r) is an unsurpassed pedagogical tool.

An Introduction to Partial Differential Equations (Texts in Applied Mathematics)

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Struggle
An extremely well written introduction to PDEs
The Best
A very good book to learn about partial differential eqn's.

An Introduction to Partial Differential Equations (Texts in Applied Mathematics)
Michael Renardy , and Robert C. Rogers
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Partial Differential Equations: Basic Theory (Texts in Applied Mathematics)
Applied Asymptotic Analysis (Graduate Studies in Mathematics,) (Graduate Studies in Mathematics)
Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)
Partial Differential Equations II: Qualitative Studies of Linear Equations (Applied Mathematical Sciences, Volume 116)
Partial Differential Equations (Applied Mathematical Sciences)

ASIN: 0387979522

Book Description

This book is intended for a three or four semester course in "Partial Differential Equations". It is based on a four-semester course taught at Virginia Polytechnic Institute and State University. The goal of this class was to provide the background necessary to initiate work on a PhD thesis in partial differential equations. The book opens with an introduction to the subject matter and its characteristics which contain the Cauchy-Kovalevskaya Theorem and Holmgren's Uniqueness Theorem. Conversation laws and shocks are then covered, followed by maximum principles and function spaces. Linear elliptic equations and nonlinear elliptic equations are also included. The text concludes with energy methods for evolution problems and semigroup methods. In the standard graduate curriculum, the subject of partial differential equations is seldom taught with the same thoroughness as algebra or integration theory. This book is aimed at rectifying the situation, by going further than the competition. There are numerous other textbooks on partial differential equations, but few are directed at a beginning graduate audience as this one is. The level of the book is aimed at beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables, but no knowledge is required of Lebesque integration theory or functional analysis. This book provides a thorough introduction to partial differential equations, bringing the students up to the level at which research can begin.

Customer Reviews:

Struggle.......2006-10-29

This is a good book for postgraduate maths students. Even though my first degree was in maths I still could not follow the notation given in this book. I struggled with following the material and never got to the end of the book. I will have to come back to this book in a few years once I have developed the skills elsewhere.

An extremely well written introduction to PDEs.......2003-09-05

An Introduction to Partial Differential Equations by Renardy and Rogers is a very well written introduction to the huge and important area of PDEs. It covers both the classical and modern PDE theory on, compared with other expositions, a relatively low number of pages. Nevertheless, Renardy and Rogers succeed in introducing the most important concepts and explaining their interrelations, so that alltogether, the book provides the reader with the background necessary for diving safely into the more advanced literature on the subject.

It was a pleasure for me to read the book, and after nearly four years of work in PDEs, it is still my reference of choice. I would highly recommend it for students of mathematics and for mathematically inclined engineering students.

The Best.......2000-05-23

This book is the best book on advanced partial differential equations i know. It is almost self contained. Every definition is motivated. Examples are given. Buy it and enjoy

A very good book to learn about partial differential eqn's........2000-03-31

I found what I was looking for in this book to know enough about this huge theory of Partial Differential Equations. Contents of each chapter is clearly developed and no essential point is missed. If you are someone who seriously wants to learn more and apply PDE theory in your research, this book is worth picking. Although the title alludes to an introductory book bearing a simple approach, this book is far more than an introduction, and I would say some little background in PDE's would help.

Applied Partial Differential Equations: An Introduction

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Applied Partial Differential Equations: An Introduction
Alan Jeffrey
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover

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Elementary Differential Equations and Boundary Value Problems , 8th Edition, with ODE Architect CD
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Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)

ASIN: 0123822521

Book Description

This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks.

This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market.

* Includes new and important materials necessary to meet current demands made by diverse applications
* Very detailed solutions to odd numbered problems to help students
* Instructor's Manual Available

Numerical Continuation Methods: An Introduction (Springer Series in Computational Mathematics, Vol 13)

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Numerical Continuation Methods: An Introduction (Springer Series in Computational Mathematics, Vol 13)
Eugene L. Allgower , and Kurt Georg
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Basic Structured Grid Generation: With an introduction to unstructured grid generation

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A quite useful book on grid generation for beginner
Excellent book for someone comfortable with calcus

Basic Structured Grid Generation: With an introduction to unstructured grid generation
M Farrashkhalvat , and J P Miles
Manufacturer: Butterworth-Heinemann
ProductGroup: Book
Binding: Paperback

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ASIN: 0750650583

Book Description

Finite element, finite volume and finite difference methods use grids to solve the numerous differential equations that arise in the modelling of physical systems in engineering. Structured grid generation forms an integral part of the solution of these procedures. Basic Structured Grid Generation provides the necessary mathematical foundation required for the successful generation of boundary-conforming grids and will be an important resource for postgraduate and practising engineers.

The treatment of structured grid generation starts with basic geometry and tensor analysis before moving on to identify the variety of approaches that can be employed in the generation of structured grids. The book then introduces unstructured grid generation by explaining the basics of Delaunay triangulation and advancing front techniques. A companion website fully supports this book by providing numerical codes in FORTRAN 77/90 for both structured and unstructured grid generation which will help the reader to develop their understanding and make progress in grid generation.

* A practical, straightforward approach to this complex subject for engineers and students.
* A key technique for modelling physical systems.
* Companion website provides free access to grid generation codes.

Customer Reviews:

A quite useful book on grid generation for beginner.......2006-11-06

The first chapter on tensor analysis is quite appealing and it is still refreshing for me who has experience with tensor analysis. The last chapter on unstructured grid generation is very helpful for me. I think it is a useful book for beginner in this field and can be a valuable reference book for experienced.

In computational fluid mechanics and solid mechanics, finite volume and finite element methods can deal with unstructured meshes relatively easily. So some of the grid generation techniques for finite difference method described in this book maybe less important than, say, 20 years ago.

Excellent book for someone comfortable with calcus.......2006-03-24

I am a CFD engineer but no grid generation person. I bought this book due to its low price ($15 for a pdf format). I am not disappointed with this book at all. If you are comfortable with calculus and somewhat familar with index notation, the derivation in this book is very logical. I was able to use this book to generate a structural mesh using the algebraic method and differential method. The variational method seems to require funtional background and that is beyond me. Another good aspect about this book is that it gives the final equations that one needs to solve and a procedure that one needs to use to generate the grid. A good example is the Winslow method. I was able to use the equations in the book easily to generate the grid. Anyway, I would recommend this book to people who can read the first five pages of it without too much trouble. If you struggle with the first a few pages, this is probably not a good book for you.

An Introduction to Homogenization (Oxford Lecture Series in Mathematics and Its Applications, 17)

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An Introduction to Homogenization (Oxford Lecture Series in Mathematics and Its Applications, 17)
Doina Cioranescu , and Patrizia Donato
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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Homogenization and Porous Media (Interdisciplinary Applied Mathematics)
Random Heterogeneous Materials

ASIN: 0198565542

Book Description

This book provides an introduction to the mathematical theory of homogenization, which describes the replacement of a real composite material by a fictitious homogeneous one. The aim of the theory is to describe the macroscopic properties of the composite by taking into account the properties of the microscopic structure. The first four chapters cover variational methods for partial differential equations, which is the natural framework of homogenization theory. The text then discusses the homogenization of several kinds of second order boundary value problems. Particular attention is given to the classical examples of the steady and non-steady heat equations, the wave equation and the linearized system of elasticity. All topics are illustrated by figures and numerous examples.

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