Schaum's Outline of Partial Differential Equations (Schaum's)

Book Description

If you want top grades and thorough understanding of partial differential equations, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 290 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dreary minutiae, SchaumÕs Outlines have sold more than 30 million copies worldwideÑand this guide will show you why!

Customer Reviews:

Partial Differential Equations review.......2007-01-04

I have found it helpful and inciteful with the more difficult differential equations that can be attempted.

Good if you've forgotten.......2006-04-22

This book contains mostly routine exercises of the subject. If you want to dig a bit further and sharpen your skills: try Krasnov's A Book of Problems in Ordinary Differential Equations. Language: English
ISBN: 5030009493

Not up to par with other Schaum's outlines on mathematics.......2006-04-21

This is one of the more poorly written Schaum's outlines I have encountered. The theory is very murky and the author gives no clear direction as to where he is going with this material and what it all means. PDE is a hard enough subject without working a bunch of meaningless problems that leave you wondering what it is you are supposed to have learned. Instead, I suggest you read "Introduction to Partial Differential Equations with Applications" by Zachmanoglou and Thoe in order to understand the mathematical underpinnings of PDE. Then read "Partial Differential Equations for Scientists and Engineers" to get a thorough feel for how PDE is used to solve real-world problems. Both books usually sell used for under $10 each, making them cost-effective alternatives to this Schaum's outline.

Duchateau a poor teacher.......2003-11-01

I have not read this book, but if it is anything like the author's previous attempts at writing it will leave you feeling angry. I read his advanced calculus book and it was awful. I found 16 mistakes on one page! This was the first book on advanced calculus I read and I was unable to follow the logic sequence. It wasn't until later after reading other books and mastering the subject that I discovered why. The examples were full of major errors. Not only that but he wastes a great deal of space repeating assumptions before each new section. As a result the actual material covered is sparse.

It is a very good book.......2003-06-15

This is a very good introduction to partial
differential equations.It contains the most
common methods in PDE namely: characteristics
method, Fourier method, Green method, finite
difference methods, variational methods and
finite element method. I have used it as a
textbook or suplementary text. It is really
an undergraduate text which provides a wide
introduction to PDE. I have a copy and recommend
it to every person interested in learning PDE.

Tensors, Differential Forms, and Variational Principles

Average customer rating:

One of the best books I've studied on invariant variational principles.
Cryptic
Helpful for the advanced student
Not for self study
A MUST, if one wants to learn the subject

Tensors, Differential Forms, and Variational Principles
David Lovelock , and Hanno Rund
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Tensor Analysis on Manifolds
Differential Geometry
A First Course in General Relativity
Introduction to Tensor Calculus, Relativity and Cosmology
General Relativity

ASIN: 0486658406

Book Description

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments.

Customer Reviews:

One of the best books I've studied on invariant variational principles........2007-07-29

I bought this book six years ago for the exercises on tensor analysis and differential forms and it has become one of my favorite texts on invariant variational principles. The authors develop their account of tensors in a clear and logical manner, with several diagrams in the first few chapters to highlight geometrical concepts. The authors provide a commentary in words to accompany the mathematical exposition. I appreciate their pointing out the various implications of the results they develop and I found the exercises helpful and a useful aid to the development of the theory.

Chapter 6 on the calculus of variations for invariance problems under coordinate transformations is one of the best I have studied. Their explanation of the theorems of Noether and reference to Caratheodory's work clearly explain some of the deeper concepts of invariance. The authors include worked examples which demonstrate the application of the ideas as they are developed. Variational principles are developed further in subsequent chapters. Chapter 8 describes the application variational principles to invariant field theories and the Einstein vacuum field equations.

Cryptic.......2007-02-23

I think I have a decent handle on the prerequisites for this subject, and I frankly found this to be cryptic. Perhaps the style is a bit archaic; but, I found some of the general relativity texts to give a better introduction to the sujbect of tensors. I would not recommend this as an introductory text.

Helpful for the advanced student.......2007-01-30

This is a helpful book for the advanced undergraduate/graduate student. It contains difficult mathematics, so it is a good overview of the matter, but not for the enthusiastic "layman" (pardon my language). This is because a lot of math knowledge is presupposed.

Not for self study.......2006-04-21

I bought this book togheter with Kay - Tensor analysis - when I began to study tensors. Kay could be not a masterpiece, but you can use it to learn the subject with some efforts but without a teacher. Don't try to do the same thing with Lovelock. May be this book is very profound, but you have better avoiding it as a self study text.

A MUST, if one wants to learn the subject.......2005-09-11

The two authors must be experts in this field. Without wasting words, they always well motivate, why something is done. It starts at a gradual pace, and is never extremely demanding mathematically.
It is rare, that one finds a flawless book, but this is certainly one!

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)

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It is my bible!

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Gilles Aubert , and Pierre Kornprobst
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Geometric Level Set Methods in Imaging, Vision, and Graphics

Accessories:

Partial Differential Equations (Graduate Texts in Mathematics)
Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics)
Hyperbolic Problems and Regularity Questions (Trends in Mathematics)

ASIN: 0387322000

Book Description

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them.

Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields.

During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches.

Customer Reviews:

It is my bible!.......2004-07-01

This book not only includes the state-of-art image processig techniques using math methods, but also provides very good numerical schemes for these methods. This book is written by mathematicians, but engineers still can easily implemente many commonly used image processing algorithm, just follow the detailed numerical difference schemes provided in the appendix.

Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MPS-SIAM Series on Optimization)

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Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization (MPS-SIAM Series on Optimization)
Hedy Attouch , Giuseppe Buttazzo , and Gérard Michaille
Manufacturer: SIAM, Society for Industrial and Applied Mathematics
ProductGroup: Book
Binding: Paperback

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ASIN: 0898716004

Product Description

This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization is not just for students, however; it is a comprehensive guide for anyone who wants to approach the field of variational analysis in a systematic way, starting from the most classical examples and working up to a research level. This book also contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. Organized in a way that makes it accessible to a large audience, the book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. The last chapters in Part I introduce finite element methods and spectral analysis methods, the two most powerful tools that allow the computation of approximate solutions of variational problems. In Part II, BV(W) spaces are introduced and new trends in variational analysis are presented. In this part the reader is introduced to the flexibility of variational methods.

Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)

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Variational Methods for Potential Operator Equations: With Applications to Nonlinear Elliptic Equations (De Gruyter Studies in Mathematics)
Jan Chabrowski
Manufacturer: Walter de Gruyter
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Binding: Hardcover

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ASIN: 311015269X

Convex Analysis and Variational Problems (Classics in Applied Mathematics)

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Convex Analysis and Variational Problems (Classics in Applied Mathematics)
Ivar Ekeland , and Roger Témam
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

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Sobolev Spaces, Second Edition (Pure and Applied Mathematics, Volume 140) (Pure and Applied Mathematics)

ASIN: 0898714508

Book Description

No one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)

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Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems (Ergebnisse der Mathematik und ihrer Grenzgebiete. ... / A Series of Modern Surveys in Mathematics)
Michael Struwe
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Calculus of Variations (Cambridge Studies in Advanced Mathematics)
Functional Analysis (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

ASIN: 3540664793

Book Description

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Springer Monographs in Mathematics)

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Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Springer Monographs in Mathematics)
Igor Chudinovich , and Christian Constanda
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1852338881

Book Description

The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces. The analysis, performed in spaces of distributions, is applicable to a wide variety of data with less smoothness than that required in the corresponding classical problems, and is very useful for constructing error estimates in numerical computations. This illustrative model was chosen because of its practical importance and some unusual mathematical features, but the solution technique can easily be adapted to many other hyperbolic systems of partial differential equations arising in continuum mechanics.

Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods

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Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Tony Chan , and Jianhong Shen
Manufacturer: Society for Industrial and Applied Mathematic
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ASIN: 089871589X

Product Description

At no other time in human history have the influence and impact of image processing on modern society, science, and technology been so explosive. Image processing has become a critical component in contemporary science and technology and has many important applications. This book develops the mathematical foundation of modern image processing and low-level computer vision, and presents a general framework from the analysis of image structures and patterns to their processing. The core mathematical and computational ingredients of several important image processing tasks are investigated. The book bridges contemporary mathematics with state-of-the-art methodologies in modern image processing while organizing the vast contemporary literature into a coherent and logical structure. Image processing has traditionally been built on the machinery of Fourier and spectral analysis; however, in the past few decades numerous novel competing methods and tools have emerged. These diversified approaches, although seemingly distinct, are in fact intrinsically connected. The authors integrate this diversity of modern image processing approaches by revealing the few common threads connecting them. Some newer emergent integration efforts have also been highlighted and analyzed. Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods is systematic and well organized. The authors first investigate the geometric, functional, and atomic structures of images and then rigorously develop and analyze several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples. This book is written for graduate students and researchers in applied mathematics, computer science, electrical engineering, and other disciplines who are interested in problems in imaging and computer vision. It can be used as a reference by scientists with specific tasks in image processing, as well as by researchers with a general interest in finding out about the latest advances. Contents List of Figures; Preface; Chapter 1: Introduction; Chapter 2: Some Modern Image Analysis Tools; Chapter 3: Image Modeling and Representation; Chapter 4: Image Denoising; Chapter 5: Image Deblurring; Chapter 6: Image Inpainting; Chapter 7: Image Processing: Segmentation; Bibliography; Index.

Variational Analysis (Grundlehren der mathematischen Wissenschaften)

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An instant classic in variational analysis and optimization

Variational Analysis (Grundlehren der mathematischen Wissenschaften)
R. Tyrrell Rockafellar , and Roger J.-B. Wets
Manufacturer: Springer
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Binding: Hardcover

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Variational Analysis and Generalized Differentiation I: Basic Theory (Grundlehren der mathematischen Wissenschaften)
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ASIN: 3540627723

Book Description

From its origins in the minimization of integral functionals, the notion of 'variations' has evolved greatly in connection with applications in optimization, equilibrium, and control. It refers not only to constrained movement away from a point, but also to modes of perturbation and approximation that are best describable by 'set convergence', variational convergence of functions' and the like. This book develops a unified framework and, in finite dimension, provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, maximal monotone mappings, second-order subderivatives, measurable selections and normal integrands.

Customer Reviews:

An instant classic in variational analysis and optimization.......2000-07-27

A winner of the prestigious Lanchester prize in 1997 (the very year it was published), this book is an instant classic. Written by two eminent researchers in the field, it is a handy reference on convex analysis, duality, optimality conditions, set-valued mappings, epigraphical convergence and variational problems.

Resulting analysis is applicable to a wide variety of problems in mathematical optimization, operations research, management science, economics and engineering. New and unpublished structural results have been derived in this book and presented in the light of new developments in this area. To give an example, "Variational Analysis" advances some of the results in the princeton classic "Convex Analysis" (an almost necessary read for any researcher in mathematical optimization) also written by the first author of this book. To my knowledge, there is no other book at this time which compiles all the results in this area under one hood.

The book follows a theorem-proof format for most part. Thus, it serves more as a reference than a textbook. A complete reading would be daunting given the length and density of material in the text.

This book is worth buying if you are a researcher in mathematical optimization. To quote the citation of the Lanchester award:

"In all, this book should serve as a landmark in the technical progress of optimization, an essential technical tool of operations research and the management sciences."

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