Average customer rating:
- very nice conceptual overview
- Not for the practitioner
- Trash
- Excellent Introduction, Sparse on Details
- A Good Introductory Survey
|
Scientific Computing
Michael T. Heath
Manufacturer: The McGraw-Hill Companies, Inc.
ProductGroup: Book
Binding: Hardcover
 General
| Algorithms
| Programming
| Computers & Internet
| Subjects
| Books
General
| Computers & Internet
| Subjects
| Books
Research
| Education
| Science
| Subjects
| Books
Methodology & Statistics
| Experiments, Instruments & Measurement
| Science
| Subjects
| Books
General
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Science
| Subjects
| Books
Probability & Statistics
| Applied
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Computer Science & Information Systems
| New & Used Textbooks
| Stores
| Books
Algorithms
| Computer Science & Information Systems
| New & Used Textbooks
| Stores
| Books
Statistics
| Mathematics
| Sciences
| New & Used Textbooks
| Stores
| Books
General
| Mathematics
| Sciences
| New & Used Textbooks
| Stores
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Computers & Internet
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Similar Items:
-
Numerical Computing with Matlab
-
Numerical Analysis: Mathematics of Scientific Computing
-
Financial Risk Management: A Practitioner's Guide to Managing Market and Credit Risk (with CD-ROM)
-
Real-Time Rendering (2nd Edition)
-
Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)
ASIN: 0072399104 |
Book Description
Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.
Customer Reviews:
very nice conceptual overview.......2006-07-22
Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.
Not for the practitioner.......2005-11-17
If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.
Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.
He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.
I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.
Trash.......2005-10-14
If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.
Excellent Introduction, Sparse on Details.......2004-11-20
While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.
A Good Introductory Survey.......2002-11-05
This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.
Book Description
This highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide available upon request. 1982 edition.
Customer Reviews:
Review by BSM.......2007-09-09
Good book to gain an understanding of the basics involved in PDE's. Could use more worked through examples as applied to practical problems.
Wanna teach yourself PDE's?.......2007-08-07
If you want to teach yourself PDE's, then this is certainly a great, and affordable book to get started with. As other reviewers have said, the book could certainly go into more depth, but there is no one book that can completely teach you one subject. My advice would definitely be to use this book to get started, and to use other books to go further.
Simply Great!.......2007-06-27
The book is simple, interesting to read, just like a story book or a news article, and can be used as an introductory textbook for PDEs.
A great book..........2007-05-18
This is a great book for PDE I use it a lot in my school and in my job.
Great Reference.......2007-05-13
This book is an ideal companion for a graduate, or undergraduate, course in partial differential equations. There are worked examples and very useful definitions throughout the text. Additionally, the text is written as lessons and any lesson can be read and understood without reading the previous lessons. The best part is that this book is an order of magnitude cheaper than most college level texts and is largely more valuable.
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.
Book Description
One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Key features include:
* Applications to a wide variety of physical problems in numerous interdisciplinary areas
* Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry
* Historical comments on partial differential equations
* Solutions and hints to selected exercises
* A comprehensive bibliography—comprised of many standard texts and reference books, as well as a set of selected classic and recent papers—for readers interested in learning more about the modern treatment of the subject
Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.
Also by L. Debnath:
Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.
Customer Reviews:
Aimed at the Person who needs to do Real Work.......2007-04-05
Partial Differential equations are really the first time that the science or entineering student begins to see that math can really represent real life situations that are more complex than the almost trivial examples he has studied up until now.
This book, now in its fourth edition reflects comments made by users: students, faculty and researchers as well as covering the major new discoveries of methods for the solution of partial differential equations in the years since the last edition. The book is aimed at the advanced undergraduate or beginning graduate student, and it should be useful as a research reference for professionals in mathematics, science, engineering and the other applied sciences. In addition other fields of study from the social sciented to financial analysis have begin to use more advanced mathematics in their calculations.
The intent in this book is to provide the working physicist/engineer or whatever with the tools he needs to perform his work. In a few places this has meant a slight slacking of the rigor normally required by the pure mathematician in favor of producing solutions that give the user the answers he needs.
Average customer rating:
- Very good and helpful book for the engineer with fundamental
|
Numerical Methods for Partial Differential Equations (Computer Science and Scientific Computing)
William F. Ames
Manufacturer: Academic Press
ProductGroup: Book
Binding: Hardcover
General
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Science
| Subjects
| Books
Calculus
| Pure Mathematics
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
Mathematical Analysis
| Mathematics
| Science
| Subjects
| Books
Number Systems
| Mathematics
| Science
| Subjects
| Books
General
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Mathematical Analysis
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
Number Systems
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
ASIN: 012056761X |
Book Description
This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems.
Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation.
Key Features
* Material on finite elements and finite differences have been merged, and now constitute equal partners
* Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods
* References have been updated, and reflect the additional material
* Self-contained nature of the Second Edition has been maintained
* Very suitable for PDE courses
Customer Reviews:
Very good and helpful book for the engineer with fundamental.......2005-02-16
This book is very detail on how to generate numerical methods for partial differential equations. Staring from basics, the author proceeds with detailed examples and more complicated ideas. This is book will be very helpful for the people having basic computational knowledge and scientific computing experience.
But the book is written in 1977. Some difficult ideas will be easier to be implemented on large scale computers such as Linux clusters or SGI machines. I also found one small shortcoming is that the problem complexity is not detailed discussed. This will be very important now for comparing different algorithms to accomplish the same problem.
Book Description
The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The material is organized into four groups of two chapters each, covering the Poisson equation (chapters 1 & 2); the convection-diffucion equation
(chapters 3 & 4); the Stokes equations (chapters 5 & 6); and the Navier-Stokes equations (chapters 7 & 8). These equations represent important models within the domain of computational fluid dynamics, but they also arise in many other settings. For each PDE model, there is a chapter concerned with
finite element discretization. For each problem and associated solvers there is a description of how to compute along with theoretical analysis which guides the choice of approaches. Illustrative numerical results occur throughout the book, which have been computed with the freely downloadable
IFISS software. All numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the 'computational laboratory' provided by the software. This book provides an excellent introduction to finite elements, iterative linear solvers
and scientific computing aimed at graduates in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing. Including theoretical problems and practical exercises closely tied with freely downloadable MATLAB software, this book is an ideal teaching and learning
resource.
Book Description
This text will be divided into two books which cover the topic of numerical partial differential equations. Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student, this text offers a means of coming out of a course with a large number of methods which provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.
Customer Reviews:
Good, practical book for FDM applied to PDE.......2004-04-16
This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM). The theory and practice of FDM is discussed in detail and numerous practical examples (heat equation, convection-diffusion) in one and two space variables are given. In particular, Alternating Direction Implicit (ADI) methods are the standard means of solving PDE in 2 and 3 dimensions.
In almost all cases model problems are taken in order to show how the schemes work for initial value problems, initial boundary value problem with Dirichlet and Neumann boundary conditions.
This book is a *must* for those in science, engineering and quantitative financial analysis. It digs into the nitty-gritty of mapping a PDE to a FDM scheme while taking nasty boundary conditions into consideration. The resulting algorithms are documented are are easily programmed in C++ or other language.
The book does not cover topics that are also important: operator splitting (Marchuk/Janenko), non-constant coefficient PDEs, nonlinearities. Finally, the book uses von Neumann analysis as a means of proving stability (getting a bit long in the tooth). There are more robust methods that use monotone schemes, M-matrices and the maximum principle. You should consult other specialised references.
This is Volume I of a two-volume set (Volume II deals with Conversation Laws and first-order hyperbolic as well as Elliptic problems.
(...)
Numerical Partial Differential Equations.......2000-01-20
Thomas wrote a good book on a quite specialized subject. Although finite difference schemes have been traditionally viewed as a game field for physicists, they are given today much more commercial attention as financial option market evolves. Those who seek standard numerical recipes are advised to read this book. You will enjoy it (easy reading) and learn. But the book may not satisfy quests of a more rigorous readership. It abuses the Fourier method in stability analysis while considering only PDEs with constant coefficients. The bibliographical work has not been done at all. In addition, the cover does not state that this is the first book of two. I'd also advise to read G.Marchuk "Methods of Numerical Mathematics" (Springer, 1982) where a more general approach for stability of numerical schemes is developed.
Book Description
The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving.
Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience.
This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide an up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes.
Topic and Features:
• Nonlinear equations including nonlinear conservation laws;
• Dispersive wave equations and the Schrodinger equation;
• Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform;
• Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this web site.
This text/reference is an excellent resources designed to introduce advanced students in mathematics, engineering and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.
Customer Reviews:
Not bad, but the 2nd edition will hopefully be better.......2002-02-03
This is a fairly challenging text. It's currently being used in my undergrad PDE course, and the flow of material is a bit out of the ordinary. The book starts off with the method of characteristics and weak solutions, which are slightly more sophisticated and unusual topics than some of the later material, making it difficult to get started. The focus on using Matlab is nice, and most things are fairly well-explained. Typographical errors are rampant, however, making it very poor for self-study (you need someone to point out the errors to you).
All in all, not bad -- the second edition will hopefully be much better, and if you have a decent grounding in multivariate calc and ODE's, you'll be OK.
An excellent rough draft of a textbook........1998-12-22
Cooper's book does some things quite well. While most courses on PDE's are reduced to repetitive applications of separation of variables and Fourier series, Cooper offers a new approach. He goes by equation rather than by technique, and introduces nonlinear equations and numerical methods very early. Separation of variables and Fourier series do not come up until Chapter 4. The first chapter, which reviews elements of analysis, is a very good reference. MATLAB is well incorporated throughout the text.
The reason I do not rate this book more highly is that the writing is unbelievably sloppy. There are at least five typos per chapter, usually more. Crucial things, like Green's first identity, are misprinted. There are dozens of typos in the answers in the back, which makes it very hard to check your work.
Judging just by the content, this is a very good book. However, the misprints in the math (to say nothing of those in the text) are so severe that I would not recommend buying it until a better-proofread edition comes out.
Book Description
Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering. · Parabolic, hyperbolic, and elliptic equations with constant and variable coefficients · New exact solutions to linear equations and boundary value problems · Equations and problems of general form that depend on arbitrary functions · Formulas for constructing solutions to nonhomogeneous boundary value problems · Second- and higher-order equations and boundary value problems An introductory section outlines the basic definitions, equations, problems, and methods of mathematical physics. It also provides useful formulas for expressing solutions to boundary value problems of general form in terms of the Green's function. Two supplements at the end of the book furnish more tools and information: Supplement A lists the properties of common special functions, including the gamma, Bessel, degenerate hypergeometric, and Mathieu functions, and Supplement B describes the methods of generalized and functional separation of variables for nonlinear partial differential equations.
Average customer rating:
|
Numerical Methods For Differential Equations: Fundamental Concepts For Scientific & Engineering Applications
Michael A. Celia , and
William G. Gray
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Paperback
General
| Applied
| Mathematics
| Science
| Subjects
| Books
Differential Equations
| Applied
| Mathematics
| Science
| Subjects
| Books
General
| Mathematics
| Science
| Subjects
| Books
Mathematical Analysis
| Mathematics
| Science
| Subjects
| Books
Differential Equations
| Applied
| Mathematics
| Professional Science
| Professional & Technical
| Subjects
| Books
General
| Computers & Internet
| Subjects
| Books
All Titles
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Computers & Internet
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Professional
| Qualifying Textbooks - Fall 2007
| Stores
| Books
Science
| Qualifying Textbooks - Fall 2007
| Stores
| Books
ASIN: 0136269613 |
Books:
- Speaking of Slavery: Color, Ethnicity, and Human Bondage in Italy (Conjunctions of Religion and Power in the Medieval Past)
- Surgical Pathology Dissection: An Illustrated Guide
- Sustainable Energy: Choosing Among Options
- The Active Side of Infinity
- The Anatomy Coloring Book (3rd Edition)
- The Apocalypse Code: Find Out What the Bible REALLY Says About the End Times . . . and Why It Matters Today
- The Complete Art of War (History and Warfare)
- The Design of CMOS Radio-Frequency Integrated Circuits, Second Edition
- The Divine Matrix: Bridging Time, Space, Miracles, and Belief
- The Elephant's Secret Sense: The Hidden Life of the Wild Herds of Africa
Books Index
Books Home
Recommended Books
- Politics Lost: How American Democracy Was Trivialized By People Who Think You're Stupid
- Praise Habit: Finding God In Sunsets And Sushi
- Mefisto
- Landscaping Your Home: Creative Ideas from America's Best Gardeners
- I Hope You Dance
- Mathematical Methods and Algorithms for Signal Processing
- Lord John and the Private Matter
- Wildflowers of Houston and Southeast Texas
- Jack Welch and the GE Way: Management Insights and Leadership Secrets of the Legendary CEO
- The Union Must Stand: The Civil War Diary of John Quincy Adams Campbell, Fifth Iowa Volunteer Infant
